Newton's laws of motion

8378:, and conceived of motion as always through a medium, rather than through space. In addition, some concepts often termed "Aristotelian" might better be attributed to his followers and commentators upon him. These commentators found that Aristotelian physics had difficulty explaining projectile motion. Aristotle divided motion into two types: "natural" and "violent". The "natural" motion of terrestrial solid matter was to fall downwards, whereas a "violent" motion could push a body sideways. Moreover, in Aristotelian physics, a "violent" motion requires an immediate cause; separated from the cause of its "violent" motion, a body would revert to its "natural" behavior. Yet, a javelin continues moving after it leaves the thrower's hand. Aristotle concluded that the air around the javelin must be imparted with the ability to move the javelin forward. 8353: 15997: 753: 8494: 4063: 3392:

direction, and its effect is not diminished by horizontal movement. If the cannonball is launched with a greater initial horizontal velocity, then it will travel farther before it hits the ground, but it will still hit the ground in the same amount of time. However, if the cannonball is launched with an even larger initial velocity, then the curvature of the Earth becomes significant: the ground itself will curve away from the falling cannonball. A very fast cannonball will fall away from the inertial straight-line trajectory at the same rate that the Earth curves away beneath it; in other words, it will be in orbit (imagining that it is not slowed by air resistance or obstacles).

905:, is based on the idea of specifying positions using numerical coordinates. Movement is represented by these numbers changing over time: a body's trajectory is represented by a function that assigns to each value of a time variable the values of all the position coordinates. The simplest case is one-dimensional, that is, when a body is constrained to move only along a straight line. Its position can then be given by a single number, indicating where it is relative to some chosen reference point. For example, a body might be free to slide along a track that runs left to right, and so its location can be specified by its distance from a convenient zero point, or 8280: 8699: 1967: 8572: 5136: 8295: 8320: 15985: 2386: 16009: 8470: 8630: 2760: 4375: 766: 4347:. Without friction to dissipate a body's energy into heat, the body's energy will trade between potential and (non-thermal) kinetic forms while the total amount remains constant. Any gain of kinetic energy, which occurs when the net force on the body accelerates it to a higher speed, must be accompanied by a loss of potential energy. So, the net force upon the body is determined by the manner in which the potential energy decreases. 7955: 13462:

Aristotelian theory of buoyancy affirms that bodies in a fluid are supported by the resistance of the fluid to being divided by the penetrating object, just as a large piece of wood supports an axe striking it or honey supports a spoon. According to this theory, a boat should sink in shallow water more than in high seas, just as an axe can easily penetrate and even break a small piece of wood, but cannot penetrate a large piece.

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momentum, also holds, as does the conservation of momentum. However, the definition of momentum is modified. Among the consequences of this is the fact that the more quickly a body moves, the harder it is to accelerate, and so, no matter how much force is applied, a body cannot be accelerated to the speed of light. Depending on the problem at hand, momentum in special relativity can be represented as a three-dimensional vector,

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the total kinetic energy). The question of what is conserved during all other processes, like inelastic collisions and motion slowed by friction, was not resolved until the 19th century. Debates on this topic overlapped with philosophical disputes between the metaphysical views of Newton and Leibniz, and variants of the term "force" were sometimes used to denote what we would call types of energy. For example, in 1742,

6134:, the dynamics of a system are represented by a function called the Hamiltonian, which in many cases of interest is equal to the total energy of the system. The Hamiltonian is a function of the positions and the momenta of all the bodies making up the system, and it may also depend explicitly upon time. The time derivatives of the position and momentum variables are given by partial derivatives of the Hamiltonian, via 2275: 16045: 16021: 9065:

Kepler's kinematical description of the solar system into a far more powerful dynamical theory because he added concepts from Galileo's experimental methods – force, mass, momentum, and gravitation. The truly external observer will only get as far as Kepler. Dynamical concepts are formulated on the basis of what we can set up, control, and measure." See, for example, Caspar and Hellman.

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and ideas would be meaningful—then to give a digest in English of his great work. Diagrams were added when necessary to the original text and proofs of various problems in physical mechanics and astronomy included. ... or almost a hundred years after its appearance the book continued to serve as a textbook for higher mathematics and astronomy in English schools.

4873: 8649:(1644), Descartes introduced the idea that during a collision between bodies, a "quantity of motion" remains unchanged. Descartes defined this quantity somewhat imprecisely by adding up the products of the speed and "size" of each body, where "size" for him incorporated both volume and surface area. Moreover, Descartes thought of the universe as a 5147:. That is, qualitatively speaking, physical systems obeying Newton's laws can exhibit sensitive dependence upon their initial conditions: a slight change of the position or velocity of one part of a system can lead to the whole system behaving in a radically different way within a short time. Noteworthy examples include the three-body problem, the 4612:. This follows from the fact that the internal forces within the collection, the forces that the objects exert upon each other, occur in balanced pairs by Newton's third law. In a system of two bodies with one much more massive than the other, the center of mass will approximately coincide with the location of the more massive body. 8265:

will vary. The Ehrenfest theorem says, roughly speaking, that the equations describing how these expectation values change over time have a form reminiscent of Newton's second law. However, the more pronounced quantum effects are in a given situation, the more difficult it is to derive meaningful conclusions from this resemblance.

5059: 12823:...the usual assumption of Newtonian mechanics is that the forces are determined by the simultaneous positions (and possibly their derivatives) of the particles, and that they are related by Newton's third law. No such assumption is possible in special relativity since simultaneity is not an invariant concept in that theory. 5572: 7292: 8182:

times relative to another. So, in a given observer's frame of reference, action and reaction may not be exactly opposite, and the total momentum of interacting bodies may not be conserved. The conservation of momentum is restored by including the momentum stored in the field that describes the bodies' interaction.

8587:(1673), put forth the hypothesis that "By the action of gravity, whatever its sources, it happens that bodies are moved by a motion composed both of a uniform motion in one direction or another and of a motion downward due to gravity." Newton's second law generalized this hypothesis from gravity to all forces. 7591: 2783:. The speed attained during free fall is proportional to the elapsed time, and the distance traveled is proportional to the square of the elapsed time. Importantly, the acceleration is the same for all bodies, independently of their mass. This follows from combining Newton's second law of motion with his 8200:. A curved path like an orbit, attributed to a gravitational force in Newtonian mechanics, is not the result of a force deflecting a body from an ideal straight-line path, but rather the body's attempt to fall freely through a background that is itself curved by the presence of other masses. A remark by 8683:, and the rule that interactions between bodies do not change the motion of their center of mass. In a later manuscript, Newton added a law of action and reaction, while saying that this law and the law regarding the center of mass implied one another. Newton probably settled on the presentation in the 8979:

an observer who sees one body accelerate without a matching acceleration of some other body to compensate would conclude, not that a force is acting, but that they are not an inertial observer. Landau and Lifshitz bypass the question by starting with the Lagrangian formalism rather than the Newtonian.

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Galileo recognized that in projectile motion, the Earth's gravity affects vertical but not horizontal motion. However, Galileo's idea of inertia was not exactly the one that would be codified into Newton's first law. Galileo thought that a body moving a long distance inertially would follow the curve

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It is mathematically possible for a collection of point masses, moving in accord with Newton's laws, to launch some of themselves away so forcefully that they fly off to infinity in a finite time. This unphysical behavior, known as a "noncollision singularity", depends upon the masses being pointlike

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The angular momentum of a collection of point masses, and thus of an extended body, is found by adding the contributions from each of the points. This provides a means to characterize a body's rotation about an axis, by adding up the angular momenta of its individual pieces. The result depends on the

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is that which a body has when it is in actual motion." In modern terminology, "dead force" and "living force" correspond to potential energy and kinetic energy respectively. Conservation of energy was not established as a universal principle until it was understood that the energy of mechanical work

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is a theory of physics originally developed in order to understand microscopic phenomena: behavior at the scale of molecules, atoms or subatomic particles. Generally and loosely speaking, the smaller a system is, the more an adequate mathematical model will require understanding quantum effects. The

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provides an expression for the force upon a charged body that can be plugged into Newton's second law in order to calculate its acceleration. According to the Lorentz force law, a charged body in an electric field experiences a force in the direction of that field, a force proportional to its charge

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Newton's law of universal gravitation states that any body attracts any other body along the straight line connecting them. The size of the attracting force is proportional to the product of their masses, and inversely proportional to the square of the distance between them. Finding the shape of the

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upon the body, and the amount of work done is equal to the change in the body's kinetic energy. In many cases of interest, the net work done by a force when a body moves in a closed loop — starting at a point, moving along some trajectory, and returning to the initial point — is zero. If this is the

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that interpolates between projectile motion and uniform circular motion. A cannonball that is lobbed weakly off the edge of a tall cliff will hit the ground in the same amount of time as if it were dropped from rest, because the force of gravity only affects the cannonball's momentum in the downward

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In no sense was it a mere translation of Laplace's work. Instead it endeavoured to explain his method ". . . by which these results were deduced from one general equation of the motion of matter" and to bring the reader's mathematical skill to the point where the exposition of Laplace's mathematics

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affirmed that solid water should have a greater weight than liquid water for the same volume. We know that this statement is incorrect because the density of ice is lower than that of water (hydrogen bonds create an open crystal structure in the solid phase), and for this reason ice can float. The

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as a definition of "force". See also Frautschi et al., as well as Feynman, Leighton and Sands, who argue that the second law is incomplete without a specification of a force by another law, like the law of gravity. Kleppner and Kolenkow argue that the second law is incomplete without the third law:

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One textbook observes that a block sliding down an inclined plane is what "some cynics view as the dullest problem in all of physics". Another quips, "Nobody will ever know how many minds, eager to learn the secrets of the universe, found themselves studying inclined planes and pulleys instead, and

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The concept of energy became a key part of Newtonian mechanics in the post-Newton period. Huygens' solution of the collision of hard spheres showed that in that case, not only is momentum conserved, but kinetic energy is as well (or, rather, a quantity that in retrospect we can identify as one-half

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without requiring physical contact. For example, the Sun and the Earth pull on each other gravitationally, despite being separated by millions of kilometres. This contrasts with the idea, championed by Descartes among others, that the Sun's gravity held planets in orbit by swirling them in a vortex

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The concepts invoked in Newton's laws of motion — mass, velocity, momentum, force — have predecessors in earlier work, and the content of Newtonian physics was further developed after Newton's time. Newton combined knowledge of celestial motions with the study of events on Earth and showed that one

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is used to calculate the expectation values of a position measurement or a momentum measurement. These expectation values will generally change over time; that is, depending on the time at which (for example) a position measurement is performed, the probabilities for its different possible outcomes

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Newton's third law must be modified in special relativity. The third law refers to the forces between two bodies at the same moment in time, and a key feature of special relativity is that simultaneity is relative. Events that happen at the same time relative to one observer can happen at different

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of the orbit, and thus the type of conic section, is determined by the energy and the angular momentum of the orbiting body. Planets do not have sufficient energy to escape the Sun, and so their orbits are ellipses, to a good approximation; because the planets pull on one another, actual orbits are

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Significant aspects of the motion of an extended body can be understood by imagining the mass of that body concentrated to a single point, known as the center of mass. The location of a body's center of mass depends upon how that body's material is distributed. For a collection of pointlike objects

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Newtonian physics treats matter as being neither created nor destroyed, though it may be rearranged. It can be the case that an object of interest gains or loses mass because matter is added to or removed from it. In such a situation, Newton's laws can be applied to the individual pieces of matter,

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Classical mechanics can be mathematically formulated in multiple different ways, other than the "Newtonian" description (which itself, of course, incorporates contributions from others both before and after Newton). The physical content of these different formulations is the same as the Newtonian,

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that assigns a velocity vector to each point in space and time. A small object being carried along by the fluid flow can change velocity for two reasons: first, because the velocity field at its position is changing over time, and second, because it moves to a new location where the velocity field

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is the total mass of the collection. In the absence of a net external force, the center of mass moves at a constant speed in a straight line. This applies, for example, to a collision between two bodies. If the total external force is not zero, then the center of mass changes velocity as though it

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By Newton's second law, the first term is the total force upon the first body, and the second term is the total force upon the second body. If the two bodies are isolated from outside influences, the only force upon the first body can be that from the second, and vice versa. By Newton's third law,

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thinker active during the sixth century, found this absurd: the same medium, air, was somehow responsible both for sustaining motion and for impeding it. If Aristotle's idea were true, Philoponus said, armies would launch weapons by blowing upon them with bellows. Philoponus argued that setting a

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In special relativity, the rule that Wilczek called "Newton's Zeroth Law" breaks down: the mass of a composite object is not merely the sum of the masses of the individual pieces. Newton's first law, inertial motion, remains true. A form of Newton's second law, that force is the rate of change of

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Collections of charged bodies do not always obey Newton's third law: there can be a change of one body's momentum without a compensatory change in the momentum of another. The discrepancy is accounted for by momentum carried by the electromagnetic field itself. The momentum per unit volume of the

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no motion. The principle expressed by Newton's first law is that there is no way to say which inertial observer is "really" moving and which is "really" standing still. One observer's state of rest is another observer's state of uniform motion in a straight line, and no experiment can deem either

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and modern science. The suggestion has been made that alchemy inspired Newton's notion of "action at a distance", i.e., one body exerting a force upon another without being in direct contact. This suggestion enjoyed considerable support among historians of science until a more extensive study of

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immersed and included in the whole process – because we can act on objects around us. Our ability to intervene in nature clarifies even the motion of the planets around the sun – masses so great and distances so vast that our roles as participants seem insignificant. Newton was able to transform

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has suggested calling attention to this assumption by designating it "Newton's Zeroth Law". Another candidate for a "zeroth law" is the fact that at any instant, a body reacts to the forces applied to it at that instant. Likewise, the idea that forces add like vectors (or in other words obey the

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into Newton's second law, an equation with predictive power can be written. Newton's second law has also been regarded as setting out a research program for physics, establishing that important goals of the subject are to identify the forces present in nature and to catalogue the constituents of

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is privileged over any other. The concept of an inertial observer makes quantitative the everyday idea of feeling no effects of motion. For example, a person standing on the ground watching a train go past is an inertial observer. If the observer on the ground sees the train moving smoothly in a

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that has become proverbial among physicists summarizes the theory: "Spacetime tells matter how to move; matter tells spacetime how to curve." Wheeler himself thought of this reciprocal relationship as a modern, generalized form of Newton's third law. The relation between matter distribution and

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masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each. For instance, the Earth and the Sun can both be approximated as

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and find it to be the value predicted by the Maxwell equations. In other words, light provides an absolute standard for speed, yet the principle of inertia holds that there should be no such standard. This tension is resolved in the theory of special relativity, which revises the notions of

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bodies has much the same mathematical form as Newton's law of universal gravitation: the force is proportional to the product of the charges, inversely proportional to the square of the distance between them, and directed along the straight line between them. The Coulomb force that a charge

1845:. Often, vectors are represented visually as arrows, with the direction of the vector being the direction of the arrow, and the magnitude of the vector indicated by the length of the arrow. Numerically, a vector can be represented as a list; for example, a body's velocity vector might be 8255:

provides a connection between quantum expectation values and Newton's second law, a connection that is necessarily inexact, as quantum physics is fundamentally different from classical. In quantum physics, position and momentum are represented by mathematical entities known as

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Imagine any particle projected along a horizontal plane without friction; then we know, from what has been more fully explained in the preceding pages, that this particle will move along this same plane with a motion which is uniform and perpetual, provided the plane has no

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has a stable equilibrium in the vertical position: if motionless there, it will remain there, and if pushed slightly, it will swing back and forth. Neglecting air resistance and friction in the pivot, the force upon the pendulum is gravity, and Newton's second law becomes

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This is true for many forces including that of gravity, but not for friction; indeed, almost any problem in a mechanics textbook that does not involve friction can be expressed in this way. The fact that the force can be written in this way can be understood from the

8370:, but the history of the concepts involved is obscured by multiple factors. An exact correspondence between Aristotelian and modern concepts is not simple to establish: Aristotle did not clearly distinguish what we would call speed and force, used the same term for 5457: 3510:, the net force upon the body is the zero vector, and by Newton's second law, the body will not accelerate. If the force upon the body is proportional to the displacement from the equilibrium point, and directed to the equilibrium point, then the body will perform 7193: 1799:: a quantity with both magnitude and direction. Velocity and acceleration are vector quantities as well. The mathematical tools of vector algebra provide the means to describe motion in two, three or more dimensions. Vectors are often denoted with an arrow, as in 6008: 7073: 7431:

as mentioned above, in which the first term indicates how the function being differentiated changes over time at a fixed location, and the second term captures how a moving particle will see different values of that function as it travels from place to place:

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Only with this approach, indeed, can the exposition form a logical whole and avoid tautological definitions of the fundamental mechanical quantities. It is, moreover, essentially simpler, and leads to the most complete and direct means of solving problems in

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Various sources have proposed elevating other ideas used in classical mechanics to the status of Newton's laws. For example, in Newtonian mechanics, the total mass of a body made by bringing together two smaller bodies is the sum of their individual masses.

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can be dissipated into heat. With the concept of energy given a solid grounding, Newton's laws could then be derived within formulations of classical mechanics that put energy first, as in the Lagrangian and Hamiltonian formulations described above.

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makes quantitative the everyday idea of a push or a pull. Forces in Newtonian mechanics are often due to strings and ropes, friction, muscle effort, gravity, and so forth. Like displacement, velocity, and acceleration, force is a vector quantity.

2412:" might have caused confusion among generations of students: the "action" and "reaction" apply to different bodies. For example, consider a book at rest on a table. The Earth's gravity pulls down upon the book. The "reaction" to that "action" is 7078: 10357: 2306:, and so the total force on a body depends upon both the magnitudes and the directions of the individual forces. When the net force on a body is equal to zero, then by Newton's second law, the body does not accelerate, and it is said to be in 6939: 5288: 1735: 6107:, which relates symmetries and conservation laws. The conservation of momentum can be derived by applying Noether's theorem to a Lagrangian for a multi-particle system, and so, Newton's third law is a theorem rather than an assumption. 1614: 5111:

within a computer's memory; Newton's laws are used to calculate how the velocities will change over a short interval of time, and knowing the velocities, the changes of position over that time interval can be computed. This process is

2032:, which depends upon the amount of matter contained in a body, the speed at which that body is moving, and the direction in which it is moving. In modern notation, the momentum of a body is the product of its mass and its velocity: 8900:

Negative acceleration includes both slowing down (when the current velocity is positive) and speeding up (when the current velocity is negative). For this and other points that students have often found difficult, see McDermott et

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helps make apparent the connection between symmetries and conservation laws, and it is useful when calculating the motion of constrained bodies, like a mass restricted to move along a curving track or on the surface of a sphere.

1105: 865:), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems. In the time since Newton, new insights, especially around the concept of energy, built the field of 5103:. That is, there is no way to start from the differential equations implied by Newton's laws and, after a finite sequence of standard mathematical operations, obtain equations that express the three bodies' motions over time. 6412: 4355:

A rigid body is an object whose size is too large to neglect and which maintains the same shape over time. In Newtonian mechanics, the motion of a rigid body is often understood by separating it into movement of the body's

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is the path for which the integral of the Lagrangian is "stationary". That is, the physical path has the property that small perturbations of it will, to a first approximation, not change the integral of the Lagrangian.

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increases over the interval in question, a negative average velocity indicates a net decrease over that interval, and an average velocity of zero means that the body ends the time interval in the same place as it began.

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When the torque is zero, the angular momentum is constant, just as when the force is zero, the momentum is constant. The torque can vanish even when the force is non-zero, if the body is located at the reference point

3885: 8418:. In retrospect, the idea of impetus can be seen as a forerunner of the modern concept of momentum. The intuition that objects move according to some kind of impetus persists in many students of introductory physics. 2203: 4868:{\displaystyle {\frac {d\mathbf {L} }{dt}}=\left({\frac {d\mathbf {r} }{dt}}\right)\times \mathbf {p} +\mathbf {r} \times {\frac {d\mathbf {p} }{dt}}=\mathbf {v} \times m\mathbf {v} +\mathbf {r} \times \mathbf {F} .} 4285:, the energy carried by heat flow, is a type of kinetic energy not associated with the macroscopic motion of objects but instead with the movements of the atoms and molecules of which they are made. According to the 8398:, that would be contained within the body itself. As long as its impetus was sustained, the body would continue to move. In the following centuries, versions of impetus theory were advanced by individuals including 7670: 3136: 8642:

suggested that gravitational attractions were reciprocal — that, for example, the Moon pulls on the Earth while the Earth pulls on the Moon — but he did not argue that such pairs are equal and opposite. In his

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predicts that electromagnetic waves will travel through empty space at a constant, definite speed. Thus, some inertial observers seemingly have a privileged status over the others, namely those who measure the

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differs from the Newtonian formulation by considering entire trajectories at once rather than predicting a body's motion at a single instant. It is traditional in Lagrangian mechanics to denote position with

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The study of the behavior of massive bodies using Newton's laws is known as Newtonian mechanics. Some example problems in Newtonian mechanics are particularly noteworthy for conceptual or historical reasons.

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The modern concept of inertia is credited to Galileo. Based on his experiments, Galileo concluded that the "natural" behavior of a moving body was to keep moving, until something else interfered with it. In

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argue that the Lagrangian formulation makes the conceptual content of classical mechanics more clear than starting with Newton's laws. Lagrangian mechanics provides a convenient framework in which to prove

6094: 7418: 6618: 5918: 2539: 6975: 6278: 4722: 2118: 3320:, such as that of the Moon around the Earth, can be approximated by uniform circular motion. In such cases, the centripetal force is gravity, and by Newton's law of universal gravitation has magnitude 4489: 107: 6536:

As in the Lagrangian formulation, in Hamiltonian mechanics the conservation of momentum can be derived using Noether's theorem, making Newton's third law an idea that is deduced rather than assumed.

3183: 3148:-shaped trajectories, because gravity affects the body's vertical motion and not its horizontal. At the peak of the projectile's trajectory, its vertical velocity is zero, but its acceleration is 8216:

The Newtonian theory of gravity is a good approximation to the predictions of general relativity when gravitational effects are weak and objects are moving slowly compared to the speed of light.

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charged body in a magnetic field experiences a force that is also proportional to its charge, in a direction perpendicular to both the field and the body's direction of motion. Using the vector

6531: 2566: 12836: 8124: 6555:. This formulation also uses Hamiltonian functions, but in a different way than the formulation described above. The paths taken by bodies or collections of bodies are deduced from a function 2140:

does not change with time, then the derivative acts only upon the velocity, and so the force equals the product of the mass and the time derivative of the velocity, which is the acceleration:

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which is a restatement of Newton's second law. The left-hand side is the time derivative of the momentum, and the right-hand side is the force, represented in terms of the potential energy.

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Among the proposals to reform the standard introductory-physics curriculum is one that teaches the concept of energy before that of force, essentially "introductory Hamiltonian mechanics".

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cautions, "Impetus is neither a force, nor a form of energy, nor momentum in the modern sense; it shares something with all these other concepts, but it is identical with none of them."

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observes, "A particle is defined to be an object of insignificant size: e.g. an electron, a tennis ball or a planet. Obviously the validity of this statement depends on the context..."

1502: 1790: 7990:), then the force will be perpendicular to the charge's motion, just as in the case of uniform circular motion studied above, and the charge will circle (or more generally move in a 2836: 2343:— acceleration implies force, force implies acceleration — some other statement about force must also be made. For example, an equation detailing the force might be specified, like 1622: 5567:{\displaystyle {\frac {\partial v}{\partial t}}+(\mathbf {\nabla } \cdot \mathbf {v} )\mathbf {v} =-{\frac {1}{\rho }}\mathbf {\nabla } P+\nu \nabla ^{2}\mathbf {v} +\mathbf {f} ,} 4031: 1160:

velocity, a measure of a body's speed and direction of movement at a single moment of time, rather than over an interval. One notation for the instantaneous velocity is to replace

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It is not yet known whether or not the Euler and Navier–Stokes equations exhibit the analogous behavior of initially smooth solutions "blowing up" in finite time. The question of

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often by friction or viscous drag, in which case energy bleeds out of the oscillator and the amplitude of the oscillations decreases over time. Also, a harmonic oscillator can be

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One reason that the harmonic oscillator is a conceptually important example is that it is good approximation for many systems near a stable mechanical equilibrium. For example, a

3272: 1507: 7287:{\displaystyle -{\frac {\partial }{\partial t}}\mathbf {\nabla } S={\frac {1}{m}}\left(\mathbf {\nabla } S\cdot \mathbf {\nabla } \right)\mathbf {\nabla } S+\mathbf {\nabla } V.} 4439: 1244: 4073:, propel matter in one direction to push the craft in the other. This means that the mass being pushed, the rocket and its remaining onboard fuel supply, is constantly changing. 8813:

Modern presentations of Newton's laws use the mathematics of vectors, a topic that was not developed until the late 19th and early 20th centuries. Vector algebra, pioneered by

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When Newton's laws are applied to rotating extended bodies, they lead to new quantities that are analogous to those invoked in the original laws. The analogue of mass is the

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Second Law of Nature: Each moving thing if left to itself moves in a straight line; so any body moving in a circle always tends to move away from the centre of the circle.

8319: 8032: 5444: 5230: 5034: 5012: 4895: 4677: 4655: 4259: 4158: 2712: 2690: 2561: 2367: 1819: 1917:, indicating that it is moving at 3 metres per second along the horizontal axis and 4 metres per second along the vertical axis. The same motion described in a different 9914: 9508: 5707: 3359: 1843: 6713:, analogously to how a light ray propagates in the direction perpendicular to its wavefront. This is simplest to express for the case of a single point mass, in which 3314: 1987:

Every object perseveres in its state of rest, or of uniform motion in a right line, except insofar as it is compelled to change that state by forces impressed thereon.

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of a chosen type is performed. Quantum mechanics allows the physicist to calculate the probability that a chosen measurement will elicit a particular result. The

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To every action, there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

2324:, which schematically portrays a body of interest and the forces applied to it by outside influences. For example, a free body diagram of a block sitting upon an 1996:: the natural behavior of a body is to move in a straight line at constant speed. A body's motion preserves the status quo, but external forces can perturb this. 3811: 2939: 1294: 1271: 909:, with negative numbers indicating positions to the left and positive numbers indicating positions to the right. If the body's location as a function of time is 8196:

is a theory of gravity that advances beyond that of Newton. In general relativity, the gravitational force of Newtonian mechanics is reimagined as curvature of

8144: 7887: 7312: 6812: 6788: 6731: 6711: 6691: 6667: 6196: 6176: 6156: 5678: 5422: 4610: 4589: 3905: 3772: 3752: 3456: 3436: 3379: 3232: 3212: 3166: 3059: 3039: 3019: 2999: 2979: 2959: 2916: 2896: 2876: 2856: 2143: 2138: 1414: 1394: 1347: 1198: 1149: 15303: 7175:{\displaystyle -\mathbf {\nabla } {\frac {\partial S}{\partial t}}={\frac {1}{2m}}\mathbf {\nabla } \left(\mathbf {\nabla } S\right)^{2}+\mathbf {\nabla } V.} 8279: 5104: 7624:

is a special case of Newton's second law, adapted for the case of describing a small object bombarded stochastically by even smaller ones. It can be written

2023:

The change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed.

