1161:, the net force acting on them is therefore zero (all forces acting on them cancel each other out). If the car enters a curve that bends to the left, the passenger experiences an apparent force that seems to be pulling them towards the right. This is the fictitious centrifugal force. It is needed within the passengers' local frame of reference to explain their sudden tendency to start accelerating to the right relative to the car—a tendency which they must resist by applying a lefttward force to the car (for instance, a frictional force against the seat) in order to remain in a fixed position inside. Since they push the seat toward the right, Newton's third law says that the seat pushes them towards the left. The centrifugal force must be included in the passenger's reference frame (in which the passenger remains at rest): it counteracts the leftward force applied to the passenger by the seat, and explains why this otherwise unbalanced force does not cause them to accelerate. However, it would be apparent to a stationary observer watching from an overpass above that the frictional force exerted on the passenger by the seat is not being balanced; it constitutes a net force to the left, causing the passenger to accelerate toward the inside of the curve, as they must in order to keep moving with the car rather than proceeding in a straight line as they otherwise would. Thus the "centrifugal force" they feel is the result of a "centrifugal tendency" caused by inertia. Similar effects are encountered in aeroplanes and
2710:
1935:
1250:, the same two real forces act upon the object. However, the object is moving in a circular path as the Earth rotates and therefore experiencing a centripetal acceleration. When considered in an inertial frame (that is to say, one that is not rotating with the Earth), the non-zero acceleration means that force of gravity will not balance with the force from the spring. In order to have a net centripetal force, the magnitude of the restoring force of the spring must be less than the magnitude of force of gravity. This reduced restoring force in the spring is reflected on the scale as less weight — about 0.3% less at the equator than at the poles. In the Earth reference frame (in which the object being weighed is at rest), the object does not appear to be accelerating; however, the two real forces, gravity and the force from the spring, are the same magnitude and do not balance. The centrifugal force must be included to make the sum of the forces be zero to match the apparent lack of acceleration.
2705:{\displaystyle {\begin{aligned}{\boldsymbol {a}}&={\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}={\frac {\mathrm {d} }{\mathrm {d} t}}{\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}={\frac {\mathrm {d} }{\mathrm {d} t}}\left(\left+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ \right)\\&=\left+{\boldsymbol {\omega }}\times \left+{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}+{\boldsymbol {\omega }}\times {\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}\\&=\left+{\boldsymbol {\omega }}\times \left+{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}+{\boldsymbol {\omega }}\times \left(\left+{\boldsymbol {\omega }}\times {\boldsymbol {r}}\ \right)\\&=\left+{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}+2{\boldsymbol {\omega }}\times \left+{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})\ .\end{aligned}}}
3682:
742:
1143:) is required. These fictitious forces are necessary for the formulation of correct equations of motion in a rotating reference frame and allow Newton's laws to be used in their normal form in such a frame (with one exception: the fictitious forces do not obey Newton's third law: they have no equal and opposite counterparts). Newton's third law requires the counterparts to exist within the same frame of reference, hence centrifugal and centripetal force, which do not, are not action and reaction (as is sometimes erroneously contended).
755:
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1123:" is generally taken to be an inertial frame. Any system can be analyzed in an inertial frame (and so with no centrifugal force). However, it is often more convenient to describe a rotating system by using a rotating frame—the calculations are simpler, and descriptions more intuitive. When this choice is made, fictitious forces, including the centrifugal force, arise.
1193:, in this case provided by the string, must be continuously applied to the stone. As soon as it is removed (for example if the string breaks) the stone moves in a straight line, as viewed from above. In this inertial frame, the concept of centrifugal force is not required as all motion can be properly described using only real forces and Newton's laws of motion.
1222:" at any point on the Earth's surface is actually a combination of gravitational and centrifugal forces. However, the fictitious forces can be of arbitrary size. For example, in an Earth-bound reference system (where the earth is represented as stationary), the fictitious force (the net of Coriolis and centrifugal forces) is enormous and is responsible for the
3609:)} are sometimes called centrifugal forces. In the case of motion in a central potential the Lagrangian centrifugal force has the same form as the fictitious centrifugal force derived in a co-rotating frame. However, the Lagrangian use of "centrifugal force" in other, more general cases has only a limited connection to the Newtonian definition.