8512:, who recognized that inertial motion should be motion in a straight line. Descartes published his laws of nature (laws of motion) with this correction in 7627: 5709:. The simplest example is a massive point particle, the Lagrangian for which can be written as the difference between its kinetic and potential energies: 3194:

When a body is in uniform circular motion, the force on it changes the direction of its motion but not its speed. For a body moving in a circle of radius

3064: 14925: 9905: 7718:

is a force that varies randomly from instant to instant, representing the net effect of collisions with the surrounding particles. This is used to model

13109:

Schaffer, Kathryn; Barreto Lemos, Gabriela (24 May 2019). "Obliterating Thingness: An Introduction to the "What" and the "So What" of Quantum Physics".

8609:

forces, and unable to find a quantitatively satisfactory explanation of his law of gravity in terms of an aetherial model, Newton eventually declared, "

8038:

works by applying electric and/or magnetic fields to moving charges and measuring the resulting acceleration, which by the Lorentz force law yields the

5377:{\displaystyle {\frac {\partial v}{\partial t}}+(\mathbf {\nabla } \cdot \mathbf {v} )\mathbf {v} =-{\frac {1}{\rho }}\mathbf {\nabla } P+\mathbf {f} ,} 2779:

If a body falls from rest near the surface of the Earth, then in the absence of air resistance, it will accelerate at a constant rate. This is known as

2208: 12621: 4925: 8551:

had worked out his own, concise version of the law in 1656. It was not published until 1703, eight years after his death, in the opening paragraph of

1619:

is to velocity as velocity is to position: it is the derivative of the velocity with respect to time. Acceleration can likewise be defined as a limit:

15933: 9710: 6817: 6017: 5107:

can be applied to obtain useful, albeit approximate, results for the three-body problem. The positions and velocities of the bodies can be stored in

5075:

is constant, or by applying a duality transformation to a 2-dimensional harmonic oscillator. However it is solved, the result is that orbits will be

8910:

Per Cohen and Whitman. For other phrasings, see Eddington and Frautschi et al. Andrew Motte's 1729 translation rendered Newton's "nisi quatenus" as

8617:'s theories of motion and gravity, the first grounds for judging them must be the successful predictions they made. And indeed, since Newton's time 7317: 3381:

is the mass of the larger body being orbited. Therefore, the mass of a body can be calculated from observations of another body orbiting around it.

2069:

where all three quantities can change over time. Newton's second law, in modern form, states that the time derivative of the momentum is the force:

11635: 6201: 4686: 8722:

Newton expressed his second law by saying that the force on a body is proportional to its change of motion, or momentum. By the time he wrote the

8656:

During the 1650s, Huygens studied collisions between hard spheres and deduced a principle that is now identified as the conservation of momentum.

5648:. Due to the breadth of these topics, the discussion here will be confined to concise treatments of how they reformulate Newton's laws of motion. 2072: 898:

pointlike when considering the orbit of the former around the latter, but the Earth is not pointlike when considering activities on its surface.

14619: 14521: 8779:

would employ it as a basic premise in the 1740s. Euler pioneered the study of rigid bodies and established the basic theory of fluid dynamics.

6467:

which reproduces the familiar statement that a body's momentum is the product of its mass and velocity. The time derivative of the momentum is

5116:

to calculate, approximately, the bodies' trajectories. Generally speaking, the shorter the time interval, the more accurate the approximation.

15271: 8327: 8302: 869:

on his foundations. Limitations to Newton's laws have also been discovered; new theories are necessary when objects move at very high speeds (

857: 15068: 15054: 15037: 10756: 8679:, he listed four laws: the principle of inertia, the change of motion by force, a statement about relative motion that would today be called 797: 13170:"Investigating and improving student understanding of the probability distributions for measuring physical observables in quantum mechanics" 8534:

First Law of Nature: Each thing when left to itself continues in the same state; so any moving body goes on moving until something stops it.

4273:

after Newton's time, but it has become an inseparable part of what is considered "Newtonian" physics. Energy can broadly be classified into

11706: 8559:

Hypothesis I: Any body already in motion will continue to move perpetually with the same speed and in a straight line unless it is impeded.

5156: 4305: 3619: 10794: 6470: 2918:

is the distance from the center of the Earth to the body's location, which is very nearly the radius of the Earth. Setting this equal to

386: 15360: 13664: 13560: 11953: 10684: 8858: 5615: 505: 6417: 5911:

provides the mathematical tools for finding this path. Applying the calculus of variations to the task of finding the path yields the

3549: 1848: 7617:

that a gas exerts upon the container holding it as the aggregate of many impacts of atoms, each imparting a tiny amount of momentum.

5771: 3140:

If the body is not released from rest but instead launched upwards and/or horizontally with nonzero velocity, then free fall becomes

2339:

of force, i.e., a force is that which exists when an inertial observer sees a body accelerating. In order for this to be more than a

11947:

LeGresley, Sarah E.; Delgado, Jennifer A.; Bruner, Christopher R.; Murray, Michael J.; Fischer, Christopher J. (13 September 2019).

6558: 2492: 1250:

of the position with respect to time. It can roughly be thought of as the ratio between an infinitesimally small change in position

15483: 14903:

from 1799 to 1805, a work collecting in one place all the theoretical and empirical results of the research predicated on Newton's

13097:

It is a fundamental quantum doctrine that a measurement does not, in general, reveal a pre-existing value of the measured property.

11949:"Calculus-enhanced energy-first curriculum for introductory physics improves student performance locally and in downstream courses" 8853: 2784: 2344: 2035: 478: 7435: 15908: 15885: 15641: 15589: 4635:

Angular momentum is calculated with respect to a reference point. If the displacement vector from a reference point to a body is

10680:"Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context" 9108:

Newton's papers became possible, after which it fell out of favor. However, it does appear that Newton's alchemy influenced his

8185:

Newtonian mechanics is a good approximation to special relativity when the speeds involved are small compared to that of light.

5210:

has a different value. Consequently, when Newton's second law is applied to an infinitesimal portion of fluid, the acceleration

2004:

straight line at a constant speed, then a passenger sitting on the train will also be an inertial observer: the train passenger

15493: 15231: 12424:

Chu, Caroline S.; Lebrilla, Carlito B. (2010). "Introduction to Modern Techniques in Mass Spectrometry". In Jue, Thomas (ed.).

11344: 8618: 4444: 1446: 63: 11291: 10379: 8789:(1798–1825) forsook geometry and developed mechanics purely through algebraic expressions, while resolving questions that the 5170:

is an expression of Newton's second law adapted to fluid dynamics. A fluid is described by a velocity field, i.e., a function

17: 15151: 14856: 14680: 14589: 14365: 14269: 14182: 14072: 13866: 13527: 13483: 13344: 13307: 13024: 12986: 12887: 12846: 12785:"Four-Dimensional Formulations of Newtonian Mechanics and Their Relation to the Special and the General Theory of Relativity" 12689: 12443: 12253: 11923: 11883: 11796: 11747: 11605: 11354: 11309: 11059: 10804: 10766: 10495: 10470: 10154: 10113: 9977: 9793: 9648: 9568: 9429: 9330: 9285: 9206: 9074:

Aristotelian physics also had difficulty explaining buoyancy, a point that Galileo tried to resolve without complete success.

8245: 7594:

A simulation of a larger, but still microscopic, particle (in yellow) surrounded by a gas of smaller particles, illustrating

6126:

was a key development in modern physics and can be conveniently stated in the language of Lagrangian or Hamiltonian mechanics

2790: 2314:

if, when the position of the body is changed slightly, the body remains near that equilibrium. Otherwise, the equilibrium is

15520: 14614: 13807: 13259: 8715: 833:

A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force.

11378:

Breen, Barbara J.; Weidert, Christine E.; Lindner, John F.; Walker, Lisa May; Kelly, Kasey; Heidtmann, Evan (April 2008).

9042:

Discussions can be found in, for example, Frautschi et al., Panofsky and Phillips, Goldstein, Poole and Safko, and Werner.

8407: 5712: 3237: 15619: 15330: 14886: 14763: 14395: 6533:

which, upon identifying the negative derivative of the potential with the force, is just Newton's second law once again.

2775:, deviating from a parabolic arc because of air resistance, spin, and deformation into a non-spherical shape upon impact. 1203: 460: 8785: 8248:

for a measurement is the average of the possible results it might yield, weighted by their probabilities of occurrence.

16105: 15532: 13812: 13556:"Exploring the preinstruction and postinstruction non-Newtonian world views as measured by the Force Concept Inventory" 8093: 6003:{\displaystyle {\frac {d}{dt}}\left({\frac {\partial L}{\partial {\dot {q}}}}\right)={\frac {\partial L}{\partial q}}.} 5099:

If a third mass is added, the Kepler problem becomes the three-body problem, which in general has no exact solution in

3168:

downwards, as it is at all times. Setting the wrong vector equal to zero is a common confusion among physics students.

15510: 7068:{\displaystyle -{\frac {\partial S}{\partial t}}={\frac {1}{2m}}\left(\mathbf {\nabla } S\right)^{2}+V(\mathbf {q} ).} 15322: 15189: 14141: 14108: 13273: 13239: 12767: 12731: 12595: 12487: 12400: 11838: 10899: 10182: 10142: 10058: 9144: 8084: 5072: 790: 15918: 15743: 11869: 8988:

See, for instance, Moebs et al., Gonick and Huffman, Low and Wilson, Stocklmayer et al., Hellingman, and Hodanbosi.

8241: 5167: 1921:

will be represented by different numbers, and vector algebra can be used to translate between these alternatives.

1796: 1296:

over which it occurs. More carefully, the velocity and all other derivatives can be defined using the concept of a

31: 15996: 5173: 2416:

the support force from the table holding up the book, but the gravitational pull of the book acting on the Earth.

1928:

are used with a technical meaning. Moreover, words which are synonymous in everyday speech are not so in physics:

752: 16085: 15938: 15840: 15738: 15559: 14899:

These advances in our understanding of planetary motion led Laplace to produce the four principal volumes of his

12585: 10048: 8771:. This form of the second law was written (for the special case of constant force) at least as early as 1716, by 5250: 126: 8948: 4062: 1504:

Instantaneous velocity can be defined as the limit of the average velocity as the time interval shrinks to zero:

16095: 8843: 8415: 8352: 381: 121: 38: 10515: 8742:

does not express acceleration as the second derivative of position, and so it does not give the second law as

8698: 5166:

by considering a fluid as composed of infinitesimal pieces, each exerting forces upon neighboring pieces. The

2009:

point of view to be correct or incorrect. There is no absolute standard of rest. Newton himself believed that

1744: 1131:) is used, per tradition, to mean "change in". A positive average velocity means that the position coordinate 16090: 16080: 15823: 13770: 10097: 6941:

The relation to Newton's laws can be seen by considering a point mass moving in a time-independent potential

6099: 5247:, and there is a net force upon it if the fluid pressure varies from one side of it to another. Accordingly, 3274:

and is directed toward the center of the circle. The force required to sustain this acceleration, called the

8601:. Newton considered aetherial explanations of force but ultimately rejected them. The study of magnetism by 6693:. Bodies move over time in such a way that their trajectories are perpendicular to the surfaces of constant 4078:

keeping track of which pieces belong to the object of interest over time. For instance, if a rocket of mass

2662:{\displaystyle {\frac {d\mathbf {p} }{dt}}={\frac {d\mathbf {p} _{1}}{dt}}+{\frac {d\mathbf {p} _{2}}{dt}}.} 2303: 16065: 15733: 10199: 7857:, and it points in the exact opposite direction. Coulomb's law is thus consistent with Newton's third law. 6548: 3998: 783: 770: 531: 454: 376: 219: 8493: 15928: 15787: 15584: 15096: 14791: 14423: 13966: 13413: 13174: 12517: 12335: 12286: 12193: 12144: 12074: 11824: 11547: 11477: 11433: 11384: 11236: 11187: 11138: 10984: 10932: 10834: 10204: 10006: 9363: 8602: 5912: 5108: 4398: 450: 251: 15678: 14572:

Smith, George E. (December 2020). "Newton's Laws of Motion". In Schliesser, Eric; Smeenk, Chris (eds.).

9824:

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics

8232:. Instead of thinking about quantities like position, momentum, and energy as properties that an object 6551:

provides yet another formulation of classical mechanics, one which makes it mathematically analogous to

2205:

As the acceleration is the second derivative of position with respect to time, this can also be written

229: 15975: 15728: 15723: 15646: 15549: 15478: 15337: 15224: 11875: 8311: 6736: 5451: 5139:

Three double pendulums, initialized with almost exactly the same initial conditions, diverge over time.

847:

If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

670: 559: 278: 13891: 10678:

Carli, Marta; Lippiello, Stefania; Pantano, Ornella; Perona, Mario; Tormen, Giuseppe (19 March 2020).

10519: 6623: 2463: 2434: 16013: 15693: 15609: 15263: 13053: 12789: 12386: 8838: 8805:

wrote, "Dead force consists of a simple tendency to motion: such is that of a spring ready to relax;

8734:

he made no explicit use of it, perhaps because he believed geometrical arguments in the tradition of

8676: 7699: 6944: 5619: 4110: 3995:), and so this expression simplifies to the equation for a simple harmonic oscillator with frequency 3774:

can be calculated knowing, for example, the position and velocity the body has at a given time, like

2732:), and the idea that forces change the energy of a body, have both been described as a "fourth law". 424: 15142:(1996). "The Emergence of Vector Calculus in Physics: The Early Decades". In Schubring, Gert (ed.). 14211:"William R. Newman. Newton the Alchemist: Science, Enigma, and the Quest for Nature's "Secret Fire"" 10200:"The role of competing knowledge structures in undermining learning: Newton's second and third laws" 7965: 4967: 16100: 15564: 15505: 15488: 15473: 15418: 14786: 12972: 12330: 9024:

Among the many textbook treatments of this point are Hand and Finch and also Kleppner and Kolenkow.

8645: 8583: 8514: 8206: 7958:

The Lorentz force law in effect: electrons are bent into a circular trajectory by a magnetic field.

6934:{\displaystyle -{\frac {\partial S}{\partial t}}=H\left(\mathbf {q} ,\mathbf {\nabla } S,t\right).} 4900: 3705: 2420: 700: 544: 14921:"Émilie Du Châtelet's interpretation of the laws of motion in the light of 18th century mechanics" 8000: 5644:, leads to further insight about symmetry, and can be developed into sophisticated techniques for 5427: 5213: 5017: 4995: 4878: 4660: 4638: 4289:, when a force acts upon a body while that body moves along the line of the force, the force does 4242: 4141: 2787:. The latter states that the magnitude of the gravitational force from the Earth upon the body is 2695: 2673: 2544: 2350: 1802: 16075: 15542: 15295: 14920: 10790: 9818: 9638: 8802: 7606: 6135: 5631:

but they provide different insights and facilitate different types of calculations. For example,

2729: 2714:

is known to be constant, it follows that the forces have equal magnitude and opposite direction.

2010: 650: 414: 15144:

Hermann Günther Graßmann (1809–1877): Visionary Mathematician, Scientist and Neohumanist Scholar

14977: 11791:. Providence, RI: American Mathematical Society and Clay Mathematics Institute. pp. 57–67. 11783: 11630: 11472: 11231: 11182: 10829: 10300: 9454: 8653:, that is, filled with matter, so all motion required a body to displace a medium as it moved. 5683: 690: 15913: 15903: 15668: 15631: 15604: 15498: 14706:"The mathematical form of measurement and the argument for Proposition I in Newton's Principia" 13227: 13111: 12873: 12717: 11037: 9265: 9230: 8888: 8848: 8826: 8672:. Newton cited the work of Huygens, Wren, and Wallis to support the validity of his third law. 8201: 8174:, which depends upon the body's speed. Alternatively, momentum and force can be represented as 8080: 8054: 5908: 5100: 4344: 4067: 3511: 3411: 3384: 3323: 2307: 1824: 1730:{\displaystyle a={\frac {dv}{dt}}=\lim _{\Delta t\to 0}{\frac {v(t+\Delta t)-v(t)}{\Delta t}}.} 695: 512: 13234:. Translated by Hemley, Susan Reid; Ostrowsky, Nicole; Ostrowsky, Dan. John Wiley & Sons. 12877: 3281: 16070: 15960: 15867: 15753: 15748: 15537: 15450: 15425: 15217: 14096: 12675: 9134: 8399: 8153: 7675: 6670: 6131: 5637: 5135: 3974: 3954: 3930: 3910: 3685: 2424: 2423:. The latter remains true even in cases where Newton's statement does not, for instance when 1609:{\displaystyle {\frac {ds}{dt}}=\lim _{\Delta t\to 0}{\frac {s(t+\Delta t)-s(t)}{\Delta t}}.} 1163: 1110: 705: 680: 366: 184: 14581: 9006:

For the former, see Greiner, or Wachter and Hoeber. For the latter, see Tait and Heaviside.

2298:

along the direction of the plane that could be applied, for example, by friction or a string

2013:

existed, but that the only measures of space or time accessible to experiment are relative.

15874: 15594: 15351: 15105: 14991: 14934: 14800: 14481: 14432: 13975: 13673: 13569: 13422: 13183: 13072: 12918: 12798: 12630: 12536: 12344: 12295: 12202: 12153: 12093: 12034: 11962: 11556: 11496: 11393: 11297: 11245: 11147: 11098: 10993: 10941: 10843: 10693: 10606: 10553: 10425: 10314: 10265: 10213: 9923: 9832: 9517: 9468: 9372: 9354: 9312: 8814: 8780: 8610: 8591: 8544: 8039: 7833: 7806: 7779: 7752: 6123: 6104: 5882: 5855: 5656: 5632: 5387: 5092: 4057: 3517: 1419: 1352: 968: 941: 906: 725: 685: 593: 589: 581: 571: 361: 354: 110: 14467: 13016:

Einstein's Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity

8745: 5826: 5577: 4081: 1966: 1303: 912: 720: 8: 16049: 15683: 15663: 15579: 15569: 15430: 14785:

Marquina, J. E.; Marquina, M. L.; Marquina, V.; Hernández-Gómez, J. J. (1 January 2017).

13686: 13659: 13617: 13582: 13555: 13010: 12642: 11975: 11948: 11089: 11041: 10706: 10679: 10416: 10256: 9269: 9100: 8680: 8669: 8571: 8427: 7995: 7602: 7421: 5645: 5641: 5595: 5233: 5152: 5071:. The Kepler problem can be solved in multiple ways, including by demonstrating that the 4286: 3777: 3487: 3461: 3401: 2670:

these forces have equal magnitude but opposite direction, so they cancel when added, and

1297: 866: 500: 441: 419: 164: 159: 154: 54: 15146:. Boston Studies in the Philosophy of Science. Vol. 187. Kluwer. pp. 197–210. 15109: 14995: 14938: 14812: 14804: 14485: 14436: 14390: 13979: 13677: 13573: 13426: 13187: 13076: 12922: 12802: 12634: 12540: 12356: 12348: 12299: 12206: 12157: 12097: 12038: 11966: 11560: 11500: 11397: 11301: 11249: 11151: 11102: 10997: 10945: 10847: 10697: 10653: 10557: 10429: 10318: 10269: 10217: 9927: 9836: 9521: 9472: 9376: 9234: 8563:

According to Huygens, this law was already known by Galileo and Descartes among others.

8071:

in such a way that all inertial observers will agree upon the speed of light in vacuum.

7182:

Interchanging the order of the partial derivatives on the left-hand side, and using the

5446:

stands for an external influence like a gravitational pull. Incorporating the effect of

4232:{\displaystyle \mathbf {F} =M{\frac {d\mathbf {v} }{dt}}-\mathbf {u} {\frac {dM}{dt}}\,} 3041:

can be taken to be constant. This particular value of acceleration is typically denoted

2921: 1276: 1253: 15989: 15898: 15614: 15527: 15255: 15194: 15015: 14958: 14824: 14754: 14735: 14644: 14554: 14546: 14335: 14327: 14240: 14210: 14043: 13942: 13934: 13837: 13751: 13743: 13699: 13642: 13595: 13489: 13389: 13209: 13165: 13146: 13120: 13088: 13062: 12954: 12713: 12654: 12560: 12526: 12368: 12117: 12083: 12050: 12025: 11998: 11912: 11733: 11672: 11644: 11520: 11486: 11269: 11212: 11019: 10867: 10729: 10631: 10579: 10511: 10338: 10040: 9848: 9681: 9634: 9484: 9320: 9179: 9103:

called him "the last of the magicians" to describe his place in the transition between

8687:

with three primary laws and then other statements reduced to corollaries, during 1685.

8548: 8257: 8193: 8129: 7872: 7297: 6797: 6773: 6716: 6696: 6676: 6652: 6181: 6161: 6141: 6011: 5663: 5407: 5053: 4595: 4574: 3890: 3757: 3737: 3441: 3421: 3388: 3364: 3217: 3197: 3151: 3044: 3024: 3004: 2984: 2964: 2944: 2901: 2881: 2861: 2841: 2409: 2393: 2123: 1399: 1379: 1332: 1183: 1134: 874: 870: 630: 371: 246: 214: 174: 14013: 13787: 10460: 7420:

This is another re-expression of Newton's second law. The expression in brackets is a

1100:{\displaystyle {\frac {\Delta s}{\Delta t}}={\frac {s(t_{1})-s(t_{0})}{t_{1}-t_{0}}}.} 15984: 15857: 15829: 15711: 15688: 15636: 15554: 15440: 15157: 15147: 15121: 15019: 15007: 15003: 14982: 14950: 14907:. From that time forward, Newtonian science sprang from Laplace's work, not Newton's. 14862: 14852: 14828: 14816: 14727: 14705: 14686: 14676: 14648: 14636: 14595: 14585: 14558: 14538: 14497: 14448: 14371: 14361: 14339: 14319: 14275: 14265: 14244: 14232: 14188: 14178: 14170: 14147: 14137: 14114: 14104: 14078: 14068: 14047: 14035: 14018: 13991: 13946: 13872: 13862: 13829: 13755: 13703: 13691: 13646: 13634: 13599: 13587: 13533: 13523: 13497: 13479: 13448: 13381: 13350: 13340: 13313: 13303: 13279: 13269: 13235: 13213: 13201: 13150: 13138: 13092: 13030: 13020: 12992: 12982: 12958: 12946: 12909: 12883: 12852: 12842: 12814: 12784: 12763: 12737: 12727: 12695: 12685: 12658: 12646: 12601: 12591: 12581: 12552: 12493: 12483: 12469: 12439: 12406: 12396: 12372: 12360: 12311: 12259: 12249: 12218: 12169: 12121: 12109: 12054: 12002: 11990: 11929: 11919: 11889: 11879: 11844: 11834: 11802: 11792: 11774:(2006). "Existence and smoothness of the Navier–Stokes equation". In Carlson, James; 11771: 11753: 11743: 11676: 11664: 11611: 11601: 11572: 11512: 11508: 11450: 11409: 11360: 11350: 11336: 11328: 11305: 11287: 11273: 11261: 11257: 11216: 11204: 11200: 11163: 11114: 11065: 11055: 11045: 11023: 11011: 10957: 10905: 10895: 10871: 10859: 10855: 10810: 10800: 10772: 10762: 10733: 10721: 10635: 10623: 10571: 10491: 10466: 10441: 10342: 10330: 10326: 10305: 10281: 10247: 10229: 10178: 10150: 10119: 10109: 10101: 10064: 10054: 9983: 9973: 9941: 9886: 9852: 9799: 9789: 9736: 9654: 9644: 9574: 9564: 9554: 9535: 9488: 9480: 9459: 9435: 9425: 9388: 9336: 9326: 9291: 9281: 9273: 9212: 9202: 9167:. Translated by Cohen, I.B.; Whitman, A. Los Angeles: University of California Press. 9140: 8661: 8459: 8395: 8252: 8229: 8224: 8053:

There is subtle conceptual conflict between electromagnetism and Newton's first law:

8035: 7865: 7621: 7610: 4621: 3275: 3141: 2754: 2428: 2427:

as well as material bodies carry momentum, and when momentum is defined properly, in

2340: 2321: 2279: 2000: 1918: 878: 640: 597: 554: 549: 490: 266: 256: 149: 15178: 14962: 14739: 13612: 12564: 11524: 8433: 16025: 15817: 15793: 15769: 15599: 15345: 15113: 14999: 14942: 14808: 14719: 14628: 14577: 14530: 14489: 14440: 14311: 14293: 14224: 14027: 13983: 13926: 13821: 13803: 13735: 13681: 13626: 13577: 13438: 13430: 13336: 13191: 13130: 13080: 12936: 12926: 12806: 12638: 12544: 12431: 12352: 12303: 12210: 12161: 12101: 12069: 12042: 11980: 11970: 11654: 11564: 11504: 11442: 11401: 11253: 11196: 11155: 11106: 11001: 10949: 10924: 10851: 10711: 10701: 10615: 10597: 10583: 10561: 10544: 10535: 10433: 10411: 10322: 10273: 10221: 10015: 10001: 9931: 9881:

Resnick, Robert; Halliday, David (1966). "Section 5-4: Mass; Newton's Second Law".

9840: 9691: 9626: 9525: 9476: 9380: 8942: 8868: 8818: 8657: 8650: 8613:": whether or not a model like Descartes's vortices could be found to underlie the 8438: 7741: 7693: 5113: 5049: 4679:, then the body's angular momentum with respect to that point is, using the vector 4625: 4299: 4278: 2961:

cancels from both sides of the equation, leaving an acceleration that depends upon

735: 715: 660: 655: 601: 576: 431: 289: 234: 209: 15091: 13961: 13408: 12512: 12281: 12188: 12139: 11728:(2021). "Struggles with the Continuum". In Anel, Mathieu; Catren, Gabriel (eds.). 11542: 11428: 11379: 11133: 10251: 9936: 9909: 9779: 9530: 9503: 8945:) take the conservation of momentum as a fundamental physical principle and treat 3182: 2771:. In between bounces, the ball's height as a function of time is close to being a 15805: 15574: 15468: 13515: 13048: 12978:

The Disordered Cosmos: A Journey into Dark Matter, Spacetime, and Dreams Deferred

12277: 11690: 11543:"A unit on oscillations, determinism and chaos for introductory physics students" 11084: 10252:"Changing the Order of Newton's Laws—Why & How the Third Law Should be First" 10089: 10036: 9967: 9359:"Student difficulties in connecting graphs and physics: Examples from kinematics" 9083: 9051:

Details can be found in the textbooks by, e.g., Cohen-Tannoudji et al. and Peres.

8707: 8639: 8597: 8509: 8455: 8390: 8386: 8286: 8210: 8047: 7745: 7719: 7595: 6158:

constrained to move in a straight line, under the effect of a potential. Writing

5148: 3948: 3177: 2385: 730: 675: 625: 620: 539: 14946: 14848:

Forces and Fields: The Concept of Action at a Distance in the History of Physics

14418: 12435: 11698: 9844: 9358: 9178:

Newton, Isaac; Chittenden, N. W.; Motte, Andrew; Hill, Theodore Preston (1846).

7609:

applies Newton's laws of motion to large numbers (typically on the order of the

6407:{\displaystyle {\frac {dp}{dt}}=-{\frac {\partial {\mathcal {H}}}{\partial q}}.} 16001: 15848: 15673: 15656: 15626: 15413: 14666: 14302: 14215: 13196: 13169: 13134: 12931: 12904: 12755: 12473: 11820: 11538: 11332: 10925:"Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks" 10649: 10105: 9728: 9711:"Mistranslation of Newton's First Law Discovered after Nearly Nearly 300 Years" 9630: 9316: 8776: 8505: 8171: 8059: 5608: 5607:

and able to approach one another arbitrarily closely, as well as the lack of a

5068: 5058: 4564:{\displaystyle \mathbf {R} =\sum _{i=1}^{N}{\frac {m_{i}\mathbf {r} _{i}}{M}},} 4383: 4369: 4357: 4282: 4274: 3278:, is therefore also directed toward the center of the circle and has magnitude 2325: 1128: 757: 665: 566: 283: 14723: 14632: 14534: 14279: 14118: 13084: 13034: 12996: 12905:"Free fall in curved spacetime—how to visualise gravity in general relativity" 12856: 12810: 12425: 11933: 11757: 11615: 9740: 9216: 6337:{\displaystyle {\frac {dq}{dt}}={\frac {\partial {\mathcal {H}}}{\partial p}}} 16059: 15893: 15775: 15717: 15161: 15125: 15011: 14881: 14820: 14731: 14690: 14640: 14599: 14542: 14501: 14472: 14452: 14323: 14236: 14206: 14192: 14082: 14039: 14009: 13995: 13876: 13833: 13695: 13655: 13638: 13608: 13591: 13537: 13501: 13452: 13385: 13354: 13317: 13205: 13142: 12950: 12818: 12699: 12650: 12556: 12364: 12315: 12263: 12222: 12173: 12113: 11994: 11893: 11865: 11806: 11668: 11576: 11516: 11454: 11413: 11364: 11265: 11208: 11167: 11118: 11069: 11015: 10980:"A unified, contemporary approach to teaching energy in introductory physics" 10961: 10863: 10814: 10725: 10627: 10619: 10575: 10445: 10407: 10375: 10334: 10285: 10233: 10123: 10044: 9987: 9945: 9803: 9658: 9578: 9539: 9455:"Students' use of the principle of energy conservation in problem situations" 9439: 9392: 9340: 9295: 8772: 8451: 7894: 5076: 4680: 3992: 2764: 2724: 2397: 814: 645: 472: 14866: 14375: 14031: 13374:

Annali della Scuola Normale Superiore di Pisa. Classe di Lettere e Filosofia

13283: 12741: 12605: 12497: 11848: 10909: 10776: 7945:{\displaystyle \mathbf {F} =q\mathbf {E} +q\mathbf {v} \times \mathbf {B} .} 6790:

changes most steeply. In other words, the momentum of the point mass is the

2759: 1924:

The study of mechanics is complicated by the fact that household words like

16037: 15781: 15651: 15460: 15435: 15398: 15240: 14954: 14259: 14151: 13014: 12976: 12239: 12135: 12046: 12020: 11779: 11775: 11725: 10752: 10601: 10170: 9196: 9104: 9015:

Among the many textbook explanations of this are Frautschi et al. and Boas.

8411: 8307: 6119: 5144: 5130: 3880:{\displaystyle {\frac {d^{2}\theta }{dt^{2}}}=-{\frac {g}{L}}\sin \theta ,} 2329: 2283: 852: 837: 710: 635: 324: 204: 14851:(Dover reprint ed.). Mineola, N.Y.: Dover Publications. p. 189. 14670: 14062: 13856: 12679: 12410: 12243: 11232:"Bohlin transformation: the hidden symmetry that connects Hooke to Newton" 11049: 10068: 9783: 9419: 8462:. Descartes knew about this controversy and did not wish to get involved. 2198:{\displaystyle \mathbf {F} =m{\frac {d\mathbf {v} }{dt}}=m\mathbf {a} \,.} 15799: 15408: 15287: 15185: 15139: 14846: 14101:

The Foundations of Newton's Alchemy: Or, "the Hunting of the Greene Lyon"

13255: 12721: 12477: 12016: 11828: 11694: 11659: 11593: 11340: 10975: 10889: 10716: 9235:"Classical Dynamics: University of Cambridge Part II Mathematical Tripos" 9198:

Techniques of Classical Mechanics: from Lagrangian to Newtonian mechanics

8665: 8454:

worldview, and in 1633 this view had given rise a great conflict between

8175: 7731: 6552: 5852:. The physical path that the particle will take between an initial point 2768: 1416:

can be made arbitrarily small by choosing an input sufficiently close to

15090:

Silva, Cibelle Celestino; de Andrade Martins, Roberto (September 2002).

15069:"History of the Conservation of Energy: Booms, Blood, and Beer (Part 3)" 15055:"History of the Conservation of Energy: Booms, Blood, and Beer (Part 2)" 15038:"History of the Conservation of Energy: Booms, Blood, and Beer (Part 1)" 14550: 14516: 13789:

Two new sciences, including centers of gravity & force of percussion

13493: 13393: 13369: 13019:. Providence, Rhode Island: American Mathematical Society. p. 143. 12513:"Self-torque and angular momentum balance for a spinning charged sphere" 9695: 9553:

Urone, Paul Peter; Hinrichs, Roger; Dirks, Kim; Sharma, Manjula (2021).

7590: 15923: 15811: 14842: 14784: 14353: 13841: 13792:. Translated by Drake, S. University of Wisconsin Press. pp. 217 . 13630: 13443: 13409:"Experiments on buoyancy and surface tension following Galileo Galilei" 12941: 12838:

Curvature of Space and Time, with an Introduction to Geometric Analysis

12390: 12105: 11907: 10085: 8938: 8822: 7187: 7183: 6669:. The Hamiltonian is incorporated into the Hamilton–Jacobi equation, a 3406: 3187: 2401: 1795:

Position, when thought of as a displacement from an origin point, is a

1247: 902: 836:

At any instant of time, the net force on a body is equal to the body's

495: 169: 15117: 14493: 14331: 14297: 13987: 13938: 13914: 13747: 13723: 13554:

Eaton, Philip; Vavruska, Kinsey; Willoughby, Shannon (25 April 2019).

13478:(2nd ed.). Institute of Classical Studies, University of London. 13434: 12548: 12307: 12214: 12165: 11985: 11568: 11446: 11405: 11159: 11134:"Student understanding of the angular momentum of classical particles" 11006: 10979: 10437: 10277: 10225: 10019: 5625: 2400:. This pushes the rocket upwards, without regard to the ground or the 840:

multiplied by its mass or, equivalently, the rate at which the body's

15033: 11110: 11036: 10566: 10539: 9415: 9264: 9181:

Newton's Principia: The Mathematical Principles of Natural Philosophy

8590:

One important characteristic of Newtonian physics is that forces can

8469: 8375: 8367: 8261: 8197: 8147: 7735: 5447: 5088: 5067:

orbits that an inverse-square force law will produce is known as the

4387: 4045: 2780: 2750: 517: 14444: 13825: 12619:

Werner, Reinhard F. (9 October 2014). "Comment on "What Bell did"".

10953: 9384: 8629: 8436:

introduced the concept of inertia by way of his "laws of nature" in

7665:{\displaystyle m\mathbf {a} =-\gamma \mathbf {v} +\mathbf {\xi } \,} 3131:{\displaystyle g={\frac {GM}{r^{2}}}\approx \mathrm {9.8~m/s^{2}} .} 15445: 15386: 15209: 15183: 14710: 14315: 14261:

Dutch Light: Christiaan Huygens and the Making of Science in Europe

14228: 13930: 13739: 13125: 13067: 12531: 12088: 11830:

The Conceptual Foundations of the Statistical Approach in Mechanics

11738: 11649: 9686: 9560: 9033:

Treatments can be found in, e.g., Chabay et al. and McCallum et al.

8806: 8403: 7954: 7614: 6791: 5084: 4295: 3804: 3145: 2772: 2029: 1153: 841: 436: 319: 294: 13660:"University student conceptual resources for understanding forces" 11914:

Out of the Shadows: Contributions of 20th Century Women to Physics

11491: 8529:

Ball in circular motion has string cut and flies off tangentially.

8525: 6414:

Evaluating these partial derivatives, the former equation becomes

6124:

a celebrated theorem that relates symmetries and conservation laws

2320:

A common visual representation of forces acting in concert is the

2265:{\displaystyle \mathbf {F} =m{\frac {d^{2}\mathbf {s} }{dt^{2}}}.} 15403: 15391: 15279: 11631:"From Newton's second law to Euler's equations of perfect fluids" 9096: 9060:

As one physicist writes, "Physical theory is possible because we

8727: 8371: 8325:

Newton's first and second laws, in Latin, from the original 1687

5244: 5080: 4956:{\displaystyle \mathbf {\tau } =\mathbf {r} \times \mathbf {F} .} 4261:

is the net external force (e.g., a planet's gravitational pull).

1993: 1975: 409: 262: 179: 14064:

Science and Culture in the Nineteenth Century: Recreating Newton

9890: 9625: 9165:

The Principia, The Mathematical Principles of Natural Philosophy

9112:, in particular, how he thought about the combination of colors. 8714:

Here, Somerville deduces the inverse-square law of gravity from

2419:

Newton's third law relates to a more fundamental principle, the

1910:{\displaystyle \mathbf {v} =(\mathrm {3~m/s} ,\mathrm {4~m/s} )} 15957: 13265: 11910:(2006). "Emmy Noether". In Byers, Nina; Williams, Gary (eds.). 9672:

Hoek, D. (2023). "Forced Changes Only: A New Take on Inertia".

9109: 8735: 8306:, with hand-written corrections for the second edition, in the 6853:{\displaystyle \mathbf {v} ={\frac {1}{m}}\mathbf {\nabla } S.} 6089:{\displaystyle {\frac {d}{dt}}(m{\dot {q}})=-{\frac {dV}{dq}},} 4922:

point in the same direction. The remaining term is the torque,

4629: 4270: 2408:

Overly brief paraphrases of the third law, like "action equals

2389: 2274: 818: 468: 314: 224: 14177:(2nd ed.). Cambridge University Press. pp. 454–484. 13051:(1993). "Hidden variables and the two theorems of John Bell". 10412:"Newton's Zeroth Law: Learning from Listening to Our Students" 8864:

List of textbooks on classical mechanics and quantum mechanics

7413:{\displaystyle \left\mathbf {\nabla } S=-\mathbf {\nabla } V.} 7294:

Gathering together the terms that depend upon the gradient of

6613:{\displaystyle S(\mathbf {q} _{1},\mathbf {q} _{2},\ldots ,t)} 5243:. The mass of an infinitesimal portion depends upon the fluid 5040:

chosen axis, the shape of the body, and the rate of rotation.

4374: 3458:

axis, and suppose an equilibrium point exists at the position

2534:{\displaystyle \mathbf {p} =\mathbf {p} _{1}+\mathbf {p} _{2}} 14468:"The vis viva dispute: A controversy at the dawn of dynamics" 13613:"Impetus-Like Reasoning as Continuous with Newtonian Physics" 9643:(Advanced ed.). Cambridge : Cambridge University Press. 7991: 7613:) of particles. Kinetic theory can explain, for example, the 6273:{\displaystyle {\mathcal {H}}(p,q)={\frac {p^{2}}{2m}}+V(q).} 5163: 4717:{\displaystyle \mathbf {L} =\mathbf {r} \times \mathbf {p} .} 3317: 1971: 822: 304: 299: 241: 15184:

Chakrabarty, Deepto; Dourmashkin, Peter; Tomasik, Michelle;

14419:"The young Huygens solves the problem of elastic collisions" 14298:"The First English Version of Newton's Hypotheses non fingo" 13407:

Straulino, S.; Gambi, C. M. C.; Righini, A. (January 2011).

12511:

Bonga, Béatrice; Poisson, Eric; Yang, Huan (November 2018).

11946: 10356:

Hodanbosi, Carol (August 1996). Fairman, Jonathan G. (ed.).

9903: 8821:, stemmed from and largely supplanted the earlier system of 8675:

Newton arrived at his set of three laws incrementally. In a

5062:

Animation of three points or bodies attracting to each other

3186:

Two objects in uniform circular motion, orbiting around the

2431:

as well. In Newtonian mechanics, if two bodies have momenta

15179:

Newton’s Laws of Dynamics - The Feynman Lectures on Physics

13653: 13606: 12841:. Providence, Rhode Island: American Mathematical Society. 10677: 9915:

Physical Review Special Topics - Physics Education Research

9509:

Physical Review Special Topics - Physics Education Research

8794: 8347: 5823:

and the potential energy is some function of the position,

4379: 3144:. When air resistance can be neglected, projectiles follow 2113:{\displaystyle \mathbf {F} ={\frac {d\mathbf {p} }{dt}}\,.} 309: 272: 16032: 14173:(2016). "A preliminary reassessment of Newton's alchemy". 13861:. New York: Cambridge University Press. pp. 175–180. 12392:

The principles of electromagnetic theory and of relativity

9353: 8710:'s expanded version of the first two volumes of Laplace's 8624: 7889:

and to the strength of the electric field. In addition, a

7730:

Newton's three laws can be applied to phenomena involving

6115: 1999:

The modern understanding of Newton's first law is that no

14358:

Concepts of Force: A Study in the Foundations of Dynamics

11918:. Cambridge: Cambridge University Press. pp. 83–96. 11377: 9177: 8466:

was not published until 1664, ten years after his death.

8359: 7585: 4724:

Taking the time derivative of the angular momentum gives

4484:{\displaystyle \mathbf {r} _{1},\ldots ,\mathbf {r} _{N}} 4044:

by an applied force, which can lead to the phenomenon of

102:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}} 13858:

Pierre Gassendi and the Birth of Early Modern Philosophy

12331:"Breaking Newton's third law: electromagnetic instances" 11730:

New Spaces in Physics: Formal and Conceptual Reflections

11427:

McCandlish, David (July 1973). Shirer, Donald L. (ed.).

10923:

Billah, K. Yusuf; Scanlan, Robert H. (1 February 1991).

9868:

An Introduction to the Physics of Mass, Length, and Time

9552: 9421:

Mathematical Methods for Optical Physics and Engineering

6770:, and the point mass moves in the direction along which 4615: 1974:, rather than in straight lines, because of the Earth's 938:, then its average velocity over the time interval from 37:"F=ma" redirects here. For the physics competition, see 15089: 14360:. Mineola, N.Y.: Dover Publications. pp. 91, 127. 13553: 13226: 12879:

Geons, Black Holes, and Quantum Foam: A Life in Physics

12070:"The Hamilton–Jacobi equation: An alternative approach" 9972:(2nd ed.). Cambridge: Cambridge University Press. 8928:

decided to switch to some more interesting profession."

2328:

can illustrate the combination of gravitational force,

12189:"Hydrodynamic Analogy to the Hamilton–Jacobi Equation" 9357:; Rosenquist, Mark L.; van Zee, Emily H. (June 1987). 7580: 825:

acting on it. These laws, which provide the basis for

15973: 13769:

Galilei, G. (1954) . Crew, H.; De Salvio, A. (eds.).

13406: 13108: 11629:

Han-Kwan, Daniel; Iacobelli, Mikaela (7 April 2021).

11132:

Close, Hunter G.; Heron, Paula R. L. (October 2011).

10602:"Galileo and Oresme: Who Is Modern? Who Is Medieval?" 10246: 9870:. United Kingdom: University Press. pp. 126–128. 8951: 8748: 8156: 8132: 8096: 8003: 7968: 7903: 7875: 7836: 7809: 7782: 7755: 7702: 7678: 7630: 7438: 7320: 7300: 7196: 7081: 6978: 6972:, in which case the Hamilton–Jacobi equation becomes 6947: 6866: 6820: 6800: 6776: 6739: 6719: 6699: 6679: 6655: 6626: 6561: 6473: 6420: 6350: 6286: 6204: 6184: 6164: 6144: 6020: 5921: 5885: 5858: 5829: 5774: 5715: 5686: 5666: 5580: 5460: 5430: 5410: 5390: 5291: 5253: 5216: 5176: 5020: 4998: 4970: 4928: 4903: 4881: 4730: 4689: 4663: 4641: 4598: 4577: 4497: 4447: 4401: 4308: 4245: 4166: 4144: 4113: 4084: 4001: 3977: 3957: 3933: 3913: 3893: 3814: 3780: 3760: 3740: 3708: 3688: 3622: 3552: 3520: 3490: 3464: 3444: 3424: 3367: 3326: 3284: 3240: 3220: 3200: 3154: 3067: 3047: 3027: 3007: 2987: 2967: 2947: 2924: 2904: 2884: 2864: 2844: 2793: 2698: 2676: 2569: 2547: 2495: 2489:

respectively, then the total momentum of the pair is

2466: 2437: 2353: 2211: 2146: 2126: 2075: 2038: 1851: 1827: 1805: 1747: 1625: 1510: 1449: 1422: 1402: 1382: 1355: 1335: 1306: 1279: 1256: 1206: 1186: 1166: 1137: 1113: 998: 971: 944: 915: 66: 13915:"Christiaan Huygens' The Motion of Colliding Bodies" 13476:

Philoponus and the Rejection of Aristotelian Science

11473:"Integrability and chaos: the classical uncertainty" 10250:; Rayner, John P.; Gore, Michael M. (October 2012). 10035: 9910:"Do students use and understand free-body diagrams?" 9280:(6th ed.). Hoboken, NJ: Wiley. pp. 76–78. 8726:

he had already developed calculus (which he called "

8342: 4335:{\displaystyle \mathbf {F} =-\mathbf {\nabla } U\,.} 4294:

case, then the force can be written in terms of the

3675:{\displaystyle x(t)=A\cos \omega t+B\sin \omega t\,} 1246:

This denotes that the instantaneous velocity is the

30:"Newton's laws" redirects here. For other uses, see 14926:

Studies in History and Philosophy of Science Part A

13913:Blackwell, Richard J.; Huygens, Christiaan (1977). 12580: 12482:(2nd ed.). Mineola, N.Y.: Dover Publications. 11323: 11321: 10974: 10462:

Classical Mechanics: Point Particles and Relativity

9502:Brookes, David T.; Etkina, Eugenia (25 June 2009). 9453:Driver, Rosalind; Warrington, Lynda (1 July 1985). 9158: 9156: 6526:{\displaystyle {\frac {dp}{dt}}=-{\frac {dV}{dq}},} 5626:

Relation to other formulations of classical physics

5616:

existence and smoothness of Navier–Stokes solutions

2282:for a block on an inclined plane, illustrating the 14787:"Leonhard Euler and the mechanics of rigid bodies" 12622:Journal of Physics A: Mathematical and Theoretical 11911: 11819: 9184:. University of California Libraries. Daniel Adee. 8970: 8763: 8522:) in 1644, with the heliocentric part toned down. 8162: 8138: 8118: 8026: 7982: 7944: 7881: 7849: 7822: 7795: 7768: 7710: 7684: 7664: 7570: 7412: 7306: 7286: 7174: 7067: 6964: 6933: 6852: 6806: 6782: 6762: 6725: 6705: 6685: 6661: 6641: 6612: 6525: 6459: 6406: 6336: 6272: 6190: 6170: 6150: 6088: 6002: 5898: 5871: 5844: 5815: 5760: 5701: 5672: 5586: 5566: 5438: 5416: 5396: 5376: 5277: 5224: 5201: 5043: 5028: 5006: 4984: 4955: 4914: 4889: 4867: 4716: 4671: 4649: 4604: 4583: 4563: 4483: 4433: 4334: 4253: 4231: 4152: 4130: 4099: 4025: 3983: 3963: 3939: 3919: 3899: 3879: 3792: 3766: 3746: 3726: 3694: 3674: 3608: 3538: 3502: 3476: 3450: 3430: 3373: 3353: 3308: 3266: 3226: 3206: 3160: 3130: 3053: 3033: 3013: 2993: 2973: 2953: 2933: 2910: 2890: 2870: 2850: 2830: 2706: 2684: 2661: 2555: 2533: 2481: 2452: 2361: 2264: 2197: 2132: 2112: 2061: 2028:By "motion", Newton meant the quantity now called 1909: 1837: 1813: 1784: 1729: 1608: 1496: 1435: 1408: 1388: 1368: 1341: 1321: 1288: 1265: 1238: 1192: 1172: 1143: 1119: 1099: 984: 957: 930: 101: 15934:Statal Institute of Higher Education Isaac Newton 14257: 12971: 12726:(2nd ed.). Oxford: Oxford University Press. 11628: 11429:"Solutions to the Three-Body Problem by Computer" 11380:"Invitation to embarrassingly parallel computing" 9819:"A note on rods and clocks in Newton's Principia" 8119:{\displaystyle \mathbf {p} =m\gamma \mathbf {v} } 6860:The Hamilton–Jacobi equation for a point mass is 5143:Newton's laws of motion allow the possibility of 4350: 2717: 1982:Translated from Latin, Newton's first law reads, 16057: 14576:. Oxford University Press. Online before print. 14103:. Cambridge University Press. pp. 211–212. 13912: 13302:. Cambridge University Press. pp. 310–311. 13220: 12510: 12468: 11732:. Cambridge University Press. pp. 281–326. 11636:Proceedings of the American Mathematical Society 11600:. Princeton University Press. pp. 363–364. 11349:. Princeton University Press. pp. 726–728. 11318: 11296:. American Mathematical Society. pp. 8–12. 11280: 10524:. Vol. 15 (9th ed.). pp. 715–716. 9965: 9452: 9260: 9258: 9153: 8285:Isaac Newton (1643–1727), in a 1689 portrait by 7075:Taking the gradient of both sides, this becomes 6460:{\displaystyle {\frac {dq}{dt}}={\frac {p}{m}},} 3609:{\displaystyle m{\frac {d^{2}x}{dt^{2}}}=-kx\,.} 2335:Newton's second law is sometimes presented as a 1656: 1535: 1451: 14067:. New York: Taylor & Francis. p. 147. 12590:(3rd ed.). San Francisco: Addison Wesley. 12464: 12462: 11183:"Another comment on "Eccentricity as a vector"" 10654:"Frequently Asked Questions: Projectile Motion" 10198:Low, David J.; Wilson, Kate F. (January 2017). 9880: 9424:. Cambridge, U.K.: Cambridge University Press. 9311: 9133:Thornton, Stephen T.; Marion, Jerry B. (2004). 8605:and others created a precedent for thinking of 8366:The subject of physics is often traced back to 7744:for the electric force between two stationary, 5816:{\displaystyle T={\frac {1}{2}}m{\dot {q}}^{2}} 4281:, due to a body's position relative to others. 3927:is its angle from the vertical. When the angle 2744: 14620:The British Journal for the History of Science 14522:The British Journal for the History of Science 14165: 14163: 14161: 12674: 12430:. Totowa, NJ: Humana Press. pp. 137–154. 12248:(4th ed.). Weinheim, Germany: Wiley-VCH. 12067: 10799:(1st ed.). New York: Spiegel & Grau. 10084: 9966:Kleppner, Daniel; Kolenkow, Robert J. (2014). 9132: 8228:conceptual underpinning of quantum physics is 7860:Electromagnetism treats forces as produced by 1992:Newton's first law expresses the principle of 851:The three laws of motion were first stated by 15225: 14918: 13163: 12712: 12681:General Relativity and the Einstein Equations 10978:; Sherwood, Bruce; Titus, Aaron (July 2019). 10922: 10883: 10881: 10828:Topper, D.; Vincent, D. E. (1 January 1999). 10827: 10758:Mathematical Methods in the Physical Sciences 10485: 10169: 9501: 9255: 8230:very different from that of classical physics 8046:electromagnetic field is proportional to the 5119: 4051: 2767:photographed at 25 frames per second using a 2062:{\displaystyle \mathbf {p} =m\mathbf {v} \,,} 863:Mathematical Principles of Natural Philosophy 791: 15092:"Polar and axial vectors versus quaternions" 14757:Philosophiae Naturalis Principia Mathematica 13474:Sorabji, Richard (2010). "John Philoponus". 12584:; Poole, Charles P.; Safko, John L. (2002). 12459: 11833:. New York: Dover Publications. p. 18. 11707:Notices of the American Mathematical Society 11470: 11327: 11286: 11082: 10830:"An analysis of Newton's projectile diagram" 10406: 8421: 7571:{\displaystyle \left=\left={\frac {d}{dt}}.} 6198:for the body's momentum, the Hamiltonian is 5202:{\displaystyle \mathbf {v} (\mathbf {x} ,t)} 3616:This differential equation has the solution 14158: 14136:. Cambridge University Press. p. 390. 12423: 11471:Masoliver, Jaume; Ros, Ana (1 March 2011). 10796:How I Killed Pluto and Why It Had It Coming 10100:. Vol. 1. Translated by Sykes, J. B.; 10004:(1958). "On the Classical Laws of Motion". 9961: 9959: 9957: 9955: 9785:Classical dynamics: A Contemporary Approach 9778: 9640:The Mechanical Universe: Mechanics and Heat 9136:Classical Dynamics of Particles and Systems 8668:would apply momentum conservation to study 8566: 5278:{\displaystyle \mathbf {a} =\mathbf {F} /m} 1273:to the infinitesimally small time interval 901:The mathematical description of motion, or 889:Newton's laws are often stated in terms of 858:Philosophiæ Naturalis Principia Mathematica 817:that describe the relationship between the 15232: 15218: 14517:"Some Reflections on Newton's "Principia"" 13890:Descartes, R. (2008) . Bennett, J. (ed.). 13665:Physical Review Physics Education Research 13561:Physical Review Physics Education Research 12868: 12866: 11954:Physical Review Physics Education Research 11588: 11586: 11426: 11131: 10878: 10685:Physical Review Physics Education Research 10298: 10053:. Reading, Mass.: Addison-Wesley Pub. Co. 9788:. Cambridge : Cambridge University Press. 9307: 9305: 8971:{\displaystyle \mathbf {F} =m\mathbf {a} } 8859:List of scientific laws named after people 8339:theory of mechanics could encompass both. 7190:on the first term on the right-hand side, 6280:In this example, Hamilton's equations are 3171: 798: 784: 14613:Patterson, Elizabeth C. (December 1969). 14612: 14416: 13962:"Is Newton's second law really Newton's?" 13889: 13721: 13685: 13581: 13442: 13195: 13124: 13066: 13009: 12940: 12930: 12762:. W. W. Norton and Company. p. 224. 12530: 12087: 11984: 11974: 11770: 11737: 11658: 11648: 11490: 11005: 10894:. Cambridge: Cambridge University Press. 10887: 10715: 10705: 10648: 10565: 10534: 10355: 10197: 10080: 10078: 10050:The Feynman Lectures on Physics, Volume 1 9935: 9685: 9591: 9529: 9139:(5th ed.). Brooke Cole. p. 49. 8937:For example, José and Saletan (following 8793:had left open, like a full theory of the 8504:of the Earth. This idea was corrected by 8381: 7994:) around the magnetic field lines at the 7661: 4328: 4228: 3671: 3602: 2191: 2106: 2055: 1497:{\displaystyle \lim _{t\to t_{0}}f(t)=L.} 14975: 14675:(1st ed.). Oxford: Pergamon Press. 14205: 13959: 13298:Fuchs, Christopher A. (6 January 2011). 12902: 12385: 11689: 10888:Hand, Louis N.; Finch, Janet D. (1998). 10596: 10540:"The Transverse Momentum of an Electron" 10486:Wachter, Armin; Hoeber, Henning (2006). 10000: 9952: 9596:. New York: Macmillan. pp. 123–125. 9546: 8854:List of equations in classical mechanics 8697: 8628: 8619:every attempt at such a model has failed 8570: 8524: 8492: 8468: 8351: 7953: 7803:is equal in magnitude to the force that 7589: 6114: 5232:has two terms, a combination known as a 5134: 5057: 4373: 4360:and movement around the center of mass. 4061: 3405: 3181: 2758: 2384: 2273: 1970:Artificial satellites move along curved 1965: 1785:{\displaystyle {\frac {d^{2}s}{dt^{2}}}} 14060: 13854: 13802: 13785: 13768: 13473: 13367: 12872: 12863: 12834: 12329:Kneubil, Fabiana B. (1 November 2016). 12328: 11583: 11083:Lyublinskaya, Irina E. (January 1998). 10747: 10745: 10743: 10458: 10374: 9865: 9816: 9727: 9302: 9126: 8738:to be more rigorous. Consequently, the 8625:Momentum conservation and the third law 7738:, though subtleties and caveats exist. 6138:. The simplest example is a point mass 2831:{\displaystyle F={\frac {GMm}{r^{2}}},} 2310:. A state of mechanical equilibrium is 14: 16058: 14703: 14514: 14388: 14352: 14169: 13908: 13906: 13808:"Science in the Renaissance: A Survey" 13775:. Dover Publications Inc. p. 268. 13717: 13715: 13658:; Heron, Paula R. L. (30 March 2021). 13330: 13300:Coming of Age with Quantum Information 13230:; Diu, Bernard; Laloë, Franck (2005). 13047: 12754: 12618: 12276: 12245:A Modern Course in Statistical Physics 12238: 12186: 11864: 11346:The Princeton Companion to Mathematics 11230:Saggio, Maria Luisa (1 January 2013). 11229: 11180: 10410:; Redish, Edward F. (1 January 2005). 10075: 10031: 10029: 9774: 9772: 9770: 9709:Pappas, Stephanie (5 September 2023). 9708: 9162: 8690: 8660:would later deduce the same rules for 7586:Thermodynamics and statistical physics 2347:. By inserting such an expression for 1737:Consequently, the acceleration is the 27:Laws in physics about force and motion 15484:Newton's law of universal gravitation 15213: 15138: 14978:"History of physical terms: "energy"" 14879: 14841: 14752: 14672:The Origins of Infinitesimal Calculus 14665: 14582:10.1093/oxfordhb/9780199930418.013.35 14571: 14465: 14292: 14095: 13772:Dialogues Concerning Two New Sciences 13654:Robertson, Amy D.; Goodhew, Lisa M.; 13607:Robertson, Amy D.; Goodhew, Lisa M.; 13514: 13297: 13254: 12782: 12670: 12668: 12576: 12574: 12427:Biomedical Applications of Biophysics 12234: 12232: 12140:"Mixed States in Classical Mechanics" 12134: 11906: 11860: 11858: 11466: 11464: 11331:(2008). "The Three-Body Problem". In 11085:"Central collisions—The general case" 10789: 10140: 9768: 9766: 9764: 9762: 9760: 9758: 9756: 9754: 9752: 9750: 9621: 9619: 9617: 9615: 9613: 9611: 9609: 9607: 9605: 9603: 9410: 9408: 9406: 9404: 9402: 8394:body into motion imparted a quality, 8188: 8074: 5124: 4616:Rotational analogues of Newton's laws 4026:{\displaystyle \omega ={\sqrt {g/L}}} 2345:Newton's law of universal gravitation 480:Newton's law of universal gravitation 15642:Newton's theorem of revolving orbits 15239: 15032: 14131: 14008: 13883: 13687:10.1103/PhysRevPhysEducRes.17.010121 13583:10.1103/PhysRevPhysEducRes.15.010123 13522:. University of Pennsylvania Press. 13261:Quantum Theory: Concepts and Methods 12015: 11976:10.1103/PhysRevPhysEducRes.15.020126 11724: 11537: 11054:(6th ed.). Hoboken, NJ: Wiley. 10761:(3rd ed.). Hoboken, NJ: Wiley. 10751: 10740: 10707:10.1103/PhysRevPhysEducRes.16.010111 10510: 10141:Moebs, William; et al. (2023). 9671: 9414: 9229: 9194: 8219: 8205:spacetime curvature is given by the 8055:Maxwell's theory of electromagnetism 5761:{\displaystyle L(q,{\dot {q}})=T-V,} 4269:Physicists developed the concept of 3267:{\displaystyle a={\frac {v^{2}}{r}}} 15590:Leibniz–Newton calculus controversy 15331:standing on the shoulders of giants 14919:Reichenberger, Andrea (June 2018). 14887:Stanford Encyclopedia of Philosophy 14764:Stanford Encyclopedia of Philosophy 14417:Erlichson, Herman (February 1997). 14396:Stanford Encyclopedia of Philosophy 13903: 13712: 13611:; Heron, Paula R. L. (March 2021). 13370:"Aristotle's Hydrostatical Physics" 12684:. Oxford: Oxford University Press. 12479:Classical Electricity and Magnetism 12068:Houchmandzadeh, Bahram (May 2020). 11592: 11293:Poincaré and the Three Body Problem 10465:. New York: Springer. p. 135. 10026: 9095:Newton himself was an enthusiastic 7725: 7581:Relation to other physical theories 4491:, the center of mass is located at 4434:{\displaystyle m_{1},\ldots ,m_{N}} 1239:{\displaystyle v={\frac {ds}{dt}}.} 461:Mechanics of planar particle motion 69: 24: 15172: 14976:Frontali, Clara (September 2014). 14880:Smith, George (19 December 2007). 14753:Smith, George (20 December 2007). 14389:Slowik, Edward (15 October 2021). 13518:(1982). Sargent, Steven D. (ed.). 12665: 12571: 12229: 11855: 11461: 11051:Calculus: Single and Multivariable 9817:Brading, Katherine (August 2019). 9747: 9733:Introduction to Special Relativity 9600: 9399: 9278:Calculus: Single and Multivariable 8997:See, for example, Frautschi et al. 8677:1684 manuscript written to Huygens 8543:According to American philosopher 8236:, one considers what result might 7538: 7517: 7513: 7489: 7478: 7450: 7446: 7400: 7386: 7371: 7360: 7332: 7328: 7274: 7263: 7253: 7242: 7216: 7206: 7202: 7162: 7140: 7129: 7101: 7093: 7086: 7027: 6993: 6985: 6910: 6881: 6873: 6840: 6542: 6392: 6385: 6380: 6325: 6318: 6313: 6207: 5988: 5980: 5952: 5944: 5539: 5525: 5488: 5472: 5464: 5356: 5319: 5303: 5295: 5036:are directed along the same line. 4628:, and the counterpart of force is 4321: 4264: 3907:is the length of the pendulum and 3395: 3234:, its acceleration has a magnitude 3115: 3106: 2290:), the downward force of gravity ( 1900: 1892: 1878: 1870: 1715: 1689: 1660: 1594: 1568: 1539: 1167: 1114: 1010: 1002: 25: 16117: 14466:Smith, George E. (October 2006). 14175:The Cambridge Companion to Newton 13520:On the Threshold of Exact Science 12981:. New York, NY: Bold Type Books. 10490:. New York: Springer. p. 6. 10488:Compendium of theoretical physics 9908:; Etkina, Eugenia (1 June 2009). 9504:""Force," ontology, and language" 8716:Kepler's laws of planetary motion 8343:Antiquity and medieval background 8085:Acceleration (special relativity) 6763:{\displaystyle S(\mathbf {q} ,t)} 4624:, the counterpart of momentum is 4363: 3414:undergoes simple harmonic motion. 2858:is the mass of the falling body, 829:, can be paraphrased as follows: 16043: 16031: 16019: 16007: 15995: 15983: 15919:Isaac Newton Group of Telescopes 15132: 15083: 15026: 14969: 14912: 14873: 14835: 14778: 14746: 14697: 14659: 14606: 14565: 14508: 14459: 14410: 14382: 14346: 14286: 14258:Aldersey-Williams, Hugh (2020). 14251: 14199: 14125: 14089: 14054: 14002: 13960:Pourciau, Bruce (October 2011). 13953: 13848: 13796: 13779: 13762: 13544: 13508: 13467: 13400: 13361: 13324: 13290: 13248: 13157: 13102: 13041: 13003: 12965: 12903:Kersting, Magdalena (May 2019). 11871:Statistical Physics of Particles 11699:"Off to infinity in finite time" 11181:Mungan, Carl E. (1 March 2005). 9594:The Nature of the Physical World 9089: 9077: 9068: 9054: 9045: 8964: 8953: 8918:which Hoek argues was erroneous. 8444:Traité du monde et de la lumière 8318: 8293: 8278: 8112: 8098: 7970: 7962:If the electric field vanishes ( 7935: 7927: 7916: 7905: 7649: 7635: 7530: 7055: 6955: 6902: 6822: 6747: 6642:{\displaystyle \mathbf {q} _{i}} 6629: 6585: 6570: 6178:for the position coordinate and 5601: 5557: 5549: 5504: 5496: 5450:turns the Euler equation into a 5432: 5367: 5335: 5327: 5263: 5255: 5218: 5186: 5178: 5162:Newton's laws can be applied to 5157:Fermi–Pasta–Ulam–Tsingou problem 5022: 5000: 4972: 4946: 4938: 4908: 4883: 4875:The first term vanishes because 4858: 4850: 4842: 4831: 4812: 4798: 4790: 4767: 4738: 4707: 4699: 4691: 4665: 4643: 4542: 4499: 4471: 4450: 4378:The total center of mass of the 4310: 4247: 4204: 4185: 4168: 4146: 4115: 3190:(center of mass of both objects) 2700: 2678: 2635: 2603: 2577: 2549: 2521: 2506: 2497: 2482:{\displaystyle \mathbf {p} _{2}} 2469: 2453:{\displaystyle \mathbf {p} _{1}} 2440: 2355: 2332:, friction, and string tension. 2237: 2213: 2187: 2165: 2148: 2091: 2077: 2051: 2040: 1853: 1830: 1807: 884: 765: 764: 751: 84: 15939:Newton International Fellowship 15620:generalized Gauss–Newton method 15533:Newton's method in optimization 12896: 12828: 12783:Havas, Peter (1 October 1964). 12776: 12748: 12706: 12612: 12504: 12417: 12379: 12322: 12282:"Two Models of Brownian Motion" 12270: 12187:Weiner, J. H. (November 1974). 12180: 12128: 12061: 12021:"Teaching Energy Before Forces" 12009: 11940: 11900: 11813: 11764: 11718: 11683: 11622: 11531: 11420: 11371: 11223: 11174: 11125: 11076: 11030: 10968: 10916: 10821: 10783: 10671: 10642: 10590: 10528: 10504: 10479: 10452: 10400: 10368: 10349: 10292: 10240: 10191: 10177:. HarperPerennial. p. 50. 10163: 10134: 9994: 9897: 9874: 9859: 9810: 9721: 9702: 9665: 9585: 9495: 9446: 9036: 9027: 9018: 9009: 9000: 8991: 8982: 8931: 8921: 8904: 8894: 8553:De Motu Corporum ex Percussione 7711:{\displaystyle \mathbf {\xi } } 6965:{\displaystyle V(\mathbf {q} )} 5044:Multi-body gravitational system 4131:{\displaystyle \mathbf {v} (t)} 2692:is constant. Alternatively, if 1821:, or in bold typeface, such as 14704:Dunlop, Katherine (May 2012). 13722:Blackwell, Richard J. (1966). 12882:. W. W. Norton & Company. 12643:10.1088/1751-8113/47/42/424011 10301:"Newton's third law revisited" 9347: 9223: 9188: 9171: 8881: 8844:History of classical mechanics 8428:Galileo Galilei § Inertia 8348:Aristotle and "violent" motion 7983:{\displaystyle \mathbf {E} =0} 7059: 7051: 6959: 6951: 6757: 6743: 6607: 6565: 6264: 6258: 6224: 6212: 6110: 6054: 6036: 5839: 5833: 5740: 5719: 5500: 5484: 5331: 5315: 5196: 5182: 4985:{\displaystyle \mathbf {r} =0} 4351:Rigid-body motion and rotation 4277:, due to a body's motion, and 4138:, ejects matter at a velocity 4125: 4119: 4094: 4088: 3632: 3626: 3546:, Newton's second law becomes 2718:Candidates for additional laws 1904: 1860: 1710: 1704: 1695: 1680: 1666: 1589: 1583: 1574: 1559: 1545: 1482: 1476: 1458: 1316: 1310: 1063: 1050: 1041: 1028: 925: 919: 39:United States Physics Olympiad 13: 1: 14813:10.1088/0143-0807/38/1/015001 14574:The Oxford Handbook of Newton 12357:10.1088/0143-0807/37/6/065201 11785:The Millennium Prize Problems 10299:Hellingman, C. (March 1992). 10098:Course of Theoretical Physics 9937:10.1103/PhysRevSTPER.5.010108 9782:; Saletan, Eugene J. (1998). 9531:10.1103/PhysRevSTPER.5.010110 9325:. Macmillan. pp. 84–85. 9119: 5651: 4915:{\displaystyle m\mathbf {v} } 4160:relative to the rocket, then 4036:A harmonic oscillator can be 3727:{\displaystyle {\sqrt {k/m}}} 2016: 1944:has a different meaning than 1156:gives the means to define an 387:Koopman–von Neumann mechanics 15560:Newton's theorem about ovals 10175:The Cartoon Guide to Physics 10147:University Physics, Volume 1 9969:An introduction to mechanics 8712:Traité de mécanique céleste. 8446:) written 1629–33. However, 8027:{\displaystyle \omega =qB/m} 5768:where the kinetic energy is 5439:{\displaystyle \mathbf {f} } 5225:{\displaystyle \mathbf {a} } 5096:not exactly conic sections. 5029:{\displaystyle \mathbf {r} } 5014:and the displacement vector 5007:{\displaystyle \mathbf {F} } 4890:{\displaystyle \mathbf {v} } 4672:{\displaystyle \mathbf {p} } 4650:{\displaystyle \mathbf {r} } 4254:{\displaystyle \mathbf {F} } 4153:{\displaystyle \mathbf {u} } 2785:law of universal gravitation 2745:Uniformly accelerated motion 2707:{\displaystyle \mathbf {p} } 2685:{\displaystyle \mathbf {p} } 2556:{\displaystyle \mathbf {p} } 2541:, and the rate of change of 2373: 2362:{\displaystyle \mathbf {F} } 2302:The forces acting on a body 2286:perpendicular to the plane ( 1961: 1814:{\displaystyle \mathbf {s} } 455:Non-inertial reference frame 7: 15929:Sir Isaac Newton Sixth Form 15585:Corpuscular theory of light 15511:Schrödinger–Newton equation 15097:American Journal of Physics 14947:10.1016/j.shpsa.2018.01.006 14901:Traité de mécanique céleste 14792:European Journal of Physics 14424:American Journal of Physics 13967:American Journal of Physics 13724:"Descartes' Laws of Motion" 13414:American Journal of Physics 13175:European Journal of Physics 12723:Flat and Curved Space-times 12518:American Journal of Physics 12436:10.1007/978-1-60327-233-9_6 12336:European Journal of Physics 12287:American Journal of Physics 12194:American Journal of Physics 12145:American Journal of Physics 12075:American Journal of Physics 11548:American Journal of Physics 11478:European Journal of Physics 11434:American Journal of Physics 11385:American Journal of Physics 11237:European Journal of Physics 11188:European Journal of Physics 11139:American Journal of Physics 10985:American Journal of Physics 10933:American Journal of Physics 10835:European Journal of Physics 10205:American Journal of Physics 10007:American Journal of Physics 9845:10.1016/j.shpsb.2017.07.004 9364:American Journal of Physics 8832: 8786:Traité de mécanique céleste 8581:Christiaan Huygens, in his 4390:is on top of the pen's tip. 2735: 2392:work by producing a strong 1741:of position, often written 382:Appell's equation of motion 252:Inertial frame of reference 10: 16122: 15338:Notes on the Jewish Temple 15188:; Vuletic, Vladan (2016). 