1000:, as it might be called, a subject about which I have more to say than I am able to do at present. But, in order that those interested in these things can sooner enjoy these new and not useless speculations, and in order that their publication not be prevented by some accident, I have decided, contrary to my plan, to add this fifth part .
2841:. Therefore, the observer perceives the extra terms as contributions due to fictitious forces. These terms in the apparent acceleration are independent of mass; so it appears that each of these fictitious forces, like gravity, pulls on an object in proportion to its mass. When these forces are added, the equation of motion has the form:
2844:
1126:
In a reference frame rotating about an axis through its origin, all objects, regardless of their state of motion, appear to be under the influence of a radially (from the axis of rotation) outward force that is proportional to their mass, to the distance from the axis of rotation of the frame, and to
1118:
All measurements of position and velocity must be made relative to some frame of reference. For example, an analysis of the motion of an object in an airliner in flight could be made relative to the airliner, to the surface of the Earth, or even to the Sun. A reference frame that is at rest (or one
1083:
was proposed where, instead of absolute rotation, the motion of the distant stars relative to the local inertial frame gives rise through some (hypothetical) physical law to the centrifugal force and other inertia effects. Today's view is based upon the idea of an inertial frame of reference, which
995:
There is another kind of oscillation in addition to the one we have examined up to this point; namely, a motion in which a suspended weight is moved around through the circumference of a circle. From this we were led to the construction of another clock at about the same time we invented the first
1242:
in the spring, acting upward. Since the object is stationary and not accelerating, there is no net force acting on the object and the force from the spring is equal in magnitude to the force of gravity on the object. In this case, the balance shows the value of the force of gravity on the object.
30:
In the inertial frame of reference (upper part of the picture), the black ball moves in a straight line. However, the observer (brown dot) who is standing in the rotating/non-inertial frame of reference (lower part of the picture) sees the object as following a curved path due to the
Coriolis and
3418:, the balance between containment by gravitational attraction and dispersal by centrifugal force. That the Earth is itself an oblate spheroid, bulging at the equator where the radial distance and hence the centrifugal force is larger, is taken as one of the evidences for its absolute rotation.
1196:
In a frame of reference rotating with the stone around the same axis as the stone, the stone is stationary. However, the force applied by the string is still acting on the stone. If one were to apply Newton's laws in their usual (inertial frame) form, one would conclude that the stone should
3405:
In these scenarios, the effects attributed to centrifugal force are only observed in the local frame (the frame in which the object is stationary) if the object is undergoing absolute rotation relative to an inertial frame. By contrast, in an inertial frame, the observed effects arise as a
1156:
A common experience that gives rise to the idea of a centrifugal force is encountered by passengers riding in a vehicle, such as a car, that is changing direction. If a car is traveling at a constant speed along a straight road, then a passenger inside is not accelerating and, according to
1213:
around its axis. Because the rotation is slow, the fictitious forces it produces are often small, and in everyday situations can generally be neglected. Even in calculations requiring high precision, the centrifugal force is generally not explicitly included, but rather lumped in with the
3049:
From the perspective of the rotating frame, the additional force terms are experienced just like the real external forces and contribute to the apparent acceleration. The additional terms on the force side of the equation can be recognized as, reading from left to right, the
3406:
consequence of the inertia and the known forces without the need to introduce a centrifugal force. Based on this argument, the privileged frame, wherein the laws of physics take on the simplest form, is a stationary frame in which no fictitious forces need to be invoked.
1596:
1177:
If a stone is whirled round on a string, in a horizontal plane, the only real force acting on the stone in the horizontal plane is applied by the string (gravity acts vertically). There is a net force on the stone in the horizontal plane which acts toward the center.
3513:
Nevertheless, all of these systems can also be described without requiring the concept of centrifugal force, in terms of motions and forces in a stationary frame, at the cost of taking somewhat more care in the consideration of forces and motions within the system.
3489:
are used in science and industry to separate substances. In the reference frame spinning with the centrifuge, the centrifugal force induces a hydrostatic pressure gradient in fluid-filled tubes oriented perpendicular to the axis of rotation, giving rise to large
1197:
accelerate in the direction of the net applied force—towards the axis of rotation—which it does not do. The centrifugal force and other fictitious forces must be included along with the real forces in order to apply Newton's laws of motion in the rotating frame.
3409:
Within this view of physics, any other phenomenon that is usually attributed to centrifugal force can be used to identify absolute rotation. For example, the oblateness of a sphere of freely flowing material is often explained in terms of centrifugal force. The
3350:
the centrifugal force and all other fictitious forces disappear. Similarly, as the centrifugal force is proportional to the distance from object to the axis of rotation of the frame, the centrifugal force vanishes for objects that lie upon the axis.
3040:{\displaystyle {\boldsymbol {F}}-m{\frac {\mathrm {d} {\boldsymbol {\omega }}}{\mathrm {d} t}}\times {\boldsymbol {r}}-2m{\boldsymbol {\omega }}\times \left-m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})=m\left\ .}
1808:
3225:
3385:
Three scenarios were suggested by Newton to answer the question of whether the absolute rotation of a local frame can be detected; that is, if an observer can decide whether an observed object is rotating or if the observer is rotating.
3445:
is used in small engine-powered devices such as chain saws, go-karts and model helicopters. It allows the engine to start and idle without driving the device but automatically and smoothly engages the drive as the engine speed rises.
3105:
2784:. An observer unaware of the rotation would expect this to be zero in the absence of outside forces. However, Newton's laws of motion apply only in the inertial frame and describe dynamics in terms of the absolute acceleration
1131:
of the frame. This is the centrifugal force. As humans usually experience centrifugal force from within the rotating reference frame, e.g. on a merry-go-round or vehicle, this is much more well-known than centripetal force.
1075:
argument. According to Newton, in each scenario the centrifugal force would be observed in the object's local frame (the frame where the object is stationary) only if the frame were rotating with respect to absolute space.
2839:
5094:, a kind of "centrifugal force" arises ... We call this force "democratic centrifugal force". Of course, DCF is different from the ordinary centrifugal force, and it arises even in a system of zero angular momentum.
1499:
1860:
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privileges observers for which the laws of physics take on their simplest form, and in particular, frames that do not use centrifugal forces in their equations of motion in order to describe motions correctly.
1656:
96:
1930:
1721:
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1940:
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1262:, so an object at the poles is slightly closer to the center of the Earth than one at the equator; this effect combines with the centrifugal force to produce the observed weight difference.
27:
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3526:
to refer to the particular fictitious force that arises in rotating frames, there are a few limited instances in the literature of the term applied to other distinct physical concepts.
3348:
1742:
4844:
4586:
Noninertial forces, like centrifugal and
Coriolis forces, can be eliminated by jumping into a reference frame that moves with constant velocity, the frame that Newton called inertial.
3314:
3265:
4911:
3316:, and unlike the Coriolis force in particular, it is independent of the motion of the particle in the rotating frame. As expected, for a non-rotating inertial frame of reference
5000:
4866:
120:
877:
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3227:, respectively. Unlike the other two fictitious forces, the centrifugal force always points radially outward from the axis of rotation of the rotating frame, with magnitude
3582:
3292:
3180:
1616:
3494:
which push low-density particles inward. Elements or particles denser than the fluid move outward under the influence of the centrifugal force. This is effectively
2782:
3401:
about their center of mass. The tension in the string will be proportional to the centrifugal force on each sphere as it rotates around the common center of mass.
3056:
5250:
3659:, that is, a force that is centrifugally directed, which is a reactive force equal and opposite to the centripetal force that is curving the path of the mass.