15004:10.1088/0031-9120/49/5/564 13135:10.1007/s10699-019-09608-5 12387:Tonnelat, Marie-Antoinette 11876:Cambridge University Press 11509:10.1088/0143-0807/32/2/016 11258:10.1088/0143-0807/34/1/129 11201:10.1088/0143-0807/26/2/L01 10856:10.1088/0143-0807/20/1/018 10327:10.1088/0031-9120/27/2/011 9592:Eddington, Arthur (1929). 9481:10.1088/0031-9120/20/4/308 8460:Roman Catholic Inquisition 8425: 8312:Trinity College, Cambridge 8268: 8078: 5702:{\displaystyle {\dot {q}}} 5128: 5120:Chaos and unpredictability 5047: 4657:and the body has momentum 4592:were a point body of mass 4367: 4055: 4052:Objects with variable mass 3399: 3175: 2898:is Newton's constant, and 2878:is the mass of the Earth, 2748: 1376:if the difference between 36: 29: 16106:Eponymous laws of physics 15947: 15884: 15839: 15762: 15704: 15459: 15379: 15314: 15247: 14724:10.1007/s11229-011-9983-8 14633:10.1017/S0007087400010232 14535:10.1017/S000708740800188X 14061:Higgitt, Rebekah (2015). 14014:"Was Newton a Newtonian?" 13855:LoLordo, Antonia (2007). 13085:10.1103/RevModPhys.65.803 13054:Reviews of Modern Physics 12973:Prescod-Weinstein, Chanda 12811:10.1103/RevModPhys.36.938 12790:Reviews of Modern Physics 10149:. OpenStax. p. 220. 9885:. John Wiley & Sons. 8422:Inertia and the first law 8408:Abu'l-Barakāt al-Baghdādī 8300:Newton's own copy of his 7864:acting upon charges. The 5620:Millennium Prize Problems 5073:Laplace–Runge–Lenz vector 3354:{\displaystyle GMm/r^{2}} 1948:. The physics concept of 1838:{\displaystyle {\bf {s}}} 15489:post-Newtonian expansion 15369:Corruptions of Scripture 15361:Ancient Kingdoms Amended 13893:Principles of philosophy 13368:Ugaglia, Monica (2015). 13197:10.1088/1361-6404/aa57d1 12932:10.1088/1361-6552/ab08f5 12470:Panofsky, Wolfgang K. H. 12395:. Dordrecht: D. Reidel. 10620:10.4169/002557010X479965 10459:Greiner, Walter (2003). 10143:"5.5 Newton's Third Law" 9866:Feather, Norman (1959). 9735:. Wiley. pp. 8–16. 9201:. Institute of Physics. 8887:See, for example, Zain. 8874: 8704:Mechanism of the Heavens 8646:Principles of Philosophy 8584:Horologium Oscillatorium 8567:Force and the second law 8515:Principles of Philosophy 8207:Einstein field equations 6549:Hamilton–Jacobi equation 6014:of the Lagrangian gives 5609:relativistic speed limit 3418:Consider a body of mass 3309:{\displaystyle mv^{2}/r} 2421:conservation of momentum 545:Rotating reference frame 377:Hamilton–Jacobi equation 15679:Absolute space and time 15543:truncated Newton method 15516:Newton's laws of motion 15479:Newton's law of cooling 14032:10.1126/science.1088786 13296:D. Bilodeau, quoted in 13228:Cohen-Tannoudji, Claude 12874:Wheeler, John Archibald 11038:Hughes-Hallett, Deborah 10521:Encyclopædia Britannica 10387:MIT Physics Annual 2003 10173:; Huffman, Art (1991). 9629:; Olenick, Richard P.; 9266:Hughes-Hallett, Deborah 9242:University of Cambridge 8728:the science of fluxions 8595:of transparent matter, 8432:The French philosopher 8163:{\displaystyle \gamma } 7685:{\displaystyle \gamma } 7607:kinetic theory of gases 5913:Euler–Lagrange equation 5168:Euler momentum equation 4298:of a function called a 3984:{\displaystyle \theta } 3964:{\displaystyle \theta } 3940:{\displaystyle \theta } 3920:{\displaystyle \theta } 3695:{\displaystyle \omega } 3514:. Writing the force as 3438:able to move along the 3172:Uniform circular motion 2730:superposition principle 2011:absolute space and time 1956: 1349:at a given input value 1173:{\displaystyle \Delta } 1120:{\displaystyle \Delta } 1107:Here, the Greek letter 811:Newton's laws of motion 486:Newton's laws of motion 346:Newton's laws of motion 18:Newton's First Law 16086:Scientific observation 15914:Isaac Newton Telescope 15904:Isaac Newton Institute 15674:Newton–Puiseux theorem 15669:Parallelogram of force 15657:kissing number problem 15647:Newton–Euler equations 15550:Gauss–Newton algorithm 15499:gravitational constant 14515:Davies, E. B. (2009). 14132:West, Richard (1980). 14097:Dobbs, Betty Jo Teeter 13339:. Dover. p. 178. 13112:Foundations of Science 12676:Choquet-Bruhat, Yvonne 12047:10.1103/Physics.12.100 11048:; et al. (2013). 9276:; et al. (2013). 8972: 8849:List of eponymous laws 8839:Euler's laws of motion 8827:William Rowan Hamilton 8765: 8719: 8664:that Huygens had, and 8636: 8578: 8561: 8541: 8536: 8530: 8520:Principia Philosophiae 8500: 8491: 8476: 8382:Philoponus and impetus 8363: 8202:John Archibald Wheeler 8164: 8140: 8120: 8081:Relativistic mechanics 8028: 7984: 7959: 7946: 7883: 7851: 7824: 7797: 7770: 7712: 7686: 7666: 7598: 7572: 7414: 7308: 7288: 7176: 7069: 6966: 6935: 6854: 6808: 6784: 6764: 6727: 6707: 6687: 6663: 6643: 6614: 6527: 6461: 6408: 6338: 6274: 6192: 6172: 6152: 6127: 6122:, whose 1915 proof of 6090: 6004: 5909:Calculus of variations 5900: 5873: 5846: 5817: 5762: 5703: 5674: 5611:in Newtonian physics. 5588: 5568: 5452:Navier–Stokes equation 5440: 5418: 5398: 5378: 5279: 5226: 5203: 5140: 5063: 5030: 5008: 4986: 4957: 4916: 4891: 4869: 4718: 4673: 4651: 4606: 4585: 4565: 4526: 4485: 4435: 4391: 4345:conservation of energy 4336: 4255: 4233: 4154: 4132: 4101: 4074: 4027: 3985: 3965: 3941: 3921: 3901: 3881: 3794: 3768: 3748: 3728: 3696: 3676: 3610: 3540: 3512:simple harmonic motion 3504: 3478: 3452: 3432: 3415: 3375: 3355: 3310: 3268: 3228: 3208: 3191: 3162: 3132: 3055: 3035: 3015: 2995: 2975: 2955: 2935: 2912: 2892: 2872: 2852: 2832: 2776: 2708: 2686: 2663: 2557: 2535: 2483: 2454: 2405: 2363: 2308:mechanical equilibrium 2299: 2266: 2199: 2134: 2114: 2063: 1979: 1911: 1839: 1815: 1786: 1731: 1610: 1498: 1437: 1410: 1390: 1370: 1343: 1323: 1290: 1267: 1240: 1194: 1174: 1145: 1121: 1101: 986: 959: 932: 877:), or are very small ( 844:is changing with time. 513:Simple harmonic motion 426:Euler's laws of motion 220:D'Alembert's principle 103: 16096:Copernican Revolution 15868:Isaac Newton Gargoyle 15778: (nephew-in-law) 15754:Copernican Revolution 15749:Scientific Revolution 15610:Newton–Cotes formulas 15474:Newton's inequalities 15451:Structural coloration 15190:"Classical Mechanics" 13786:Galilei, G. (1974) . 13331:Caspar, Max (2012) . 12835:Stavrov, Iva (2020). 12019:(13 September 2019). 11772:Fefferman, Charles L. 10358:"Third Law of Motion" 9674:Philosophy of Science 9355:McDermott, Lillian C. 9313:Thompson, Silvanus P. 8973: 8766: 8701: 8632: 8611:I feign no hypotheses 8574: 8557: 8537: 8532: 8528: 8496: 8486: 8484:(1638) Galileo wrote: 8472: 8400:Nur ad-Din al-Bitruji 8355: 8328:Principia Mathematica 8165: 8141: 8121: 8079:Further information: 8029: 7985: 7957: 7947: 7884: 7852: 7850:{\displaystyle q_{1}} 7825: 7823:{\displaystyle q_{2}} 7798: 7796:{\displaystyle q_{2}} 7776:exerts upon a charge 7771: 7769:{\displaystyle q_{1}} 7713: 7687: 7667: 7593: 7573: 7415: 7309: 7289: 7177: 7070: 6967: 6936: 6855: 6809: 6785: 6765: 6728: 6708: 6688: 6671:differential equation 6664: 6644: 6615: 6528: 6462: 6409: 6339: 6275: 6193: 6173: 6153: 6132:Hamiltonian mechanics 6118: 6091: 6005: 5901: 5899:{\displaystyle q_{f}} 5874: 5872:{\displaystyle q_{i}} 5847: 5818: 5763: 5704: 5675: 5638:Hamiltonian mechanics 5589: 5569: 5441: 5424:is the pressure, and 5419: 5399: 5397:{\displaystyle \rho } 5379: 5280: 5227: 5204: 5138: 5083:(including circles), 5061: 5031: 5009: 4987: 4958: 4917: 4892: 4870: 4719: 4674: 4652: 4607: 4586: 4566: 4506: 4486: 4436: 4377: 4337: 4256: 4234: 4155: 4133: 4107:, moving at velocity 4102: 4065: 4028: 3986: 3966: 3942: 3922: 3902: 3882: 3795: 3769: 3749: 3729: 3697: 3677: 3611: 3541: 3539:{\displaystyle F=-kx} 3505: 3479: 3453: 3433: 3409: 3376: 3356: 3311: 3269: 3229: 3209: 3185: 3163: 3133: 3056: 3036: 3016: 2996: 2976: 2956: 2936: 2913: 2893: 2873: 2853: 2833: 2762: 2709: 2687: 2664: 2558: 2536: 2484: 2455: 2388: 2364: 2277: 2267: 2200: 2135: 2115: 2064: 1969: 1912: 1840: 1816: 1787: 1732: 1611: 1499: 1438: 1436:{\displaystyle t_{0}} 1411: 1391: 1371: 1369:{\displaystyle t_{0}} 1344: 1324: 1291: 1268: 1241: 1195: 1175: 1146: 1122: 1102: 987: 985:{\displaystyle t_{1}} 960: 958:{\displaystyle t_{0}} 933: 873:), are very massive ( 821:of an object and the 367:Hamiltonian mechanics 185:Statistical mechanics 104: 16091:Experimental physics 16081:Equations of physics 15875:Astronomers Monument 15565:Newton–Pepys problem 15538:Apollonius's problem 15506:Newton–Cartan theory 15419:Newton–Okounkov body 15352:hypotheses non fingo 15341: (c. 1680) 15036:(10 December 2018). 14391:"Descartes' Physics" 13899:. Part II, § 37, 39. 13011:Goodstein, Judith R. 11598:Fly by Night Physics 11042:McCallum, William G. 10891:Analytical Mechanics 10607:Mathematics Magazine 10380:"The Origin of Mass" 9627:Frautschi, Steven C. 9270:McCallum, William G. 9195:Zain, Samya (2019). 8949: 8815:Josiah Willard Gibbs 8781:Pierre-Simon Laplace 8764:{\displaystyle F=ma} 8746: 8670:inelastic collisions 8545:Richard J. Blackwell 8154: 8130: 8094: 8040:mass-to-charge ratio 8001: 7966: 7901: 7873: 7834: 7807: 7780: 7753: 7746:electrically charged 7700: 7676: 7628: 7436: 7318: 7298: 7194: 7079: 6976: 6945: 6864: 6818: 6798: 6774: 6737: 6717: 6697: 6677: 6653: 6624: 6559: 6471: 6418: 6348: 6284: 6202: 6182: 6162: 6142: 6136:Hamilton's equations 6018: 5919: 5883: 5856: 5845:{\displaystyle V(q)} 5827: 5772: 5713: 5684: 5664: 5657:Lagrangian mechanics 5633:Lagrangian mechanics 5587:{\displaystyle \nu } 5578: 5458: 5428: 5408: 5388: 5289: 5251: 5214: 5174: 5018: 4996: 4968: 4926: 4901: 4879: 4728: 4687: 4661: 4639: 4596: 4575: 4495: 4445: 4399: 4306: 4243: 4164: 4142: 4111: 4100:{\displaystyle M(t)} 4082: 4058:Variable-mass system 3999: 3975: 3955: 3931: 3911: 3891: 3812: 3778: 3758: 3738: 3734:, and the constants 3706: 3686: 3682:where the frequency 3620: 3550: 3518: 3488: 3462: 3442: 3422: 3365: 3324: 3282: 3238: 3218: 3214:at a constant speed 3198: 3152: 3065: 3045: 3025: 3005: 2985: 2965: 2945: 2922: 2902: 2882: 2862: 2842: 2791: 2696: 2674: 2567: 2545: 2493: 2464: 2435: 2351: 2209: 2144: 2124: 2073: 2036: 1849: 1825: 1803: 1745: 1623: 1508: 1447: 1420: 1400: 1380: 1353: 1333: 1322:{\displaystyle f(t)} 1304: 1277: 1254: 1204: 1184: 1164: 1135: 1111: 996: 969: 942: 931:{\displaystyle s(t)} 913: 590:Angular acceleration 582:Rotational frequency 362:Lagrangian mechanics 355:Analytical mechanics 111:Second law of motion 64: 16066:Classical mechanics 15684:Luminiferous aether 15632:Newton's identities 15605:Newton's cannonball 15580:Classical mechanics 15570:Newtonian potential 15431:Newtonian telescope 15110:2002AmJPh..70..958S 15042:Skulls in the Stars 14996:2014PhyEd..49..564F 14939:2018SHPSA..69....1R 14805:2017EJPh...38a5001M 14486:2006PhT....59j..31S 14437:1997AmJPh..65..149E 14264:. London: Picador. 13980:2011AmJPh..79.1015P 13678:2021PRPER..17a0121R 13618:The Physics Teacher 13574:2019PRPER..15a0123E 13427:2011AmJPh..79...32S 13188:2017EJPh...38b5705M 13166:Singh, Chandralekha 13077:1993RvMP...65..803M 12923:2019PhyEd..54c5008K 12803:1964RvMP...36..938H 12714:Ellis, George F. R. 12635:2014JPhA...47P4011W 12587:Classical Mechanics 12541:2018AmJPh..86..839B 12349:2016EJPh...37f5201K 12300:1961AmJPh..29..510M 12207:1974AmJPh..42.1026W 12158:1965AmJPh..33..146R 12098:2020AmJPh..88..353H 12039:2019PhyOJ..12..100B 11967:2019PRPER..15b0126L 11561:2004AmJPh..72..446L 11501:2011EJPh...32..431M 11398:2008AmJPh..76..347B 11302:1997ptbp.book.....B 11250:2013EJPh...34..129S 11152:2011AmJPh..79.1068C 11103:1998PhTea..36...18L 11090:The Physics Teacher 10998:2019AmJPh..87..504C 10946:1991AmJPh..59..118B 10848:1999EJPh...20...59T 10698:2020PRPER..16a0111C 10600:(1 February 2010). 10558:1905Natur..72Q.429H 10512:Tait, Peter Guthrie 10430:2005PhTea..43...41S 10417:The Physics Teacher 10319:1992PhyEd..27..112H 10270:2012PhTea..50..406S 10257:The Physics Teacher 10218:2017AmJPh..85...54L 10090:Lifshitz, Evgeny M. 10041:Leighton, Robert B. 10037:Feynman, Richard P. 9928:2009PRPER...5a0108R 9904:Rosengrant, David; 9837:2019SHPMP..67..160B 9715:Scientific American 9696:10.1017/psa.2021.38 9635:Goodstein, David L. 9522:2009PRPER...5a0110B 9473:1985PhyEd..20..171D 9377:1987AmJPh..55..503M 9163:Newton, I. (1999). 9101:John Maynard Keynes 8681:Galilean invariance 8575:Christiaan Huygens 8258:Hermitian operators 7996:cyclotron frequency 7603:statistical physics 6100:Landau and Lifshitz 6012:partial derivatives 5646:perturbation theory 5642:statistical physics 5596:kinematic viscosity 5153:dynamical billiards 4287:work-energy theorem 3971:is nearly equal to 3793:{\displaystyle t=0} 3503:{\displaystyle x=0} 3477:{\displaystyle x=0} 3402:Harmonic oscillator 3385:Newton's cannonball 1940:, for example, and 1932:is not the same as 867:classical mechanics 827:Newtonian mechanics 442:Harmonic oscillator 420:Equations of motion 55:Classical mechanics 49:Part of a series on 16014:History of science 15909:Isaac Newton Medal 15714: (birthplace) 15528:Newtonian dynamics 15426:Newton's reflector 15195:MIT OpenCourseWare 15057:. 29 December 2018 14667:Baron, Margaret E. 14171:Newman, William R. 14012:(15 August 2003). 13631:10.1119/10.0003660 13550:See, for example: 12760:Special Relativity 12582:Goldstein, Herbert 12106:10.1119/10.0000781 11825:Ehrenfest, Tatiana 11660:10.1090/proc/15349 11539:Laws, Priscilla W. 11337:Barrow-Green, June 11329:Barrow-Green, June 11288:Barrow-Green, June 11046:Gleason, Andrew M. 9906:Van Heuvelen, Alan 9322:Calculus Made Easy 9274:Gleason, Andrew M. 8968: 8803:Émilie du Châtelet 8761: 8720: 8662:elastic collisions 8637: 8579: 8549:Christiaan Huygens 8547:, Dutch scientist 8531: 8501: 8477: 8364: 8194:General relativity 8189:General relativity 8160: 8136: 8116: 8075:Special relativity 8024: 7980: 7960: 7942: 7879: 7847: 7820: 7793: 7766: 7708: 7682: 7662: 7599: 7568: 7410: 7304: 7284: 7172: 7065: 6962: 6931: 6850: 6804: 6780: 6760: 6723: 6703: 6683: 6659: 6639: 6610: 6523: 6457: 6404: 6334: 6270: 6188: 6168: 6148: 6128: 6086: 6000: 5915:for the particle, 5896: 5879:and a final point 5869: 5842: 5813: 5758: 5699: 5680:and velocity with 5670: 5640:is convenient for 5584: 5564: 5436: 5414: 5394: 5374: 5275: 5222: 5199: 5141: 5125:Nonlinear dynamics 5064: 5054:Three-body problem 5026: 5004: 4992:) or if the force 4982: 4953: 4912: 4887: 4865: 4714: 4669: 4647: 4602: 4581: 4561: 4481: 4431: 4392: 4332: 4251: 4229: 4150: 4128: 4097: 4075: 4066:Rockets, like the 4023: 3981: 3961: 3937: 3917: 3897: 3877: 3790: 3764: 3744: 3724: 3692: 3672: 3606: 3536: 3500: 3474: 3448: 3428: 3416: 3412:spring–mass system 3389:thought experiment 3371: 3351: 3306: 3264: 3224: 3204: 3192: 3158: 3128: 3051: 3031: 3011: 2991: 2971: 2951: 2941:, the body's mass 2934:{\displaystyle ma} 2931: 2908: 2888: 2868: 2848: 2828: 2777: 2769:stroboscopic flash 2704: 2682: 2659: 2553: 2531: 2479: 2450: 2406: 2359: 2300: 2262: 2195: 2130: 2110: 2059: 1980: 1907: 1835: 1811: 1782: 1727: 1673: 1606: 1552: 1494: 1472: 1433: 1406: 1386: 1366: 1339: 1319: 1289:{\displaystyle dt} 1286: 1266:{\displaystyle ds} 1263: 1236: 1190: 1170: 1141: 1117: 1097: 982: 955: 928: 875:general relativity 871:special relativity 758:Physics portal 372:Routhian mechanics 247:Frame of reference 99: 15971: 15970: 15863: (sculpture) 15830:Abraham de Moivre 15784: (professor) 15712:Woolsthorpe Manor 15664:Newton's quotient 15637:Newton polynomial 15595:Newton's notation 15326: (1661–1665) 15153:978-9-048-14758-8 15118:10.1119/1.1475326 14983:Physics Education 14858:978-0-486-44240-2 14682:978-1-483-28092-9 14615:"Mary Somerville" 14591:978-0-199-93041-8 14494:10.1063/1.2387086 14367:978-0-486-40689-3 14294:Cohen, I. Bernard 14271:978-1-5098-9333-1 14184:978-1-107-01546-3 14074:978-1-317-31495-0 13988:10.1119/1.3607433 13974:(10): 1015–1022. 13868:978-0-511-34982-9 13804:Hellman, C. Doris 13656:Scherr, Rachel E. 13609:Scherr, Rachel E. 13529:978-0-812-27831-6 13485:978-1-905-67018-5 13457:Aristotle in his 13435:10.1119/1.3492721 13346:978-0-486-15175-5 13337:Hellman, C. Doris 13309:978-0-521-19926-1 13232:Quantum Mechanics 13164:Marshman, Emily; 13026:978-1-4704-2846-4 12988:978-1-5417-2470-9 12910:Physics Education 12889:978-0-393-07948-7 12848:978-1-4704-6313-7 12718:Williams, Ruth M. 12691:978-0-19-155226-7 12549:10.1119/1.5054590 12445:978-1-60327-233-9 12308:10.1119/1.1937823 12255:978-3-527-69048-0 12215:10.1119/1.1987920 12201:(11): 1026–1028. 12166:10.1119/1.1971282 12138:(February 1965). 11925:978-0-521-82197-1 11885:978-0-521-87342-0 11798:978-0-821-83679-8 11749:978-1-108-49062-7 11607:978-0-691-18254-4 11569:10.1119/1.1649964 11447:10.1119/1.1987423 11406:10.1119/1.2834738 11356:978-0-691-11880-2 11311:978-0-8218-0367-7 11160:10.1119/1.3579141 11146:(10): 1068–1078. 11061:978-0-470-88861-2 11007:10.1119/1.5109519 10806:978-0-385-53108-5 10768:978-0-471-19826-0 10598:Nicodemi, Olympia 10536:Heaviside, Oliver 10497:978-0-387-25799-0 10472:978-0-387-21851-9 10438:10.1119/1.1845990 10408:Scherr, Rachel E. 10306:Physics Education 10278:10.1119/1.4752043 10226:10.1119/1.4972041 10156:978-1-947172-20-3 10115:978-0-080-06466-6 10045:Sands, Matthew L. 10020:10.1119/1.1934608 10002:Eisenbud, Leonard 9979:978-0-521-19811-0 9795:978-1-139-64890-5 9650:978-0-521-71590-4 9570:978-1-947172-01-2 9460:Physics Education 9431:978-0-511-91510-9 9332:978-0-312-18548-0 9287:978-0-470-88861-2 9208:978-0-750-32076-4 8592:act at a distance 8508:, Descartes, and 8253:Ehrenfest theorem 8246:expectation value 8225:Quantum mechanics 8220:Quantum mechanics 8139:{\displaystyle m} 8036:Mass spectrometry 7882:{\displaystyle q} 7866:Lorentz force law 7622:Langevin equation 7563: 7524: 7470: 7457: 7352: 7339: 7307:{\displaystyle S} 7234: 7213: 7126: 7108: 7018: 7000: 6888: 6837: 6807:{\displaystyle S} 6783:{\displaystyle S} 6726:{\displaystyle S} 6706:{\displaystyle S} 6686:{\displaystyle S} 6662:{\displaystyle t} 6518: 6492: 6452: 6439: 6399: 6369: 6332: 6305: 6250: 6191:{\displaystyle p} 6171:{\displaystyle q} 6151:{\displaystyle m} 6105:Noether's theorem 6081: 6051: 6034: 5995: 5968: 5964: 5935: 5804: 5789: 5737: 5696: 5673:{\displaystyle q} 5522: 5479: 5417:{\displaystyle P} 5353: 5310: 5105:Numerical methods 4825: 4780: 4751: 4622:moment of inertia 4605:{\displaystyle M} 4584:{\displaystyle M} 4556: 4226: 4198: 4021: 3900:{\displaystyle L} 3863: 3847: 3767:{\displaystyle B} 3747:{\displaystyle A} 3722: 3588: 3451:{\displaystyle x} 3431:{\displaystyle m} 3374:{\displaystyle M} 3276:centripetal force 3262: 3227:{\displaystyle v} 3207:{\displaystyle r} 3161:{\displaystyle g} 3142:projectile motion 3105: 3094: 3054:{\displaystyle g} 3034:{\displaystyle r} 3014:{\displaystyle r} 2994:{\displaystyle M} 2974:{\displaystyle G} 2954:{\displaystyle m} 2911:{\displaystyle r} 2891:{\displaystyle G} 2871:{\displaystyle M} 2851:{\displaystyle m} 2823: 2755:Projectile motion 2654: 2622: 2590: 2429:quantum mechanics 2322:free body diagram 2280:free body diagram 2257: 2178: 2133:{\displaystyle m} 2104: 2001:inertial observer 1919:coordinate system 1891: 1869: 1780: 1739:second derivative 1722: 1655: 1650: 1601: 1534: 1529: 1450: 1409:{\displaystyle L} 1389:{\displaystyle f} 1342:{\displaystyle L} 1231: 1193:{\displaystyle d} 1144:{\displaystyle s} 1092: 1017: 879:quantum mechanics 808: 807: 555:Centrifugal force 550:Centripetal force 506:Euler's equations 491:Relative velocity 267:Moment of inertia 97: 71: 16:(Redirected from 16113: 16048: 16047: 16046: 16036: 16035: 16024: 16023: 16022: 16012: 16011: 16010: 16000: 15999: 15988: 15987: 15979: 15959: 15854: (monotype) 15818:William Stukeley 15814: (disciple) 15794:Benjamin Pulleyn 15770:Catherine Barton 15689:Newtonian series 15600:Rotating spheres 15346:General Scholium 15241:Sir Isaac Newton 15234: 15227: 15220: 15211: 15210: 15206: 15204: 15202: 15166: 15165: 15136: 15130: 15129: 15087: 15081: 15080: 15078: 15076: 15071:. 25 August 2019 15066: 15064: 15062: 15052: 15050: 15048: 15030: 15024: 15023: 14973: 14967: 14966: 14916: 14910: 14909: 14896: 14894: 14877: 14871: 14870: 14839: 14833: 14832: 14782: 14776: 14775: 14773: 14771: 14750: 14744: 14743: 14701: 14695: 14694: 14663: 14657: 14656: 14610: 14604: 14603: 14569: 14563: 14562: 14512: 14506: 14505: 14463: 14457: 14456: 14414: 14408: 14407: 14405: 14403: 14386: 14380: 14379: 14350: 14344: 14343: 14290: 14284: 14283: 14255: 14249: 14248: 14203: 14197: 14196: 14167: 14156: 14155: 14129: 14123: 14122: 14093: 14087: 14086: 14058: 14052: 14051: 14006: 14000: 13999: 13957: 13951: 13950: 13910: 13901: 13900: 13898: 13887: 13881: 13880: 13852: 13846: 13845: 13813:Renaissance News 13800: 13794: 13793: 13783: 13777: 13776: 13766: 13760: 13759: 13719: 13710: 13707: 13689: 13650: 13603: 13585: 13548: 13542: 13541: 13516:Maier, Anneliese 13512: 13506: 13505: 13471: 13465: 13464: 13446: 13404: 13398: 13397: 13365: 13359: 13358: 13335:. 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David 12274: 12268: 12267: 12240:Reichl, Linda E. 12236: 12227: 12226: 12184: 12178: 12177: 12132: 12126: 12125: 12091: 12065: 12059: 12058: 12013: 12007: 12006: 11988: 11978: 11944: 11938: 11937: 11917: 11904: 11898: 11897: 11862: 11853: 11852: 11817: 11811: 11810: 11790: 11768: 11762: 11761: 11741: 11722: 11716: 11715: 11703: 11691:Saari, Donald G. 11687: 11681: 11680: 11662: 11652: 11643:(7): 3045–3061. 