1238:
at one of the Earth's poles, there are two forces acting on the object: the Earth's gravity, which acts in a downward direction, and the equal and opposite
4372:
1258:
In fact, the observed weight difference is more — about 0.53%. Earth's gravity is a bit stronger at the poles than at the equator, because the Earth is
5159:"The intrinsic derivative and centrifugal forces in general relativity: II. Applications to circular orbits in some stationary axisymmetric spacetimes"
2787:
3375:
When analysed in a rotating reference frame of the planet, centrifugal force causes rotating planets to assume the shape of an oblate spheroid.
1033:
1687:
935:
786:
4565:
3886:
3426:
The operations of numerous common rotating mechanical systems are most easily conceptualized in terms of centrifugal force. For example:
375:
1822:
996:
one. I originally intended to publish here a lengthy description of these clocks, along with matters pertaining to circular motion and
4817:, there are three types of terms. The first involves the second derivative of the generalized co-ordinates. The second is quadratic in
494:
4354:
1631:
1312:
of time—such as the velocity and acceleration vectors of an object—will differ from its time derivatives in the stationary frame. If
467:
4162:
3662:
The concept of the reactive centrifugal force is sometimes used in mechanics and engineering. It is sometimes referred to as just
3785:
5051:
Geometrical
Structures Of Phase Space In Multi-dimensional Chaos: Applications to chemical reaction dynamics in complex systems
3652:
the other body that provides the centripetal force and its direction is from that other body toward the body in curved motion.
3509:'s spin forces riders against a wall and allows riders to be elevated above the machine's floor in defiance of Earth's gravity.
1591:{\displaystyle {\frac {\mathrm {d} {\boldsymbol {P}}}{\mathrm {d} t}}=\left+{\boldsymbol {\omega }}\times {\boldsymbol {P}}\ ,}
52:
3637:
3483:
are production methods that use centrifugal force to disperse liquid metal or plastic throughout the negative space of a mold.
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5058:
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4779:
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4690:
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Christiaan
Huygens' the pendulum clock, or, Geometrical demonstrations concerning the motion of pendula as applied to clocks
3827:
3113:
1865:
5366:
3438:, as the engine changes speed. In the reference frame of the spinning masses, centrifugal force causes the radial movement.
3636:
is provided by a centripetal force, which is exerted on the body in curved motion by some other body. In accordance with
1283:
449:
4471:
3907:(Andrew Motte translation of 1729, revised by Florian Cajori ed.). University of California Press. pp. 10–12.
5479:
3447:
5291:
5225:
3939:
3912:
3821:
3394:. The shape of the surface becomes concave to balance the centrifugal force against the other forces upon the liquid.
843:
779:
3480:
4920:
3681:
741:
3319:
115:
4796:
1628:
in the stationary frame is the sum of its apparent rate of change in the rotating frame and a rate of rotation
370:
110:
4820:
4383:
1185:, were it not for this net force acting on the stone, the stone would travel in a straight line, according to
3297:
3230:
4814:
3695:
3595:
1293:
815:
772:
759:
520:
443:
365:
208:
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1226:
orbiting around the Earth. This is due to the large mass and velocity of the Sun (relative to the Earth).
1289:
1182:
1112:
811:
439:
240:
3584:
or a much more extensive list of variables. Within this formulation the motion is described in terms of
218:
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4983:
4849:
4477:
3997:
3813:
A Catalogue of the
Manuscripts of Christiaan Huygens including a concordance with his Oeuvres Complètes
3625:
1186:
1158:
918:
659:
548:
474:
334:
267:
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1819:
By applying the transformation above from the stationary to the rotating frame three times (twice to
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about detection of absolute motion. Newton suggested two arguments to answer the question of whether
1042:
413:
5068:
4338:
5109:"The intrinsic derivative and centrifugal forces in general relativity: I. Theoretical foundations"
4571:
3633:
3552:
3495:
1803:{\displaystyle {\boldsymbol {a}}={\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\ ,}
1273:
1108:
1012:
and replied "I pray you return my humble thanks I am glad we can expect another discourse of the
983:
910:
689:
533:
810:(also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a
3539:
3220:{\displaystyle -m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})}
639:
403:
5049:. In Mikito Toda; Tamiki Komatsuzaki; Stuart A. Rice; Tetsuro Konishi; R. Stephen Berry (eds.).