11626: 11620: 11619: 11590: 11581: 11580: 11535: 11529: 11528: 11494: 11468: 11459: 11458: 11424: 11418: 11417: 11375: 11369: 11368: 11325: 11316: 11315: 11284: 11278: 11277: 11227: 11221: 11220: 11178: 11172: 11171: 11129: 11123: 11122: 11111:10.1119/1.879949 11080: 11074: 11073: 11034: 11028: 11027: 11009: 10972: 10966: 10965: 10929: 10920: 10914: 10913: 10885: 10876: 10875: 10825: 10819: 10818: 10787: 10781: 10780: 10749: 10738: 10737: 10719: 10709: 10675: 10669: 10668: 10666: 10664: 10646: 10640: 10639: 10594: 10588: 10587: 10569: 10567:10.1038/072429a0 10532: 10526: 10525: 10508: 10502: 10501: 10483: 10477: 10476: 10456: 10450: 10449: 10404: 10398: 10397: 10395: 10393: 10384: 10372: 10366: 10365: 10362:www.grc.nasa.gov 10353: 10347: 10346: 10296: 10290: 10289: 10248:Stocklmayer, Sue 10244: 10238: 10237: 10195: 10189: 10188: 10167: 10161: 10160: 10138: 10132: 10131: 10104:(2nd ed.). 10082: 10073: 10072: 10033: 10024: 10023: 9998: 9992: 9991: 9963: 9950: 9949: 9939: 9901: 9895: 9894: 9878: 9872: 9871: 9863: 9857: 9856: 9814: 9808: 9807: 9776: 9745: 9744: 9725: 9719: 9718: 9706: 9700: 9699: 9689: 9669: 9663: 9662: 9623: 9598: 9597: 9589: 9583: 9582: 9550: 9544: 9543: 9533: 9499: 9493: 9492: 9450: 9444: 9443: 9412: 9397: 9396: 9351: 9345: 9344: 9309: 9300: 9299: 9262: 9253: 9252: 9250: 9248: 9239: 9233:(January 2015). 9227: 9221: 9220: 9192: 9186: 9185: 9175: 9169: 9168: 9160: 9151: 9150: 9130: 9113: 9093: 9087: 9081: 9075: 9072: 9066: 9058: 9052: 9049: 9043: 9040: 9034: 9031: 9025: 9022: 9016: 9013: 9007: 9004: 8998: 8995: 8989: 8986: 8980: 8977: 8975: 8974: 8969: 8967: 8956: 8935: 8929: 8925: 8919: 8908: 8902: 8898: 8892: 8885: 8819:Oliver Heaviside 8770: 8768: 8767: 8762: 8658:Christopher Wren 8633:Johannes Kepler 8482:Two New Sciences 8473:Galileo Galilei 8416:Albert of Saxony 8322: 8297: 8282: 8209:, which require 8169: 8167: 8166: 8161: 8145: 8143: 8142: 8137: 8125: 8123: 8122: 8117: 8115: 8101: 8033: 8031: 8030: 8025: 8020: 7989: 7987: 7986: 7981: 7973: 7951: 7949: 7948: 7943: 7938: 7930: 7919: 7908: 7888: 7886: 7885: 7880: 7856: 7854: 7853: 7848: 7846: 7845: 7829: 7827: 7826: 7821: 7819: 7818: 7802: 7800: 7799: 7794: 7792: 7791: 7775: 7773: 7772: 7767: 7765: 7764: 7726:Electromagnetism 7717: 7715: 7714: 7709: 7707: 7694:drag coefficient 7691: 7689: 7688: 7683: 7671: 7669: 7668: 7663: 7660: 7652: 7638: 7577: 7575: 7574: 7569: 7564: 7562: 7551: 7546: 7542: 7541: 7533: 7525: 7523: 7512: 7502: 7498: 7497: 7493: 7492: 7481: 7471: 7463: 7458: 7456: 7445: 7419: 7417: 7416: 7411: 7403: 7389: 7384: 7380: 7379: 7375: 7374: 7363: 7353: 7345: 7340: 7338: 7327: 7313: 7311: 7310: 7305: 7293: 7291: 7290: 7285: 7277: 7266: 7261: 7257: 7256: 7245: 7235: 7227: 7219: 7214: 7212: 7201: 7181: 7179: 7178: 7173: 7165: 7157: 7156: 7151: 7147: 7143: 7132: 7127: 7125: 7114: 7109: 7107: 7099: 7091: 7089: 7074: 7072: 7071: 7066: 7058: 7044: 7043: 7038: 7034: 7030: 7019: 7017: 7006: 7001: 6999: 6991: 6983: 6971: 6969: 6968: 6963: 6958: 6940: 6938: 6937: 6932: 6927: 6923: 6913: 6905: 6889: 6887: 6879: 6871: 6859: 6857: 6856: 6851: 6843: 6838: 6830: 6825: 6813: 6811: 6810: 6805: 6789: 6787: 6786: 6781: 6769: 6767: 6766: 6761: 6750: 6732: 6730: 6729: 6724: 6712: 6710: 6709: 6704: 6692: 6690: 6689: 6684: 6668: 6666: 6665: 6660: 6648: 6646: 6645: 6640: 6638: 6637: 6632: 6619: 6617: 6616: 6611: 6594: 6593: 6588: 6579: 6578: 6573: 6532: 6530: 6529: 6524: 6519: 6517: 6509: 6501: 6493: 6491: 6483: 6475: 6466: 6464: 6463: 6458: 6453: 6445: 6440: 6438: 6430: 6422: 6413: 6411: 6410: 6405: 6400: 6398: 6390: 6389: 6388: 6378: 6370: 6368: 6360: 6352: 6343: 6341: 6340: 6335: 6333: 6331: 6323: 6322: 6321: 6311: 6306: 6304: 6296: 6288: 6279: 6277: 6276: 6271: 6251: 6249: 6241: 6240: 6231: 6211: 6210: 6197: 6195: 6194: 6189: 6177: 6175: 6174: 6169: 6157: 6155: 6154: 6149: 6095: 6093: 6092: 6087: 6082: 6080: 6072: 6064: 6053: 6052: 6044: 6035: 6033: 6022: 6009: 6007: 6006: 6001: 5996: 5994: 5986: 5978: 5973: 5969: 5967: 5966: 5965: 5957: 5950: 5942: 5936: 5934: 5923: 5905: 5903: 5902: 5897: 5895: 5894: 5878: 5876: 5875: 5870: 5868: 5867: 5851: 5849: 5848: 5843: 5822: 5820: 5819: 5814: 5812: 5811: 5806: 5805: 5797: 5790: 5782: 5767: 5765: 5764: 5759: 5739: 5738: 5730: 5708: 5706: 5705: 5700: 5698: 5697: 5689: 5679: 5677: 5676: 5671: 5593: 5591: 5590: 5585: 5573: 5571: 5570: 5565: 5560: 5552: 5547: 5546: 5528: 5523: 5515: 5507: 5499: 5491: 5480: 5478: 5470: 5462: 5445: 5443: 5442: 5437: 5435: 5423: 5421: 5420: 5415: 5404:is the density, 5403: 5401: 5400: 5395: 5383: 5381: 5380: 5375: 5370: 5359: 5354: 5346: 5338: 5330: 5322: 5311: 5309: 5301: 5293: 5284: 5282: 5281: 5276: 5271: 5266: 5258: 5231: 5229: 5228: 5223: 5221: 5208: 5206: 5205: 5200: 5189: 5181: 5050:Two-body problem 5035: 5033: 5032: 5027: 5025: 5013: 5011: 5010: 5005: 5003: 4991: 4989: 4988: 4983: 4975: 4962: 4960: 4959: 4954: 4949: 4941: 4933: 4921: 4919: 4918: 4913: 4911: 4896: 4894: 4893: 4888: 4886: 4874: 4872: 4871: 4866: 4861: 4853: 4845: 4834: 4826: 4824: 4816: 4815: 4806: 4801: 4793: 4785: 4781: 4779: 4771: 4770: 4761: 4752: 4750: 4742: 4741: 4732: 4723: 4721: 4720: 4715: 4710: 4702: 4694: 4678: 4676: 4675: 4670: 4668: 4656: 4654: 4653: 4648: 4646: 4626:angular momentum 4611: 4609: 4608: 4603: 4590: 4588: 4587: 4582: 4570: 4568: 4567: 4562: 4557: 4552: 4551: 4550: 4545: 4539: 4538: 4528: 4525: 4520: 4502: 4490: 4488: 4487: 4482: 4480: 4479: 4474: 4459: 4458: 4453: 4440: 4438: 4437: 4432: 4430: 4429: 4411: 4410: 4341: 4339: 4338: 4333: 4324: 4313: 4300:scalar potential 4260: 4258: 4257: 4252: 4250: 4238: 4236: 4235: 4230: 4227: 4225: 4217: 4209: 4207: 4199: 4197: 4189: 4188: 4179: 4171: 4159: 4157: 4156: 4151: 4149: 4137: 4135: 4134: 4129: 4118: 4106: 4104: 4103: 4098: 4032: 4030: 4029: 4024: 4022: 4017: 4009: 3990: 3988: 3987: 3982: 3970: 3968: 3967: 3962: 3946: 3944: 3943: 3938: 3926: 3924: 3923: 3918: 3906: 3904: 3903: 3898: 3886: 3884: 3883: 3878: 3864: 3856: 3848: 3846: 3845: 3844: 3831: 3827: 3826: 3816: 3799: 3797: 3796: 3791: 3773: 3771: 3770: 3765: 3753: 3751: 3750: 3745: 3733: 3731: 3730: 3725: 3723: 3718: 3710: 3701: 3699: 3698: 3693: 3681: 3679: 3678: 3673: 3615: 3613: 3612: 3607: 3589: 3587: 3586: 3585: 3572: 3568: 3567: 3557: 3545: 3543: 3542: 3537: 3509: 3507: 3506: 3501: 3483: 3481: 3480: 3475: 3457: 3455: 3454: 3449: 3437: 3435: 3434: 3429: 3380: 3378: 3377: 3372: 3360: 3358: 3357: 3352: 3350: 3349: 3340: 3315: 3313: 3312: 3307: 3302: 3297: 3296: 3273: 3271: 3270: 3265: 3263: 3258: 3257: 3248: 3233: 3231: 3230: 3225: 3213: 3211: 3210: 3205: 3167: 3165: 3164: 3159: 3137: 3135: 3134: 3129: 3124: 3123: 3122: 3113: 3103: 3095: 3093: 3092: 3083: 3075: 3060: 3058: 3057: 3052: 3040: 3038: 3037: 3032: 3020: 3018: 3017: 3012: 3000: 2998: 2997: 2992: 2980: 2978: 2977: 2972: 2960: 2958: 2957: 2952: 2940: 2938: 2937: 2932: 2917: 2915: 2914: 2909: 2897: 2895: 2894: 2889: 2877: 2875: 2874: 2869: 2857: 2855: 2854: 2849: 2837: 2835: 2834: 2829: 2824: 2822: 2821: 2812: 2801: 2713: 2711: 2710: 2705: 2703: 2691: 2689: 2688: 2683: 2681: 2668: 2666: 2665: 2660: 2655: 2653: 2645: 2644: 2643: 2638: 2628: 2623: 2621: 2613: 2612: 2611: 2606: 2596: 2591: 2589: 2581: 2580: 2571: 2562: 2560: 2559: 2554: 2552: 2540: 2538: 2537: 2532: 2530: 2529: 2524: 2515: 2514: 2509: 2500: 2488: 2486: 2485: 2480: 2478: 2477: 2472: 2459: 2457: 2456: 2451: 2449: 2448: 2443: 2396:downwards using 2368: 2366: 2365: 2360: 2358: 2271: 2269: 2268: 2263: 2258: 2256: 2255: 2254: 2241: 2240: 2235: 2234: 2224: 2216: 2204: 2202: 2201: 2196: 2190: 2179: 2177: 2169: 2168: 2159: 2151: 2139: 2137: 2136: 2131: 2119: 2117: 2116: 2111: 2105: 2103: 2095: 2094: 2085: 2080: 2068: 2066: 2065: 2060: 2054: 2043: 1916: 1914: 1913: 1908: 1903: 1899: 1889: 1881: 1877: 1867: 1856: 1844: 1842: 1841: 1836: 1834: 1833: 1820: 1818: 1817: 1812: 1810: 1791: 1789: 1788: 1783: 1781: 1779: 1778: 1777: 1764: 1760: 1759: 1749: 1736: 1734: 1733: 1728: 1723: 1721: 1713: 1675: 1672: 1651: 1649: 1641: 1633: 1615: 1613: 1612: 1607: 1602: 1600: 1592: 1554: 1551: 1530: 1528: 1520: 1512: 1503: 1501: 1500: 1495: 1471: 1470: 1469: 1442: 1440: 1439: 1434: 1432: 1431: 1415: 1413: 1412: 1407: 1395: 1393: 1392: 1387: 1375: 1373: 1372: 1367: 1365: 1364: 1348: 1346: 1345: 1340: 1328: 1326: 1325: 1320: 1295: 1293: 1292: 1287: 1272: 1270: 1269: 1264: 1245: 1243: 1242: 1237: 1232: 1230: 1222: 1214: 1199: 1197: 1196: 1191: 1180:with the symbol 1179: 1177: 1176: 1171: 1150: 1148: 1147: 1142: 1126: 1124: 1123: 1118: 1106: 1104: 1103: 1098: 1093: 1091: 1090: 1089: 1077: 1076: 1066: 1062: 1061: 1040: 1039: 1023: 1018: 1016: 1008: 1000: 991: 989: 988: 983: 981: 980: 964: 962: 961: 956: 954: 953: 937: 935: 934: 929: 800: 793: 786: 773: 768: 767: 760: 756: 755: 661:Johann Bernoulli 656:Daniel Bernoulli 577:Tangential speed 481: 457: 432:Fictitious force 427: 279:Mechanical power 269: 210:Angular momentum 108: 106: 105: 100: 98: 96: 88: 87: 78: 73: 72: 46: 45: 21: 16121: 16120: 16116: 16115: 16114: 16112: 16111: 16110: 16101:Scientific laws 16056: 16055: 16054: 16044: 16042: 16030: 16020: 16018: 16008: 16006: 15994: 15982: 15974: 15972: 15967: 15966: 15965: 15964: 15963: 15956: 15943: 15899:Newton's cradle 15880: 15835: 15808: (student) 15806:William Whiston 15802: (student) 15758: 15739:Religious views 15700: 15615:Newton's method 15575:Newtonian fluid 15469:Bucket argument 15455: 15375: 15310: 15243: 15238: 15200: 15198: 15175: 15173:Further reading 15170: 15169: 15154: 15137: 15133: 15088: 15084: 15074: 15072: 15067: 15060: 15058: 15053: 15046: 15044: 15031: 15027: 14974: 14970: 14917: 14913: 14892: 14890: 14878: 14874: 14859: 14840: 14836: 14783: 14779: 14769: 14767: 14751: 14747: 14702: 14698: 14683: 14664: 14660: 14611: 14607: 14592: 14570: 14566: 14513: 14509: 14464: 14460: 14445:10.1119/1.18659 14415: 14411: 14401: 14399: 14387: 14383: 14368: 14351: 14347: 14291: 14287: 14272: 14256: 14252: 14209:(1 June 2020). 14204: 14200: 14185: 14168: 14159: 14144: 14130: 14126: 14111: 14094: 14090: 14075: 14059: 14055: 14007: 14003: 13958: 13954: 13911: 13904: 13896: 13888: 13884: 13869: 13853: 13849: 13826:10.2307/2858681 13801: 13797: 13784: 13780: 13767: 13763: 13720: 13713: 13549: 13545: 13530: 13513: 13509: 13486: 13472: 13468: 13405: 13401: 13366: 13362: 13347: 13329: 13325: 13310: 13295: 13291: 13276: 13253: 13249: 13242: 13225: 13221: 13162: 13158: 13107: 13103: 13046: 13042: 13027: 13008: 13004: 12989: 12970: 12966: 12901: 12897: 12890: 12871: 12864: 12849: 12833: 12829: 12781: 12777: 12770: 12753: 12749: 12734: 12711: 12707: 12692: 12673: 12666: 12617: 12613: 12598: 12579: 12572: 12525:(11): 839–848. 12509: 12505: 12490: 12474:Phillips, Melba 12467: 12460: 12450: 12448: 12446: 12422: 12418: 12403: 12384: 12380: 12327: 12323: 12280:(August 1961). 12275: 12271: 12256: 12237: 12230: 12185: 12181: 12133: 12129: 12066: 12062: 12014: 12010: 11945: 11941: 11926: 11905: 11901: 11886: 11863: 11856: 11841: 11821:Ehrenfest, Paul 11818: 11814: 11799: 11788: 11769: 11765: 11750: 11723: 11719: 11701: 11688: 11684: 11627: 11623: 11608: 11591: 11584: 11536: 11532: 11469: 11462: 11425: 11421: 11376: 11372: 11357: 11333:Gowers, Timothy 11326: 11319: 11312: 11285: 11281: 11228: 11224: 11179: 11175: 11130: 11126: 11081: 11077: 11062: 11035: 11031: 10973: 10969: 10954:10.1119/1.16590 10927: 10921: 10917: 10902: 10886: 10879: 10826: 10822: 10807: 10788: 10784: 10769: 10750: 10741: 10676: 10672: 10662: 10660: 10650:Scholberg, Kate 10647: 10643: 10595: 10591: 10538:(August 1905). 10533: 10529: 10509: 10505: 10498: 10484: 10480: 10473: 10457: 10453: 10405: 10401: 10391: 10389: 10382: 10373: 10369: 10354: 10350: 10297: 10293: 10245: 10241: 10196: 10192: 10185: 10168: 10164: 10157: 10139: 10135: 10116: 10108:. p. vii. 10083: 10076: 10061: 10034: 10027: 9999: 9995: 9980: 9964: 9953: 9902: 9898: 9879: 9875: 9864: 9860: 9815: 9811: 9796: 9777: 9748: 9729:Resnick, Robert 9726: 9722: 9707: 9703: 9670: 9666: 9651: 9631:Apostol, Tom M. 9624: 9601: 9590: 9586: 9571: 9556:College Physics 9551: 9547: 9500: 9496: 9451: 9447: 9432: 9413: 9400: 9385:10.1119/1.15104 9352: 9348: 9333: 9317:Gardner, Martin 9310: 9303: 9288: 9263: 9256: 9246: 9244: 9237: 9228: 9224: 9209: 9193: 9189: 9176: 9172: 9161: 9154: 9147: 9131: 9127: 9122: 9117: 9116: 9094: 9090: 9084:Anneliese Maier 9082: 9078: 9073: 9069: 9059: 9055: 9050: 9046: 9041: 9037: 9032: 9028: 9023: 9019: 9014: 9010: 9005: 9001: 8996: 8992: 8987: 8983: 8963: 8952: 8950: 8947: 8946: 8936: 8932: 8926: 8922: 8916:except insofar, 8909: 8905: 8899: 8895: 8886: 8882: 8877: 8835: 8783:'s five-volume 8747: 8744: 8743: 8730:"), but in the 8708:Mary Somerville 8696: 8640:Johannes Kepler 8634: 8627: 8603:William Gilbert 8576: 8569: 8510:Pierre Gassendi 8498: 8497:René Descartes 8474: 8456:Galileo Galilei 8430: 8424: 8391:Byzantine Greek 8387:John Philoponus 8384: 8357: 8350: 8345: 8336: 8335: 8334: 8331: 8323: 8314: 8298: 8289: 8287:Godfrey Kneller 8283: 8271: 8222: 8211:tensor calculus 8191: 8155: 8152: 8151: 8131: 8128: 8127: 8111: 8097: 8095: 8092: 8091: 8087: 8077: 8048:Poynting vector 8016: 8002: 7999: 7998: 7969: 7967: 7964: 7963: 7934: 7926: 7915: 7904: 7902: 7899: 7898: 7874: 7871: 7870: 7841: 7837: 7835: 7832: 7831: 7814: 7810: 7808: 7805: 7804: 7787: 7783: 7781: 7778: 7777: 7760: 7756: 7754: 7751: 7750: 7728: 7720:Brownian motion 7703: 7701: 7698: 7697: 7677: 7674: 7673: 7656: 7648: 7634: 7629: 7626: 7625: 7611:Avogadro number 7596:Brownian motion 7588: 7583: 7555: 7550: 7537: 7529: 7516: 7511: 7510: 7506: 7488: 7477: 7476: 7472: 7462: 7449: 7444: 7443: 7439: 7437: 7434: 7433: 7399: 7385: 7370: 7359: 7358: 7354: 7344: 7331: 7326: 7325: 7321: 7319: 7316: 7315: 7299: 7296: 7295: 7273: 7262: 7252: 7241: 7240: 7236: 7226: 7215: 7205: 7200: 7195: 7192: 7191: 7161: 7152: 7139: 7138: 7134: 7133: 7128: 7118: 7113: 7100: 7092: 7090: 7085: 7080: 7077: 7076: 7054: 7039: 7026: 7025: 7021: 7020: 7010: 7005: 6992: 6984: 6982: 6977: 6974: 6973: 6954: 6946: 6943: 6942: 6909: 6901: 6900: 6896: 6880: 6872: 6870: 6865: 6862: 6861: 6839: 6829: 6821: 6819: 6816: 6815: 6799: 6796: 6795: 6775: 6772: 6771: 6746: 6738: 6735: 6734: 6718: 6715: 6714: 6698: 6695: 6694: 6678: 6675: 6674: 6654: 6651: 6650: 6633: 6628: 6627: 6625: 6622: 6621: 6589: 6584: 6583: 6574: 6569: 6568: 6560: 6557: 6556: 6545: 6543:Hamilton–Jacobi 6510: 6502: 6500: 6484: 6476: 6474: 6472: 6469: 6468: 6444: 6431: 6423: 6421: 6419: 6416: 6415: 6391: 6384: 6383: 6379: 6377: 6361: 6353: 6351: 6349: 6346: 6345: 6324: 6317: 6316: 6312: 6310: 6297: 6289: 6287: 6285: 6282: 6281: 6242: 6236: 6232: 6230: 6206: 6205: 6203: 6200: 6199: 6183: 6180: 6179: 6163: 6160: 6159: 6143: 6140: 6139: 6113: 6073: 6065: 6063: 6043: 6042: 6026: 6021: 6019: 6016: 6015: 6010:Evaluating the 5987: 5979: 5977: 5956: 5955: 5951: 5943: 5941: 5937: 5927: 5922: 5920: 5917: 5916: 5890: 5886: 5884: 5881: 5880: 5863: 5859: 5857: 5854: 5853: 5828: 5825: 5824: 5807: 5796: 5795: 5794: 5781: 5773: 5770: 5769: 5729: 5728: 5714: 5711: 5710: 5688: 5687: 5685: 5682: 5681: 5665: 5662: 5661: 5654: 5628: 5604: 5579: 5576: 5575: 5556: 5548: 5542: 5538: 5524: 5514: 5503: 5495: 5487: 5471: 5463: 5461: 5459: 5456: 5455: 5431: 5429: 5426: 5425: 5409: 5406: 5405: 5389: 5386: 5385: 5366: 5355: 5345: 5334: 5326: 5318: 5302: 5294: 5292: 5290: 5287: 5286: 5267: 5262: 5254: 5252: 5249: 5248: 5217: 5215: 5212: 5211: 5185: 5177: 5175: 5172: 5171: 5149:double pendulum 5133: 5127: 5122: 5056: 5048:Main articles: 5046: 5021: 5019: 5016: 5015: 4999: 4997: 4994: 4993: 4971: 4969: 4966: 4965: 4945: 4937: 4929: 4927: 4924: 4923: 4907: 4902: 4899: 4898: 4882: 4880: 4877: 4876: 4857: 4849: 4841: 4830: 4817: 4811: 4807: 4805: 4797: 4789: 4772: 4766: 4762: 4760: 4756: 4743: 4737: 4733: 4731: 4729: 4726: 4725: 4706: 4698: 4690: 4688: 4685: 4684: 4664: 4662: 4659: 4658: 4642: 4640: 4637: 4636: 4618: 4597: 4594: 4593: 4576: 4573: 4572: 4546: 4541: 4540: 4534: 4530: 4529: 4527: 4521: 4510: 4498: 4496: 4493: 4492: 4475: 4470: 4469: 4454: 4449: 4448: 4446: 4443: 4442: 4425: 4421: 4406: 4402: 4400: 4397: 4396: 4372: 4366: 4353: 4320: 4309: 4307: 4304: 4303: 4267: 4265:Work and energy 4246: 4244: 4241: 4240: 4218: 4210: 4208: 4203: 4190: 4184: 4180: 4178: 4167: 4165: 4162: 4161: 4145: 4143: 4140: 4139: 4114: 4112: 4109: 4108: 4083: 4080: 4079: 4060: 4054: 4013: 4008: 4000: 3997: 3996: 3976: 3973: 3972: 3956: 3953: 3952: 3932: 3929: 3928: 3912: 3909: 3908: 3892: 3889: 3888: 3855: 3840: 3836: 3832: 3822: 3818: 3817: 3815: 3813: 3810: 3809: 3779: 3776: 3775: 3759: 3756: 3755: 3739: 3736: 3735: 3714: 3709: 3707: 3704: 3703: 3687: 3684: 3683: 3621: 3618: 3617: 3581: 3577: 3573: 3563: 3559: 3558: 3556: 3551: 3548: 3547: 3519: 3516: 3515: 3489: 3486: 3485: 3463: 3460: 3459: 3443: 3440: 3439: 3423: 3420: 3419: 3404: 3398: 3396:Harmonic motion 3366: 3363: 3362: 3345: 3341: 3336: 3325: 3322: 3321: 3298: 3292: 3288: 3283: 3280: 3279: 3253: 3249: 3247: 3239: 3236: 3235: 3219: 3216: 3215: 3199: 3196: 3195: 3180: 3178:Circular motion 3174: 3153: 3150: 3149: 3118: 3114: 3109: 3099: 3088: 3084: 3076: 3074: 3066: 3063: 3062: 3046: 3043: 3042: 3026: 3023: 3022: 3006: 3003: 3002: 2986: 2983: 2982: 2966: 2963: 2962: 2946: 2943: 2942: 2923: 2920: 2919: 2903: 2900: 2899: 2883: 2880: 2879: 2863: 2860: 2859: 2843: 2840: 2839: 2817: 2813: 2802: 2800: 2792: 2789: 2788: 2757: 2749:Main articles: 2747: 2738: 2720: 2699: 2697: 2694: 2693: 2677: 2675: 2672: 2671: 2646: 2639: 2634: 2633: 2629: 2627: 2614: 2607: 2602: 2601: 2597: 2595: 2582: 2576: 2572: 2570: 2568: 2565: 2564: 2548: 2546: 2543: 2542: 2525: 2520: 2519: 2510: 2505: 2504: 2496: 2494: 2491: 2490: 2473: 2468: 2467: 2465: 2462: 2461: 2444: 2439: 2438: 2436: 2433: 2432: 2376: 2354: 2352: 2349: 2348: 2294:), and a force 2250: 2246: 2242: 2236: 2230: 2226: 2225: 2223: 2212: 2210: 2207: 2206: 2186: 2170: 2164: 2160: 2158: 2147: 2145: 2142: 2141: 2125: 2122: 2121: 2096: 2090: 2086: 2084: 2076: 2074: 2071: 2070: 2050: 2039: 2037: 2034: 2033: 2019: 1964: 1959: 1895: 1885: 1873: 1863: 1852: 1850: 1847: 1846: 1829: 1828: 1826: 1823: 1822: 1806: 1804: 1801: 1800: 1773: 1769: 1765: 1755: 1751: 1750: 1748: 1746: 1743: 1742: 1714: 1676: 1674: 1659: 1642: 1634: 1632: 1624: 1621: 1620: 1593: 1555: 1553: 1538: 1521: 1513: 1511: 1509: 1506: 1505: 1465: 1461: 1454: 1448: 1445: 1444: 1427: 1423: 1421: 1418: 1417: 1401: 1398: 1397: 1381: 1378: 1377: 1360: 1356: 1354: 1351: 1350: 1334: 1331: 1330: 1329:has a limit of 1305: 1302: 1301: 1278: 1275: 1274: 1255: 1252: 1251: 1223: 1215: 1213: 1205: 1202: 1201: 1185: 1182: 1181: 1165: 1162: 1161: 1136: 1133: 1132: 1112: 1109: 1108: 1085: 1081: 1072: 1068: 1067: 1057: 1053: 1035: 1031: 1024: 1022: 1009: 1001: 999: 997: 994: 993: 976: 972: 970: 967: 966: 949: 945: 943: 940: 939: 914: 911: 910: 887: 804: 763: 750: 749: 742: 741: 740: 615: 607: 606: 586: 540:Circular motion 534: 524: 523: 522: 479: 449: 446: 425: 404: 396: 395: 392: 391: 349: 339: 331: 330: 329: 288: 284:Mechanical work 277: 261: 199: 191: 190: 189: 144: 136: 113: 89: 83: 79: 77: 68: 67: 65: 62: 61: 42: 35: 28: 23: 22: 15: 12: 11: 5: 16119: 16109: 16108: 16103: 16098: 16093: 16088: 16083: 16078: 16076:Texts in Latin 16073: 16068: 16053: 16052: 16040: 16028: 16016: 16004: 15992: 15969: 15968: 15955: 15954: 15952: 15951: 15949: 15945: 15944: 15942: 15941: 15936: 15931: 15926: 15921: 15916: 15911: 15906: 15901: 15896: 15890: 15888: 15882: 15881: 15879: 15878: 15871: 15864: 15855: 15845: 15843: 15837: 15836: 15834: 15833: 15832: (friend) 15827: 15826: (friend) 15821: 15820: (friend) 15815: 15809: 15803: 15797: 15791: 15790: (mentor) 15788:William Clarke 15785: 15779: 15773: 15766: 15764: 15760: 15759: 15757: 15756: 15751: 15746: 15744:Occult studies 15741: 15736: 15731: 15726: 15721: 15715: 15708: 15706: 15702: 15701: 15699: 15698: 15697: 15696: 15686: 15681: 15676: 15671: 15666: 15661: 15660: 15659: 15649: 15644: 15639: 15634: 15629: 15627:Newton fractal 15624: 15623: 15622: 15612: 15607: 15602: 15597: 15592: 15587: 15582: 15577: 15572: 15567: 15562: 15557: 15555:Newton's rings 15552: 15547: 15546: 15545: 15540: 15530: 15525: 15524: 15523: 15513: 15508: 15503: 15502: 15501: 15496: 15491: 15481: 15476: 15471: 15465: 15463: 15457: 15456: 15454: 15453: 15448: 15443: 15441:Newton's metal 15438: 15433: 15428: 15423: 15422: 15421: 15414:Newton polygon 15411: 15406: 15401: 15396: 15395: 15394: 15383: 15381: 15377: 15376: 15374: 15373: 15365: 15357: 15348:" (1713; 15342: 15334: 15327: 15318: 15316: 15315:Other writings 15312: 15311: 15309: 15308: 15300: 15292: 15284: 15276: 15268: 15260: 15251: 15249: 15245: 15244: 15237: 15236: 15229: 15222: 15214: 15208: 15207: 15181: 15174: 15171: 15168: 15167: 15152: 15131: 15104:(9): 958–963. 15082: 15025: 14990:(5): 564–573. 14968: 14911: 14882:"Isaac Newton" 14872: 14857: 14843:Hesse, Mary B. 14834: 14777: 14745: 14718:(1): 191–229. 14696: 14681: 14658: 14627:(4): 311–339. 14605: 14590: 14564: 14529:(2): 211–224. 14507: 14458: 14431:(2): 149–154. 14409: 14381: 14366: 14345: 14316:10.1086/349598 14310:(3): 379–388. 14285: 14270: 14250: 14229:10.1086/709344 14223:(2): 395–396. 14207:Nummedal, Tara 14198: 14183: 14157: 14142: 14124: 14109: 14088: 14073: 14053: 14010:Fara, Patricia 14001: 13952: 13931:10.1086/351876 13925:(4): 574–597. 13902: 13882: 13867: 13847: 13820:(4): 186–200. 13795: 13778: 13761: 13740:10.1086/350115 13734:(2): 220–234. 13711: 13709: 13708: 13651: 13625:(3): 185–188. 13604: 13543: 13528: 13507: 13484: 13466: 13399: 13380:(1): 169–199. 13360: 13345: 13323: 13308: 13289: 13274: 13247: 13240: 13219: 13156: 13101: 13061:(3): 803–815. 13040: 13025: 13002: 12987: 12964: 12895: 12888: 12862: 12847: 12827: 12797:(4): 938–965. 12775: 12768: 12747: 12732: 12705: 12690: 12664: 12629:(42): 424011. 12611: 12596: 12570: 12503: 12488: 12458: 12444: 12416: 12401: 12378: 12321: 12294:(8): 510–517. 12269: 12254: 12228: 12179: 12152:(2): 146–150. 12127: 12082:(5): 353–359. 12060: 12008: 11939: 11924: 11899: 11884: 11866:Kardar, Mehran 11854: 11839: 11812: 11797: 11763: 11748: 11717: 11682: 11621: 11606: 11582: 11555:(4): 446–452. 11541:(April 2004). 11530: 11485:(2): 431–458. 11460: 11441:(7): 928–929. 11419: 11392:(4): 347–352. 11370: 11355: 11317: 11310: 11279: 11244:(1): 129–137. 11222: 11173: 11124: 11075: 11060: 11029: 10992:(7): 504–509. 10967: 10940:(2): 118–124. 10915: 10900: 10877: 10820: 10805: 10782: 10767: 10739: 10670: 10641: 10589: 10527: 10503: 10496: 10478: 10471: 10451: 10399: 10376:Wilczek, Frank 10367: 10348: 10313:(2): 112–115. 10291: 10264:(7): 406–409. 10239: 10190: 10183: 10162: 10155: 10133: 10114: 10106:Pergamon Press 10086:Landau, Lev D. 10074: 10059: 10025: 9993: 9978: 9951: 9896: 9873: 9858: 9809: 9794: 9780:José, Jorge V. 9746: 9720: 9701: 9664: 9649: 9599: 9584: 9569: 9545: 9494: 9467:(4): 171–176. 9445: 9430: 9398: 9371:(6): 503–513. 9346: 9331: 9301: 9286: 9254: 9222: 9207: 9187: 9170: 9152: 9145: 9124: 9123: 9121: 9118: 9115: 9114: 9088: 9076: 9067: 9053: 9044: 9035: 9026: 9017: 9008: 8999: 8990: 8981: 8966: 8962: 8959: 8955: 8930: 8920: 8903: 8893: 8879: 8878: 8876: 8873: 8872: 8871: 8866: 8861: 8856: 8851: 8846: 8841: 8834: 8831: 8777:Leonhard Euler 8760: 8757: 8754: 8751: 8702:Page 157 from 8695: 8689: 8626: 8623: 8568: 8565: 8506:Isaac Beeckman 8434:René Descartes 8423: 8420: 8383: 8380: 8349: 8346: 8344: 8341: 8333: 8332: 8324: 8317: 8315: 8299: 8292: 8290: 8284: 8277: 8274: 8273: 8272: 8270: 8267: 8221: 8218: 8190: 8187: 8172:Lorentz factor 8159: 8146:is the body's 8135: 8114: 8110: 8107: 8104: 8100: 8076: 8073: 8060:speed of light 8023: 8019: 8015: 8012: 8009: 8006: 7979: 7976: 7972: 7941: 7937: 7933: 7929: 7925: 7922: 7918: 7914: 7911: 7907: 7878: 7844: 7840: 7817: 7813: 7790: 7786: 7763: 7759: 7727: 7724: 7706: 7681: 7659: 7655: 7651: 7647: 7644: 7641: 7637: 7633: 7587: 7584: 7582: 7579: 7567: 7561: 7558: 7554: 7549: 7545: 7540: 7536: 7532: 7528: 7522: 7519: 7515: 7509: 7505: 7501: 7496: 7491: 7487: 7484: 7480: 7475: 7469: 7466: 7461: 7455: 7452: 7448: 7442: 7409: 7406: 7402: 7398: 7395: 7392: 7388: 7383: 7378: 7373: 7369: 7366: 7362: 7357: 7351: 7348: 7343: 7337: 7334: 7330: 7324: 7303: 7283: 7280: 7276: 7272: 7269: 7265: 7260: 7255: 7251: 7248: 7244: 7239: 7233: 7230: 7225: 7222: 7218: 7211: 7208: 7204: 7199: 7171: 7168: 7164: 7160: 7155: 7150: 7146: 7142: 7137: 7131: 7124: 7121: 7117: 7112: 7106: 7103: 7098: 7095: 7088: 7084: 7064: 7061: 7057: 7053: 7050: 7047: 7042: 7037: 7033: 7029: 7024: 7016: 7013: 7009: 7004: 6998: 6995: 6990: 6987: 6981: 6961: 6957: 6953: 6950: 6930: 6926: 6922: 6919: 6916: 6912: 6908: 6904: 6899: 6895: 6892: 6886: 6883: 6878: 6875: 6869: 6849: 6846: 6842: 6836: 6833: 6828: 6824: 6803: 6779: 6759: 6756: 6753: 6749: 6745: 6742: 6733:is a function 6722: 6702: 6682: 6658: 6636: 6631: 6609: 6606: 6603: 6600: 6597: 6592: 6587: 6582: 6577: 6572: 6567: 6564: 6544: 6541: 6522: 6516: 6513: 6508: 6505: 6499: 6496: 6490: 6487: 6482: 6479: 6456: 6451: 6448: 6443: 6437: 6434: 6429: 6426: 6403: 6397: 6394: 6387: 6382: 6376: 6373: 6367: 6364: 6359: 6356: 6330: 6327: 6320: 6315: 6309: 6303: 6300: 6295: 6292: 6269: 6266: 6263: 6260: 6257: 6254: 6248: 6245: 6239: 6235: 6229: 6226: 6223: 6220: 6217: 6214: 6209: 6187: 6167: 6147: 6112: 6109: 6085: 6079: 6076: 6071: 6068: 6062: 6059: 6056: 6050: 6047: 6041: 6038: 6032: 6029: 6025: 5999: 5993: 5990: 5985: 5982: 5976: 5972: 5963: 5960: 5954: 5949: 5946: 5940: 5933: 5930: 5926: 5893: 5889: 5866: 5862: 5841: 5838: 5835: 5832: 5810: 5803: 5800: 5793: 5788: 5785: 5780: 5777: 5757: 5754: 5751: 5748: 5745: 5742: 5736: 5733: 5727: 5724: 5721: 5718: 5695: 5692: 5669: 5653: 5650: 5627: 5624: 5618:is one of the 5603: 5600: 5583: 5563: 5559: 5555: 5551: 5545: 5541: 5537: 5534: 5531: 5527: 5521: 5518: 5513: 5510: 5506: 5502: 5498: 5494: 5490: 5486: 5483: 5477: 5474: 5469: 5466: 5434: 5413: 5393: 5373: 5369: 5365: 5362: 5358: 5352: 5349: 5344: 5341: 5337: 5333: 5329: 5325: 5321: 5317: 5314: 5308: 5305: 5300: 5297: 5274: 5270: 5265: 5261: 5257: 5220: 5198: 5195: 5192: 5188: 5184: 5180: 5129:Main article: 5126: 5123: 5121: 5118: 5077:conic sections 5069:Kepler problem 5045: 5042: 5024: 5002: 4981: 4978: 4974: 4952: 4948: 4944: 4940: 4936: 4932: 4910: 4906: 4885: 4864: 4860: 4856: 4852: 4848: 4844: 4840: 4837: 4833: 4829: 4823: 4820: 4814: 4810: 4804: 4800: 4796: 4792: 4788: 4784: 4778: 4775: 4769: 4765: 4759: 4755: 4749: 4746: 4740: 4736: 4713: 4709: 4705: 4701: 4697: 4693: 4667: 4645: 4617: 4614: 4601: 4580: 4560: 4555: 4549: 4544: 4537: 4533: 4524: 4519: 4516: 4513: 4509: 4505: 4501: 4478: 4473: 4468: 4465: 4462: 4457: 4452: 4428: 4424: 4420: 4417: 4414: 4409: 4405: 4370:Center of mass 4368:Main article: 4365: 4364:Center of mass 4362: 4358:center of mass 4352: 4349: 4331: 4327: 4323: 4319: 4316: 4312: 4283:Thermal energy 4266: 4263: 4249: 4224: 4221: 4216: 4213: 4206: 4202: 4196: 4193: 4187: 4183: 4177: 4174: 4170: 4148: 4127: 4124: 4121: 4117: 4096: 4093: 4090: 4087: 4068:Space Shuttle 4056:Main article: 4053: 4050: 4020: 4016: 4012: 4007: 4004: 3980: 3960: 3947:is small, the 3936: 3916: 3896: 3876: 3873: 3870: 3867: 3862: 3859: 3854: 3851: 3843: 3839: 3835: 3830: 3825: 3821: 3789: 3786: 3783: 3763: 3743: 3721: 3717: 3713: 3691: 3670: 3667: 3664: 3661: 3658: 3655: 3652: 3649: 3646: 3643: 3640: 3637: 3634: 3631: 3628: 3625: 3605: 3601: 3598: 3595: 3592: 3584: 3580: 3576: 3571: 3566: 3562: 3555: 3535: 3532: 3529: 3526: 3523: 3499: 3496: 3493: 3484:. That is, at 3473: 3470: 3467: 3447: 3427: 3400:Main article: 3397: 3394: 3370: 3348: 3344: 3339: 3335: 3332: 3329: 3305: 3301: 3295: 3291: 3287: 3261: 3256: 3252: 3246: 3243: 3223: 3203: 3176:Main article: 3173: 3170: 3157: 3127: 3121: 3117: 3112: 3108: 3102: 3098: 3091: 3087: 3082: 3079: 3073: 3070: 3050: 3030: 3010: 2990: 2970: 2950: 2930: 2927: 2907: 2887: 2867: 2847: 2827: 2820: 2816: 2811: 2808: 2805: 2799: 2796: 2746: 2743: 2737: 2734: 2719: 2716: 2702: 2680: 2658: 2652: 2649: 2642: 2637: 2632: 2626: 2620: 2617: 2610: 2605: 2600: 2594: 2588: 2585: 2579: 2575: 2551: 2528: 2523: 2518: 2513: 2508: 2503: 2499: 2476: 2471: 2447: 2442: 2398:rocket engines 2394:reaction force 2383: 2382: 2375: 2372: 2357: 2330:"normal" force 2326:inclined plane 2304:add as vectors 2261: 2253: 2249: 2245: 2239: 2233: 2229: 2222: 2219: 2215: 2194: 2189: 2185: 2182: 2176: 2173: 2167: 2163: 2157: 2154: 2150: 2129: 2109: 2102: 2099: 2093: 2089: 2083: 2079: 2058: 2053: 2049: 2046: 2042: 2026: 2025: 2018: 2015: 1990: 1989: 1963: 1960: 1958: 1955: 1906: 1902: 1898: 1894: 1888: 1884: 1880: 1876: 1872: 1866: 1862: 1859: 1855: 1832: 1809: 1776: 1772: 1768: 1763: 1758: 1754: 1726: 1720: 1717: 1712: 1709: 1706: 1703: 1700: 1697: 1694: 1691: 1688: 1685: 1682: 1679: 1671: 1668: 1665: 1662: 1658: 1654: 1648: 1645: 1640: 1637: 1631: 1628: 1605: 1599: 1596: 1591: 1588: 1585: 1582: 1579: 1576: 1573: 1570: 1567: 1564: 1561: 1558: 1550: 1547: 1544: 1541: 1537: 1533: 1527: 1524: 1519: 1516: 1493: 1490: 1487: 1484: 1481: 1478: 1475: 1468: 1464: 1460: 1457: 1453: 1443:. One writes, 1430: 1426: 1405: 1385: 1363: 1359: 1338: 1318: 1315: 1312: 1309: 1285: 1282: 1262: 1259: 1235: 1229: 1226: 1221: 1218: 1212: 1209: 1200:, for example, 1189: 1169: 1140: 1116: 1096: 1088: 1084: 1080: 1075: 1071: 1065: 1060: 1056: 1052: 1049: 1046: 1043: 1038: 1034: 1030: 1027: 1021: 1015: 1012: 1007: 1004: 979: 975: 952: 948: 927: 924: 921: 918: 886: 883: 849: 848: 845: 834: 806: 805: 803: 802: 795: 788: 780: 777: 776: 775: 774: 761: 744: 743: 739: 738: 733: 728: 723: 718: 713: 708: 703: 698: 693: 688: 683: 678: 673: 668: 663: 658: 653: 648: 643: 638: 633: 628: 623: 617: 616: 613: 612: 609: 608: 605: 604: 585: 584: 579: 574: 569: 567:Coriolis force 564: 563: 562: 552: 547: 542: 536: 535: 530: 529: 526: 525: 521: 520: 515: 510: 509: 508: 503: 493: 488: 483: 476: 465: 464: 463: 458: 445: 444: 439: 434: 429: 422: 417: 412: 406: 405: 402: 401: 398: 397: 394: 393: 390: 389: 384: 379: 374: 369: 364: 358: 352: 350: 343: 340: 337: 336: 333: 332: 328: 327: 322: 317: 312: 307: 302: 297: 292: 286: 281: 275: 270: 259: 254: 249: 244: 239: 238: 237: 232: 222: 217: 212: 207: 201: 200: 197: 196: 193: 192: 188: 187: 182: 177: 172: 167: 162: 157: 152: 146: 145: 142: 141: 138: 137: 135: 134: 129: 124: 118: 115: 114: 109: 95: 92: 86: 82: 76: 58: 57: 51: 50: 26: 9: 6: 4: 3: 2: 16118: 16107: 16104: 16102: 16099: 16097: 16094: 16092: 16089: 16087: 16084: 16082: 16079: 16077: 16074: 16072: 16069: 16067: 16064: 16063: 16061: 16051: 16041: 16039: 16034: 16029: 16027: 16017: 16015: 16005: 16003: 15998: 15993: 15991: 15986: 15981: 15980: 15977: 15962: 15958: 15950: 15946: 15940: 15937: 15935: 15932: 15930: 15927: 15925: 15922: 15920: 15917: 15915: 15912: 15910: 15907: 15905: 15902: 15900: 15897: 15895: 15894:Newton (unit) 15892: 15891: 15889: 15887: 15883: 15877: 15876: 15872: 15870: 15869: 15865: 15862: 15860: 15856: 15853: 15851: 15847: 15846: 15844: 15842: 15838: 15831: 15828: 15825: 15824:William Jones 15822: 15819: 15816: 15813: 15810: 15807: 15804: 15801: 15798: 15796: (tutor) 15795: 15792: 15789: 15786: 15783: 15780: 15777: 15776:John Conduitt 15774: 15772: (niece) 15771: 15768: 15767: 15765: 15761: 15755: 15752: 15750: 15747: 15745: 15742: 15740: 15737: 15735: 15732: 15730: 15727: 15725: 15722: 15719: 15718:Cranbury Park 15716: 15713: 15710: 15709: 15707: 15705:Personal life 15703: 15695: 15692: 15691: 15690: 15687: 15685: 15682: 15680: 15677: 15675: 15672: 15670: 15667: 15665: 15662: 15658: 15655: 15654: 15653: 15652:Newton number 15650: 15648: 15645: 15643: 15640: 15638: 15635: 15633: 15630: 15628: 15625: 15621: 15618: 15617: 15616: 15613: 15611: 15608: 15606: 15603: 15601: 15598: 15596: 15593: 15591: 15588: 15586: 15583: 15581: 15578: 15576: 15573: 15571: 15568: 15566: 15563: 15561: 15558: 15556: 15553: 15551: 15548: 15544: 15541: 15539: 15536: 15535: 15534: 15531: 15529: 15526: 15522: 15521:Kepler's laws 15519: 15518: 15517: 15514: 15512: 15509: 15507: 15504: 15500: 15497: 15495: 15494:parameterized 15492: 15490: 15487: 15486: 15485: 15482: 15480: 15477: 15475: 15472: 15470: 15467: 15466: 15464: 15462: 15458: 15452: 15449: 15447: 15444: 15442: 15439: 15437: 15434: 15432: 15429: 15427: 15424: 15420: 15417: 15416: 15415: 15412: 15410: 15407: 15405: 15402: 15400: 15397: 15393: 15390: 15389: 15388: 15385: 15384: 15382: 15380:Contributions 15378: 15371: 15370: 15366: 15363: 15362: 15358: 15355: 15353: 15347: 15343: 15340: 15339: 15335: 15333:" (1675) 15332: 15328: 15325: 15324: 15320: 15319: 15317: 15313: 15306: 15305: 15301: 15298: 15297: 15293: 15290: 15289: 15285: 15282: 15281: 15277: 15274: 15273: 15269: 15266: 15265: 15261: 15258: 15257: 15253: 15252: 15250: 15246: 15242: 15235: 15230: 15228: 15223: 15221: 15216: 15215: 15212: 15197: 15196: 15191: 15187: 15182: 15180: 15177: 15176: 15163: 15159: 15155: 15149: 15145: 15141: 15135: 15127: 15123: 15119: 15115: 15111: 15107: 15103: 15099: 15098: 15093: 15086: 15070: 15056: 15043: 15039: 15035: 15029: 15021: 15017: 15013: 15009: 15005: 15001: 14997: 14993: 14989: 14985: 14984: 14979: 14972: 14964: 14960: 14956: 14952: 14948: 14944: 14940: 14936: 14932: 14928: 14927: 14922: 14915: 14908: 14906: 14902: 14889: 14888: 14883: 14876: 14868: 14864: 14860: 14854: 14850: 14849: 14844: 14838: 14830: 14826: 14822: 14818: 14814: 14810: 14806: 14802: 14799:(1): 015001. 14798: 14794: 14793: 14788: 14781: 14766: 14765: 14760: 14758: 14749: 14741: 14737: 14733: 14729: 14725: 14721: 14717: 14713: 14712: 14707: 14700: 14692: 14688: 14684: 14678: 14674: 14673: 14668: 14662: 14655: 14650: 14646: 14642: 14638: 14634: 14630: 14626: 14622: 14621: 14616: 14609: 14601: 14597: 14593: 14587: 14583: 14579: 14575: 14568: 14560: 14556: 14552: 14548: 14544: 14540: 14536: 14532: 14528: 14524: 14523: 14518: 14511: 14503: 14499: 14495: 14491: 14487: 14483: 14480:(10): 31–36. 14479: 14475: 14474: 14473:Physics Today 14469: 14462: 14454: 14450: 14446: 14442: 14438: 14434: 14430: 14426: 14425: 14420: 14413: 14398: 14397: 14392: 14385: 14377: 14373: 14369: 14363: 14359: 14355: 14349: 14341: 14337: 14333: 14329: 14325: 14321: 14317: 14313: 14309: 14305: 14304: 14299: 14295: 14289: 14281: 14277: 14273: 14267: 14263: 14262: 14254: 14246: 14242: 14238: 14234: 14230: 14226: 14222: 14218: 14217: 14212: 14208: 14202: 14194: 14190: 14186: 14180: 14176: 14172: 14166: 14164: 14162: 14153: 14149: 14145: 14143:9780521231435 14139: 14135: 14134:Never at Rest 14128: 14120: 14116: 14112: 14110:9780521273817 14106: 14102: 14098: 14092: 14084: 14080: 14076: 14070: 14066: 14065: 14057: 14049: 14045: 14041: 14037: 14033: 14029: 14026:(5635): 920. 14025: 14021: 14020: 14015: 14011: 14005: 13997: 13993: 13989: 13985: 13981: 13977: 13973: 13969: 13968: 13963: 13956: 13948: 13944: 13940: 13936: 13932: 13928: 13924: 13920: 13916: 13909: 13907: 13895: 13894: 13886: 13878: 13874: 13870: 13864: 13860: 13859: 13851: 13843: 13839: 13835: 13831: 13827: 13823: 13819: 13815: 13814: 13809: 13805: 13799: 13791: 13790: 13782: 13774: 13773: 13765: 13757: 13753: 13749: 13745: 13741: 13737: 13733: 13729: 13725: 13718: 13716: 13705: 13701: 13697: 13693: 13688: 13683: 13679: 13675: 13672:(1): 010121. 13671: 13667: 13666: 13661: 13657: 13652: 13648: 13644: 13640: 13636: 13632: 13628: 13624: 13620: 13619: 13614: 13610: 13605: 13601: 13597: 13593: 13589: 13584: 13579: 13575: 13571: 13568:(1): 010123. 13567: 13563: 13562: 13557: 13552: 13551: 13547: 13539: 13535: 13531: 13525: 13521: 13517: 13511: 13503: 13499: 13495: 13491: 13487: 13481: 13477: 13470: 13463: 13460: 13454: 13450: 13445: 13440: 13436: 13432: 13428: 13424: 13420: 13416: 13415: 13410: 13403: 13395: 13391: 13387: 13383: 13379: 13375: 13371: 13364: 13356: 13352: 13348: 13342: 13338: 13334: 13327: 13319: 13315: 13311: 13305: 13301: 13293: 13285: 13281: 13277: 13275:0-7923-2549-4 13271: 13267: 13263: 13262: 13257: 13251: 13243: 13241:0-471-16433-X 13237: 13233: 13229: 13223: 13215: 13211: 13207: 13203: 13198: 13193: 13189: 13185: 13182:(2): 025705. 13181: 13177: 13176: 13171: 13167: 13160: 13152: 13148: 13144: 13140: 13136: 13132: 13127: 13122: 13118: 13114: 13113: 13105: 13098: 13094: 13090: 13086: 13082: 13078: 13074: 13069: 13064: 13060: 13056: 13055: 13050: 13044: 13036: 13032: 13028: 13022: 13018: 13017: 13012: 13006: 12998: 12994: 12990: 12984: 12980: 12979: 12974: 12968: 12960: 12956: 12952: 12948: 12943: 12938: 12933: 12928: 12924: 12920: 12917:(3): 035008. 12916: 12912: 12911: 12906: 12899: 12891: 12885: 12881: 12880: 12875: 12869: 12867: 12858: 12854: 12850: 12844: 12840: 12839: 12831: 12824: 12820: 12816: 12812: 12808: 12804: 12800: 12796: 12792: 12791: 12786: 12779: 12771: 12769:0-393-09804-4 12765: 12761: 12757: 12756:French, A. P. 12751: 12743: 12739: 12735: 12733:0-19-850657-0 12729: 12725: 12724: 12719: 12715: 12709: 12701: 12697: 12693: 12687: 12683: 12682: 12677: 12671: 12669: 12660: 12656: 12652: 12648: 12644: 12640: 12636: 12632: 12628: 12624: 12623: 12615: 12607: 12603: 12599: 12597:0-201-31611-0 12593: 12589: 12588: 12583: 12577: 12575: 12566: 12562: 12558: 12554: 12550: 12546: 12542: 12538: 12533: 12528: 12524: 12520: 12519: 12514: 12507: 12499: 12495: 12491: 12489:0-486-43924-0 12485: 12481: 12480: 12475: 12471: 12465: 12463: 12447: 12441: 12437: 12433: 12429: 12428: 12420: 12412: 12408: 12404: 12402:90-277-0107-5 12398: 12394: 12393: 12388: 12382: 12374: 12370: 12366: 12362: 12358: 12354: 12350: 12346: 12343:(6): 065201. 12342: 12338: 12337: 12332: 12325: 12317: 12313: 12309: 12305: 12301: 12297: 12293: 12289: 12288: 12283: 12279: 12273: 12265: 12261: 12257: 12251: 12247: 12246: 12241: 12235: 12233: 12224: 12220: 12216: 12212: 12208: 12204: 12200: 12196: 12195: 12190: 12183: 12175: 12171: 12167: 12163: 12159: 12155: 12151: 12147: 12146: 12141: 12137: 12136:Rosen, Nathan 12131: 12123: 12119: 12115: 12111: 12107: 12103: 12099: 12095: 12090: 12085: 12081: 12077: 12076: 12071: 12064: 12056: 12052: 12048: 12044: 12040: 12036: 12032: 12028: 12027: 12022: 12018: 12012: 12004: 12000: 11996: 11992: 11987: 11982: 11977: 11972: 11968: 11964: 11961:(2): 020126. 11960: 11956: 11955: 11950: 11943: 11935: 11931: 11927: 11921: 11916: 11915: 11909: 11903: 11895: 11891: 11887: 11881: 11877: 11873: 11872: 11867: 11861: 11859: 11850: 11846: 11842: 11840:0-486-66250-0 11836: 11832: 11831: 11826: 11822: 11816: 11808: 11804: 11800: 11794: 11787: 11786: 11781: 11780:Wiles, Andrew 11777: 11776:Jaffe, Arthur 11773: 11767: 11759: 11755: 11751: 11745: 11740: 11735: 11731: 11727: 11726:Baez, John C. 11721: 11713: 11709: 11708: 11700: 11696: 11692: 11686: 11678: 11674: 11670: 11666: 11661: 11656: 11651: 11646: 11642: 11638: 11637: 11632: 11625: 11617: 11613: 11609: 11603: 11599: 11595: 11589: 11587: 11578: 11574: 11570: 11566: 11562: 11558: 11554: 11550: 11549: 11544: 11540: 11534: 11526: 11522: 11518: 11514: 11510: 11506: 11502: 11498: 11493: 11488: 11484: 11480: 11479: 11474: 11467: 11465: 11456: 11452: 11448: 11444: 11440: 11436: 11435: 11430: 11423: 11415: 11411: 11407: 11403: 11399: 11395: 11391: 11387: 11386: 11381: 11374: 11366: 11362: 11358: 11352: 11348: 11347: 11342: 11338: 11334: 11330: 11324: 11322: 11313: 11307: 11303: 11299: 11295: 11294: 11289: 11283: 11275: 11271: 11267: 11263: 11259: 11255: 11251: 11247: 11243: 11239: 11238: 11233: 11226: 11218: 11214: 11210: 11206: 11202: 11198: 11194: 11190: 11189: 11184: 11177: 11169: 11165: 11161: 11157: 11153: 11149: 11145: 11141: 11140: 11135: 11128: 11120: 11116: 11112: 11108: 11104: 11100: 11096: 11092: 11091: 11086: 11079: 11071: 11067: 11063: 11057: 11053: 11052: 11047: 11043: 11039: 11033: 11025: 11021: 11017: 11013: 11008: 11003: 10999: 10995: 10991: 10987: 10986: 10981: 10977: 10971: 10963: 10959: 10955: 10951: 10947: 10943: 10939: 10935: 10934: 10926: 10919: 10911: 10907: 10903: 10901:0-521-57327-0 10897: 10893: 10892: 10884: 10882: 10873: 10869: 10865: 10861: 10857: 10853: 10849: 10845: 10841: 10837: 10836: 10831: 10824: 10816: 10812: 10808: 10802: 10798: 10797: 10792: 10786: 10778: 10774: 10770: 10764: 10760: 10759: 10754: 10753:Boas, Mary L. 10748: 10746: 10744: 10735: 10731: 10727: 10723: 10718: 10717:11577/3340932 10713: 10708: 10703: 10699: 10695: 10692:(1): 010111. 10691: 10687: 10686: 10681: 10674: 10659: 10655: 10651: 10645: 10637: 10633: 10629: 10625: 10621: 10617: 10613: 10609: 10608: 10603: 10599: 10593: 10585: 10581: 10577: 10573: 10568: 10563: 10559: 10555: 10552:(1870): 429. 10551: 10547: 10546: 10541: 10537: 10531: 10523: 10522: 10517: 10513: 10507: 10499: 10493: 10489: 10482: 10474: 10468: 10464: 10463: 10455: 10447: 10443: 10439: 10435: 10431: 10427: 10423: 10419: 10418: 10413: 10409: 10403: 10388: 10381: 10377: 10371: 10363: 10359: 10352: 10344: 10340: 10336: 10332: 10328: 10324: 10320: 10316: 10312: 10308: 10307: 10302: 10295: 10287: 10283: 10279: 10275: 10271: 10267: 10263: 10259: 10258: 10253: 10249: 10243: 10235: 10231: 10227: 10223: 10219: 10215: 10211: 10207: 10206: 10201: 10194: 10186: 10184:0-06-273100-9 10180: 10176: 10172: 10171:Gonick, Larry 10166: 10158: 10152: 10148: 10144: 10137: 10130: 10125: 10121: 10117: 10111: 10107: 10103: 10099: 10095: 10091: 10087: 10081: 10079: 10070: 10066: 10062: 10060:0-201-02010-6 10056: 10052: 10051: 10046: 10042: 10038: 10032: 10030: 10021: 10017: 10013: 10009: 10008: 10003: 9997: 9989: 9985: 9981: 9975: 9971: 9970: 9962: 9960: 9958: 9956: 9947: 9943: 9938: 9933: 9929: 9925: 9922:(1): 010108. 9921: 9917: 9916: 9911: 9907: 9900: 9892: 9888: 9884: 9877: 9869: 9862: 9854: 9850: 9846: 9842: 9838: 9834: 9830: 9826: 9825: 9820: 9813: 9805: 9801: 9797: 9791: 9787: 9786: 9781: 9775: 9773: 9771: 9769: 9767: 9765: 9763: 9761: 9759: 9757: 9755: 9753: 9751: 9742: 9738: 9734: 9730: 9724: 9716: 9712: 9705: 9697: 9693: 9688: 9683: 9679: 9675: 9668: 9660: 9656: 9652: 9646: 9642: 9641: 9636: 9632: 9628: 9622: 9620: 9618: 9616: 9614: 9612: 9610: 9608: 9606: 9604: 9595: 9588: 9580: 9576: 9572: 9566: 9562: 9558: 9557: 9549: 9541: 9537: 9532: 9527: 9523: 9519: 9516:(1): 010110. 9515: 9511: 9510: 9505: 9498: 9490: 9486: 9482: 9478: 9474: 9470: 9466: 9462: 9461: 9456: 9449: 9441: 9437: 9433: 9427: 9423: 9422: 9417: 9411: 9409: 9407: 9405: 9403: 9394: 9390: 9386: 9382: 9378: 9374: 9370: 9366: 9365: 9360: 9356: 9350: 9342: 9338: 9334: 9328: 9324: 9323: 9318: 9314: 9308: 9306: 9297: 9293: 9289: 9283: 9279: 9275: 9271: 9267: 9261: 9259: 9243: 9236: 9232: 9226: 9218: 9214: 9210: 9204: 9200: 9199: 9191: 9183: 9182: 9174: 9166: 9159: 9157: 9148: 9146:0-534-40896-6 9142: 9138: 9137: 9129: 9125: 9111: 9106: 9102: 9098: 9092: 9085: 9080: 9071: 9063: 9057: 9048: 9039: 9030: 9021: 9012: 9003: 8994: 8985: 8960: 8957: 8944: 8940: 8934: 8924: 8917: 8913: 8907: 8897: 8890: 8884: 8880: 8870: 8869:Norton's dome 8867: 8865: 8862: 8860: 8857: 8855: 8852: 8850: 8847: 8845: 8842: 8840: 8837: 8836: 8830: 8828: 8824: 8820: 8816: 8811: 8808: 8804: 8798: 8796: 8792: 8788: 8787: 8782: 8778: 8774: 8773:Jakob Hermann 8758: 8755: 8752: 8749: 8741: 8737: 8733: 8729: 8725: 8717: 8713: 8709: 8705: 8700: 8694: 8688: 8686: 8682: 8678: 8673: 8671: 8667: 8663: 8659: 8654: 8652: 8648: 8647: 8641: 8631: 8622: 8620: 8616: 8612: 8608: 8604: 8600: 8599: 8593: 8588: 8586: 8585: 8573: 8564: 8560: 8556: 8554: 8550: 8546: 8540: 8535: 8527: 8523: 8521: 8517: 8516: 8511: 8507: 8495: 8490: 8485: 8483: 8471: 8467: 8465: 8461: 8457: 8453: 8449: 8445: 8441: 8440: 8435: 8429: 8419: 8417: 8413: 8409: 8405: 8401: 8397: 8392: 8388: 8379: 8377: 8373: 8369: 8361: 8354: 8340: 8330: 8329: 8321: 8316: 8313: 8309: 8305: 8304: 8296: 8291: 8288: 8281: 8276: 8275: 8266: 8263: 8259: 8254: 8249: 8247: 8243: 8239: 8235: 8231: 8226: 8217: 8214: 8212: 8208: 8203: 8199: 8195: 8186: 8183: 8179: 8177: 8173: 8157: 8149: 8133: 8108: 8105: 8102: 8086: 8082: 8072: 8070: 8066: 8061: 8056: 8051: 8049: 8043: 8041: 8037: 8021: 8017: 8013: 8010: 8007: 8004: 7997: 7993: 7977: 7974: 7956: 7952: 7939: 7931: 7923: 7920: 7912: 7909: 7896: 7895:cross product 7892: 7876: 7867: 7863: 7858: 7842: 7838: 7815: 7811: 7788: 7784: 7761: 7757: 7747: 7743: 7742:Coulomb's law 7739: 7737: 7733: 7723: 7721: 7704: 7695: 7679: 7657: 7653: 7645: 7642: 7639: 7631: 7623: 7618: 7616: 7612: 7608: 7604: 7597: 7592: 7578: 7565: 7559: 7556: 7552: 7547: 7543: 7534: 7526: 7520: 7507: 7503: 7499: 7494: 7485: 7482: 7473: 7467: 7464: 7459: 7453: 7440: 7430: 7428: 7424: 7407: 7404: 7396: 7393: 7390: 7381: 7376: 7367: 7364: 7355: 7349: 7346: 7341: 7335: 7322: 7301: 7281: 7278: 7270: 7267: 7258: 7249: 7246: 7237: 7231: 7228: 7223: 7220: 7209: 7197: 7189: 7185: 7169: 7166: 7158: 7153: 7148: 7144: 7135: 7122: 7119: 7115: 7110: 7104: 7096: 7082: 7062: 7048: 7045: 7040: 7035: 7031: 7022: 7014: 7011: 7007: 7002: 6996: 6988: 6979: 6948: 6928: 6924: 6920: 6917: 6914: 6906: 6897: 6893: 6890: 6884: 6876: 6867: 6847: 6844: 6834: 6831: 6826: 6801: 6793: 6777: 6754: 6751: 6740: 6720: 6700: 6680: 6672: 6656: 6634: 6620:of positions 6604: 6601: 6598: 6595: 6590: 6580: 6575: 6562: 6554: 6550: 6540: 6537: 6534: 6520: 6514: 6511: 6506: 6503: 6497: 6494: 6488: 6485: 6480: 6477: 6454: 6449: 6446: 6441: 6435: 6432: 6427: 6424: 6401: 6395: 6374: 6371: 6365: 6362: 6357: 6354: 6328: 6307: 6301: 6298: 6293: 6290: 6267: 6261: 6255: 6252: 6246: 6243: 6237: 6233: 6227: 6221: 6218: 6215: 6185: 6165: 6145: 6137: 6133: 6125: 6121: 6117: 6108: 6106: 6101: 6097: 6083: 6077: 6074: 6069: 6066: 6060: 6057: 6048: 6045: 6039: 6030: 6027: 6023: 6013: 5997: 5991: 5983: 5974: 5970: 5961: 5958: 5947: 5938: 5931: 5928: 5924: 5914: 5910: 5891: 5887: 5864: 5860: 5836: 5830: 5808: 5801: 5798: 5791: 5786: 5783: 5778: 5775: 5755: 5752: 5749: 5746: 5743: 5734: 5731: 5725: 5722: 5716: 5693: 5690: 5667: 5658: 5649: 5647: 5643: 5639: 5634: 5623: 5621: 5617: 5612: 5610: 5602:Singularities 5599: 5597: 5581: 5561: 5553: 5543: 5535: 5532: 5529: 5519: 5516: 5511: 5508: 5492: 5481: 5475: 5467: 5453: 5449: 5411: 5391: 5371: 5363: 5360: 5350: 5347: 5342: 5339: 5323: 5312: 5306: 5298: 5272: 5268: 5259: 5246: 5242: 5240: 5236: 5193: 5190: 5169: 5165: 5160: 5158: 5154: 5150: 5146: 5137: 5132: 5117: 5115: 5110: 5106: 5102: 5097: 5094: 5090: 5086: 5082: 5078: 5074: 5070: 5060: 5055: 5051: 5041: 5037: 4979: 4976: 4950: 4942: 4934: 4930: 4904: 4862: 4854: 4846: 4838: 4835: 4827: 4821: 4818: 4808: 4802: 4794: 4786: 4782: 4776: 4773: 4763: 4757: 4753: 4747: 4744: 4734: 4711: 4703: 4695: 4682: 4681:cross product 4633: 4631: 4627: 4623: 4613: 4599: 4578: 4558: 4553: 4547: 4535: 4531: 4522: 4517: 4514: 4511: 4507: 4503: 4476: 4466: 4463: 4460: 4455: 4441:at positions 4426: 4422: 4418: 4415: 4412: 4407: 4403: 4389: 4385: 4381: 4376: 4371: 4361: 4359: 4348: 4346: 4329: 4325: 4317: 4314: 4301: 4297: 4292: 4288: 4284: 4280: 4276: 4272: 4262: 4222: 4219: 4214: 4211: 4200: 4194: 4191: 4181: 4175: 4172: 4122: 4091: 4085: 4072: 4071: 4064: 4059: 4049: 4047: 4043: 4039: 4034: 4018: 4014: 4010: 4005: 4002: 3994: 3993:Taylor series 3978: 3958: 3950: 3934: 3914: 3894: 3874: 3871: 3868: 3865: 3860: 3857: 3852: 3849: 3841: 3837: 3833: 3828: 3823: 3819: 3806: 3801: 3787: 3784: 3781: 3761: 3741: 3719: 3715: 3711: 3689: 3668: 3665: 3662: 3659: 3656: 3653: 3650: 3647: 3644: 3641: 3638: 3635: 3629: 3623: 3603: 3599: 3596: 3593: 3590: 3582: 3578: 3574: 3569: 3564: 3560: 3553: 3533: 3530: 3527: 3524: 3521: 3513: 3497: 3494: 3491: 3471: 3468: 3465: 3445: 3425: 3413: 3408: 3403: 3393: 3390: 3386: 3382: 3368: 3346: 3342: 3337: 3333: 3330: 3327: 3319: 3303: 3299: 3293: 3289: 3285: 3277: 3259: 3254: 3250: 3244: 3241: 3221: 3201: 3189: 3184: 3179: 3169: 3155: 3147: 3143: 3138: 3125: 3119: 3110: 3100: 3096: 3089: 3085: 3080: 3077: 3071: 3068: 3048: 3028: 3008: 2988: 2968: 2948: 2928: 2925: 2905: 2885: 2865: 2845: 2825: 2818: 2814: 2809: 2806: 2803: 2797: 2794: 2786: 2782: 2774: 2770: 2766: 2765:bouncing ball 2761: 2756: 2752: 2742: 2733: 2731: 2726: 2725:Frank Wilczek 2715: 2656: 2650: 2647: 2640: 2630: 2624: 2618: 2615: 2608: 2598: 2592: 2586: 2583: 2573: 2526: 2516: 2511: 2501: 2474: 2445: 2430: 2426: 2422: 2417: 2415: 2411: 2403: 2399: 2395: 2391: 2387: 2381: 2378: 2377: 2371: 2346: 2342: 2338: 2333: 2331: 2327: 2323: 2318: 2317: 2313: 2309: 2305: 2297: 2293: 2289: 2285: 2281: 2276: 2272: 2259: 2251: 2247: 2243: 2231: 2227: 2220: 2217: 2192: 2183: 2180: 2174: 2171: 2161: 2155: 2152: 2127: 2107: 2100: 2097: 2087: 2081: 2056: 2047: 2044: 2031: 2024: 2021: 2020: 2014: 2012: 2007: 2002: 1997: 1995: 1988: 1985: 1984: 1983: 1977: 1973: 1968: 1954: 1951: 1947: 1943: 1939: 1935: 1931: 1927: 1922: 1920: 1896: 1886: 1882: 1874: 1864: 1857: 1798: 1793: 1774: 1770: 1766: 1761: 1756: 1752: 1740: 1724: 1718: 1707: 1701: 1698: 1692: 1686: 1683: 1677: 1669: 1663: 1652: 1646: 1643: 1638: 1635: 1629: 1626: 1618: 1603: 1597: 1586: 1580: 1577: 1571: 1565: 1562: 1556: 1548: 1542: 1531: 1525: 1522: 1517: 1514: 1491: 1488: 1485: 1479: 1473: 1466: 1462: 1455: 1428: 1424: 1403: 1383: 1361: 1357: 1336: 1313: 1307: 1300:. A function 1299: 1283: 1280: 1260: 1257: 1249: 1233: 1227: 1224: 1219: 1216: 1210: 1207: 1187: 1159: 1158:instantaneous 1155: 1138: 1130: 1094: 1086: 1082: 1078: 1073: 1069: 1058: 1054: 1047: 1044: 1036: 1032: 1025: 1019: 1013: 1005: 977: 973: 950: 946: 922: 916: 908: 904: 899: 896: 892: 885:Prerequisites 882: 880: 876: 872: 868: 864: 860: 859: 854: 846: 843: 839: 835: 832: 831: 830: 828: 824: 820: 816: 815:physical laws 812: 801: 796: 794: 789: 787: 782: 781: 779: 778: 772: 762: 759: 754: 748: 747: 746: 745: 737: 734: 732: 729: 727: 724: 722: 719: 717: 714: 712: 709: 707: 704: 702: 699: 697: 694: 692: 689: 687: 684: 682: 679: 677: 674: 672: 669: 667: 664: 662: 659: 657: 654: 652: 649: 647: 644: 642: 639: 637: 634: 632: 629: 627: 624: 622: 619: 618: 611: 610: 603: 599: 595: 591: 588: 587: 583: 580: 578: 575: 573: 570: 568: 565: 561: 558: 557: 556: 553: 551: 548: 546: 543: 541: 538: 537: 533: 528: 527: 519: 516: 514: 511: 507: 504: 502: 499: 498: 497: 494: 492: 489: 487: 484: 482: 477: 474: 470: 467: 466: 462: 459: 456: 452: 448: 447: 443: 440: 438: 435: 433: 430: 428: 423: 421: 418: 416: 413: 411: 408: 407: 400: 399: 388: 385: 383: 380: 378: 375: 373: 370: 368: 365: 363: 360: 359: 357: 356: 351: 348: 347: 342: 341: 335: 334: 326: 323: 321: 318: 316: 313: 311: 308: 306: 303: 301: 298: 296: 293: 291: 287: 285: 282: 280: 276: 274: 271: 268: 264: 260: 258: 255: 253: 250: 248: 245: 243: 240: 236: 233: 231: 228: 227: 226: 223: 221: 218: 216: 213: 211: 208: 206: 203: 202: 195: 194: 186: 183: 181: 178: 176: 173: 171: 168: 166: 163: 161: 158: 156: 153: 151: 148: 147: 140: 139: 133: 130: 128: 125: 123: 120: 119: 117: 116: 112: 93: 90: 80: 74: 60: 59: 56: 53: 52: 48: 47: 44: 40: 33: 19: 16071:Isaac Newton 16050:Solar System 15961:Isaac Newton 15873: 15866: 15858: 15849: 15782:Isaac Barrow 15720: (home) 15515: 15461:Newtonianism 15436:Newton scale 15399:Impact depth 15372: (1754) 15367: 15364: (1728) 15359: 15349: 15336: 15321: 15307: (1711) 15302: 15299: (1707) 15294: 15291: (1704) 15286: 15283: (1704) 15278: 15275: (1687) 15270: 15267: (1684) 15262: 15259: (1671) 15254: 15248:Publications 15199:. Retrieved 15193: 15186:Frebel, Anna 15143: 15140:Reich, Karin 15134: 15101: 15095: 15085: 15073:. Retrieved 15059:. Retrieved 15045:. Retrieved 15041: 15028: 14987: 14981: 14971: 14930: 14924: 14914: 14904: 14900: 14898: 14891:. Retrieved 14885: 14875: 14847: 14837: 14796: 14790: 14780: 14768:. Retrieved 14762: 14756: 14748: 14715: 14709: 14699: 14671: 14661: 14652: 14624: 14618: 14608: 14573: 14567: 14526: 14520: 14510: 14477: 14471: 14461: 14428: 14422: 14412: 14400:. 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Retrieved 12426: 12419: 12391: 12381: 12340: 12334: 12324: 12291: 12285: 12272: 12244: 12198: 12192: 12182: 12149: 12143: 12130: 12079: 12073: 12063: 12030: 12024: 12017:Ball, Philip 12011: 11958: 11952: 11942: 11913: 11902: 11870: 11829: 11815: 11784: 11766: 11729: 11720: 11711: 11705: 11697:(May 1995). 11695:Xia, Zhihong 11685: 11640: 11634: 11624: 11597: 11594:Zee, Anthony 11552: 11546: 11533: 11482: 11476: 11438: 11432: 11422: 11389: 11383: 11373: 11345: 11341:Leader, Imre 11292: 11282: 11241: 11235: 11225: 11195:(2): L7–L9. 11192: 11186: 11176: 11143: 11137: 11127: 11097:(1): 18–19. 11094: 11088: 11078: 11050: 11032: 10989: 10983: 10976:Chabay, Ruth 10970: 10937: 10931: 10918: 10890: 10842:(1): 59–66. 10839: 10833: 10823: 10795: 10785: 10757: 10689: 10683: 10673: 10661:. Retrieved 10657: 10644: 10614:(1): 24–32. 10611: 10605: 10592: 10549: 10543: 10530: 10520: 10506: 10487: 10481: 10461: 10454: 10424:(1): 41–45. 10421: 10415: 10402: 10390:. Retrieved 10386: 10370: 10361: 10351: 10310: 10304: 10294: 10261: 10255: 10242: 10212:(1): 54–65. 10209: 10203: 10193: 10174: 10165: 10146: 10136: 10127: 10093: 10049: 10011: 10005: 9996: 9968: 9919: 9913: 9899: 9882: 9876: 9867: 9861: 9828: 9822: 9812: 9784: 9732: 9723: 9714: 9704: 9680:(1): 60–73. 9677: 9673: 9667: 9639: 9593: 9587: 9555: 9548: 9513: 9507: 9497: 9464: 9458: 9448: 9420: 9368: 9362: 9349: 9321: 9277: 9245:. Retrieved 9241: 9225: 9197: 9190: 9180: 9173: 9164: 9135: 9128: 9105:protoscience 9091: 9079: 9070: 9061: 9056: 9047: 9038: 9029: 9020: 9011: 9002: 8993: 8984: 8933: 8923: 8915: 8911: 8906: 8896: 8883: 8825:invented by 8812: 8807:living force 8799: 8790: 8784: 8739: 8731: 8723: 8721: 8711: 8703: 8692: 8684: 8674: 8655: 8644: 8638: 8614: 8606: 8596: 8589: 8582: 8580: 8562: 8558: 8552: 8542: 8538: 8533: 8519: 8513: 8502: 8487: 8481: 8478: 8463: 8452:heliocentric 8450:purported a 8447: 8443: 8437: 8431: 8412:John Buridan 8385: 8365: 8337: 8326: 8308:Wren Library 8301: 8250: 8237: 8233: 8223: 8215: 8213:to express. 8192: 8184: 8180: 8176:four-vectors 8088: 8068: 8064: 8052: 8044: 7961: 7890: 7861: 7859: 7830:exerts upon 7740: 7729: 7619: 7600: 7426: 7422: 6546: 6538: 6535: 6129: 6120:Emmy Noether 6098: 5655: 5629: 5613: 5605: 5238: 5234: 5161: 5142: 5131:Chaos theory 5098: 5093:eccentricity 5065: 5038: 4634: 4619: 4395:with masses 4393: 4354: 4290: 4268: 4076: 4069: 4041: 4037: 4035: 3802: 3702:is equal to 3417: 3410:An undamped 3383: 3193: 3139: 2778: 2739: 2721: 2425:force fields 2418: 2413: 2407: 2379: 2336: 2334: 2319: 2315: 2311: 2301: 2295: 2291: 2287: 2284:normal force 2120:If the mass 2027: 2022: 2005: 1998: 1991: 1986: 1981: 1949: 1945: 1941: 1937: 1933: 1929: 1925: 1923: 1794: 1738: 1617:Acceleration 1616: 1157: 900: 894: 890: 888: 862: 856: 853:Isaac Newton 850: 838:acceleration 826: 810: 809: 600: / 596: / 594:displacement 592: / 485: 453: / 415:Displacement 353: 345: 344: 338:Formulations 325:Virtual work 265: / 205:Acceleration 198:Fundamentals 43: 32:Newton's law 15990:Mathematics 15861:by Paolozzi 15800:Roger Cotes 15409:Newton disc 15323:Quaestiones 15296:Arithmetica 14354:Jammer, Max 13444:2158/530056 12942:10852/74677 11908:Byers, Nina 10791:Brown, Mike 10658:Physics 361 10516:"Mechanics" 10102:Bell, J. S. 10014:: 144–159. 9831:: 160–166. 9247:12 February 9231:Tong, David 8914:instead of 8823:quaternions 8666:John Wallis 8635:(1571–1630) 8577:(1629–1695) 8499:(1596–1650) 8475:(1564–1642) 8242:measurement 7732:electricity 7188:chain rules 6553:wave optics 6111:Hamiltonian 5101:closed form 5079:, that is, 736:von Neumann 403:Core topics 16060:Categories 15948:Categories 15924:XMM-Newton 15841:Depictions 15812:John Keill 15734:Apple tree 15729:Later life 15724:Early life 15304:De Analysi 15201:17 January 15034:Gbur, Greg 14755:"Newton's 14280:1144105192 14119:1058581988 13126:1908.07936 13068:1802.10119 13035:1020305599 12997:1164503847 12857:1202475208 12532:1805.01372 12089:1910.09414 11986:1808/29610 11934:1150964892 11758:1195899886 11739:1609.01421 11714:: 538–546. 11650:2006.14924 11616:1288147292 10663:16 January 10392:13 January 10129:mechanics. 9741:1120819093 9687:2112.02339 9416:Gbur, Greg 9217:1084752471 9120:References 8889:David Tong 8724:Principia, 8691:After the 8685:Principia, 8607:immaterial 8426:See also: 8356:Aristotle 8260:, and the 7429:derivative 5652:Lagrangian 5241:derivative 5155:, and the 5089:hyperbolas 3188:barycenter 2402:atmosphere 2337:definition 2017:Second law 1248:derivative 903:kinematics 813:are three 671:d'Alembert 651:Maupertuis 614:Scientists 496:Rigid body 170:Kinematics 16026:Astronomy 15763:Relations 15272:Principia 15162:799299609 15126:0002-9505 15020:122097990 15012:0031-9120 14905:Principia 14845:(2005) . 14829:125948408 14821:0143-0807 14732:0039-7857 14691:892067655 14649:246612625 14641:0007-0874 14600:972369868 14559:145120248 14543:0007-0874 14502:0031-9228 14453:0002-9505 14356:(1999) . 14340:144575106 14324:0021-1753 14245:243203703 14237:0021-1753 14193:953450997 14083:934741893 14048:170120455 14040:0036-8075 13996:0002-9505 13947:144406041 13877:182818133 13834:0277-903X 13756:144278075 13704:243143427 13696:2469-9896 13647:233803836 13639:0031-921X 13600:149482566 13592:2469-9896 13538:495305340 13502:878730683 13453:0002-9505 13386:0392-095X 13355:874097920 13318:759812415 13214:126311599 13206:0143-0807 13151:182656563 13143:1233-1821 13093:119546199 12959:127471222 12951:0031-9120 12819:0034-6861 12700:317496332 12659:122180759 12651:1751-8113 12557:0002-9505 12476:(2005) . 12373:126380404 12365:0143-0807 12316:0002-9505 12264:966177746 12223:0002-9505 12174:0002-9505 12122:204800598 12114:0002-9505 12055:204188746 12003:203484310 11995:2469-9896 11894:860391091 11827:(1990) . 11807:466500872 11677:220127889 11669:0002-9939 11577:0002-9505 11517:0143-0807 11492:1012.4384 11455:0002-9505 11414:0002-9505 11365:682200048 11274:119949261 11266:0143-0807 11217:121740340 11209:0143-0807 11168:0002-9505 11119:0031-921X 11070:794034942 11024:197512796 11016:0002-9505 10962:0002-9505 10872:250883796 10864:0143-0807 10815:495271396 10734:215832738 10726:2469-9896 10636:122113958 10628:0025-570X 10576:0028-0836 10446:0031-921X 10343:250891975 10335:0031-9120 10286:0031-921X 10234:0002-9505 10124:898931862 10094:Mechanics 10047:(1989) . 9988:854617117 9946:1554-9178 9853:125131430 9804:857769535 9659:227002144 9579:895896190 9540:1554-9178 9489:250781921 9440:704518582 9393:0002-9505 9341:799163595 9296:794034942 9097:alchemist 8791:Principia 8740:Principia 8732:Principia 8693:Principia 8615:Principia 8464:The World 8448:The World 8439:The World 8376:viscosity 8368:Aristotle 8358:(384–322 8303:Principia 8262:Born rule 8198:spacetime 8158:γ 8148:rest mass 8109:γ 8005:ω 7932:× 7736:magnetism 7705:ξ 7680:γ 7658:ξ 7646:γ 7643:− 7539:∇ 7535:⋅ 7518:∂ 7514:∂ 7490:∇ 7486:⋅ 7479:∇ 7451:∂ 7447:∂ 7401:∇ 7397:− 7387:∇ 7372:∇ 7368:⋅ 7361:∇ 7333:∂ 7329:∂ 7275:∇ 7264:∇ 7254:∇ 7250:⋅ 7243:∇ 7217:∇ 7207:∂ 7203:∂ 7198:− 7163:∇ 7141:∇ 7130:∇ 7102:∂ 7094:∂ 7087:∇ 7083:− 7028:∇ 6994:∂ 6986:∂ 6980:− 6911:∇ 6882:∂ 6874:∂ 6868:− 6841:∇ 6649:and time 6599:… 6498:− 6393:∂ 6381:∂ 6375:− 6326:∂ 6314:∂ 6061:− 6049:˙ 5989:∂ 5981:∂ 5962:˙ 5953:∂ 5945:∂ 5802:˙ 5750:− 5735:˙ 5694:˙ 5582:ν 5540:∇ 5536:ν 5526:∇ 5520:ρ 5512:− 5493:⋅ 5489:∇ 5473:∂ 5465:∂ 5448:viscosity 5392:ρ 5357:∇ 5351:ρ 5343:− 5324:⋅ 5320:∇ 5304:∂ 5296:∂ 5109:variables 5085:parabolas 4943:× 4931:τ 4855:× 4836:× 4803:× 4787:× 4704:× 4508:∑ 4464:… 4416:… 4388:toothpick 4322:∇ 4318:− 4279:potential 4201:− 4046:resonance 4003:ω 3979:θ 3959:θ 3935:θ 3915:θ 3872:θ 3869:⁡ 3853:− 3829:θ 3690:ω 3666:ω 3663:⁡ 3648:ω 3645:⁡ 3594:− 3528:− 3097:≈ 2781:free fall 2751:Free fall 2374:Third law 2341:tautology 2316:unstable. 1962:First law 1716:Δ 1699:− 1690:Δ 1667:→ 1661:Δ 1595:Δ 1578:− 1569:Δ 1546:→ 1540:Δ 1459:→ 1168:Δ 1115:Δ 1079:− 1045:− 1011:Δ 1003:Δ 716:Liouville 598:frequency 518:Vibration 235:potential 160:Continuum 155:Celestial 132:Textbooks 15886:Namesake 15852:by Blake 15446:Spectrum 15387:Calculus 15356: ) 15256:Fluxions 14963:46923474 14955:29857796 14933:: 1–11. 14867:57579169 14740:11794836 14711:Synthese 14669:(1969). 14551:25592244 14376:40964671 14296:(1962). 14099:(1975). 13806:(1955). 13494:44216227 13394:43915795 13284:28854083 13258:(1993). 13119:: 7–26. 13013:(2018). 12975:(2021). 12758:(1968). 12742:44694623 12720:(2000). 12678:(2009). 12606:47056311 12565:53625857 12498:56526974 12451:24 March 12389:(1966). 12242:(2016). 11868:(2007). 11849:20934820 11782:(eds.). 11596:(2020). 11525:58892714 11343:(eds.). 11290:(1997). 10910:37903527 10793:(2010). 10777:61332593 10755:(2006). 10652:(2020). 10514:(1889). 10378:(2003). 10092:(1969). 9891:66-11527 9731:(1968). 9637:(2007). 9561:OpenStax 9418:(2011). 9319:(1998). 8943:Eisenbud 8833:See also 8706:(1831), 8458:and the 8404:Avicenna 8126:, where 7615:pressure 7427:material 6792:gradient 5285:becomes 5239:material 5081:ellipses 4296:gradient 4070:Atlantis 3805:pendulum 3361:, where 3146:parabola 2773:parabola 2736:Examples 2410:reaction 2370:matter. 2030:momentum 1938:pressure 1154:Calculus 895:particle 842:momentum 771:Category 696:Hamilton 681:Lagrange 676:Clairaut 641:Horrocks 602:velocity 572:Pendulum 560:reactive 532:Rotation 501:dynamics 451:Inertial 437:Friction 320:Velocity 295:Momentum 175:Kinetics 165:Dynamics 143:Branches 127:Timeline 16002:Physics 15976:Portals 15404:Inertia 15392:fluxion 15288:Queries 15280:Opticks 15264:De Motu 15106:Bibcode 15075:7 March 15061:7 March 15047:7 March 14992:Bibcode 14935:Bibcode 14893:6 March 14801:Bibcode 14770:6 March 14482:Bibcode 14433:Bibcode 14402:6 March 14152:5677169 14019:Science 13976:Bibcode 13842:2858681 13674:Bibcode 13570:Bibcode 13459:Physics 13423:Bibcode 13184:Bibcode 13073:Bibcode 12919:Bibcode 12799:Bibcode 12631:Bibcode 12537:Bibcode 12345:Bibcode 12296:Bibcode 12203:Bibcode 12154:Bibcode 12094:Bibcode 12035:Bibcode 12033:: 100. 12026:Physics 11963:Bibcode 11557:Bibcode 11497:Bibcode 11394:Bibcode 11298:Bibcode 11246:Bibcode 11148:Bibcode 11099:Bibcode 10994:Bibcode 10942:Bibcode 10844:Bibcode 10694:Bibcode 10584:4016382 10554:Bibcode 10426:Bibcode 10315:Bibcode 10266:Bibcode 10214:Bibcode 9924:Bibcode 9883:Physics 9833:Bibcode 9518:Bibcode 9469:Bibcode 9373:Bibcode 8489:limits. 8396:impetus 8372:density 8269:History 8240:when a 8170:is the 5594:is the 5245:density 4275:kinetic 4038:damped, 3316:. 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2502:= 2498:p 2475:2 2470:p 2446:1 2441:p 2404:. 2356:F 2296:f 2288:N 2260:. 2252:2 2248:t 2244:d 2238:s 2232:2 2228:d 2221:m 2218:= 2214:F 2193:. 2188:a 2184:m 2181:= 2175:t 2172:d 2166:v 2162:d 2156:m 2153:= 2149:F 2128:m 2108:. 2101:t 2098:d 2092:p 2088:d 2082:= 2078:F 2057:, 2052:v 2048:m 2045:= 2041:p 1978:. 1905:) 1901:s 1897:/ 1893:m 1887:4 1883:, 1879:s 1875:/ 1871:m 1865:3 1861:( 1858:= 1854:v 1831:s 1808:s 1775:2 1771:t 1767:d 1762:s 1757:2 1753:d 1725:. 1719:t 1711:) 1708:t 1705:( 1702:v 1696:) 1693:t 1687:+ 1684:t 1681:( 1678:v 1670:0 1664:t 1653:= 1647:t 1644:d 1639:v 1636:d 1630:= 1627:a 1604:. 1598:t 1590:) 1587:t 1584:( 1581:s 1575:) 1572:t 1566:+ 1563:t 1560:( 1557:s 1549:0 1543:t 1532:= 1526:t 1523:d 1518:s 1515:d 1492:. 1489:L 1486:= 1483:) 1480:t 1477:( 1474:f 1467:0 1463:t 1456:t 1429:0 1425:t 1404:L 1384:f 1362:0 1358:t 1337:L 1317:) 1314:t 1311:( 1308:f 1284:t 1281:d 1261:s 1258:d 1234:. 1228:t 1225:d 1220:s 1217:d 1211:= 1208:v 1188:d 1139:s 1127:( 1095:. 1087:0 1083:t 1074:1 1070:t 1064:) 1059:0 1055:t 1051:( 1048:s 1042:) 1037:1 1033:t 1029:( 1026:s 1020:= 1014:t 1006:s 978:1 974:t 951:0 947:t 926:) 923:t 920:( 917:s 861:( 799:e 792:t 785:v 475:) 94:t 91:d 85:p 81:d 75:= 70:F 41:. 34:. 20:)

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Knowledge

Newton's laws of motion

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