3856:
3270:
679:
4659:
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684:
501:
5457:
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5281:
5019:
4682:
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4538:
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3902:
3705:
3415:
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1601:
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694:
669:
355:
173:
4708:
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regulates the speed of an engine by using spinning masses that move radially, adjusting the
5378:
5331:
5180:
5130:
4351:
4209:
4127:
4049:
3535:
3431:
3100:{\displaystyle -m\mathrm {d} {\boldsymbol {\omega }}/\mathrm {d} t\times {\boldsymbol {r}}}
2722:
1619:
988:
890:
714:
674:
582:
578:
570:
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350:
343:
99:
4261:
Introduction to
Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems
4026:
Restuccia, S.; Toroš, M.; Gibson, G. M.; Ulbricht, H.; Faccio, D.; Padgett, M. J. (2019).
1668:
equal to the rate of rotation and is directed along the axis of rotation according to the
709:
8:
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43:
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is the position vector of the particle (not to be confused with radius, as used above.)
1041:("centrifugal force"). Around this time, the concept is also further evolved by Newton,
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5170:
5146:
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3640:, the body in curved motion exerts an equal and opposite force on the other body. This
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3586:
3462:
3442:
1296:
that is rotating relative to an inertial reference frame denoted the stationary frame.
1096:
1088:
1052:
In the late 18th century, the modern conception of the centrifugal force evolved as a "
1017:
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894:
619:
360:
235:
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163:
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3598:. Among the generalized forces, those involving the square of the time derivatives {(d
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5297:
5287:
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4868:. These are further classified into two types. Terms involving a product of the type
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1064:
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586:
538:
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255:
245:
138:
20:
5270:. Michigan State University, "Acceleration and force in circular motion", §5b, p. 7.
5200:
5150:
5386:
5339:
5188:
5138:
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4057:
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4736:
4543:(Reprint of Fourth Edition of 1970 ed.). Dover Publications. Chapter 4, §5.
4358:
4027:
3811:
3629:
3411:
3391:
3367:
liquids rotating around a vertical axis is an upward-opening circular paraboloid.
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1259:
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1068:
1009:
902:
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528:
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As is evident from the first terms ..., which are proportional to the square of
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3455:
954:
5505:
3687:
3502:
3108:
1235:
1162:
1136:
746:
654:
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272:
5192:
5142:
2834:{\displaystyle {\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}}
1304:
In a rotating frame of reference, the time derivatives of any vector function
1139:. If the rate of rotation of the frame changes, a third fictitious force (the
5489:
4118:
Kobayashi, Yukio (2008). "Remarks on viewing situation in a rotating frame".
3983:
3720:
3670:
centrifugal force although this usage is deprecated in elementary mechanics.
3491:
3451:
1135:
Motion relative to a rotating frame results in another fictitious force: the
1087:
Around 1914, the analogy between centrifugal force (sometimes used to create
634:
461:
5301:
5235:
3949:
966:
4069:
3766:
3710:
3498:
as generated by centrifugal force as opposed to being generated by gravity.
3476:
1736:
1046:
1005:
906:
699:
624:
313:
193:
922:, a real frame-independent Newtonian force that exists as a reaction to a
4169:. Goddard Space Flight Center Space Physics Data Facility. Archived from
3364:
3051:
1140:
1120:
26:
5175:
5125:
3632:, is accelerating toward a center at any particular point in time. This
1739:(that is, acceleration in an inertial frame) of the particle, given by:
5156:
5106:
4413:(Reprint of Second Edition of 1942 ed.). Read Books. p. 347.
4210:
The
Feynman Lectures on Physics Vol. I Ch. 12: Characteristics of Force
3486:
1119:
that moves with no rotation and at constant velocity) relative to the "
882:
484:
158:
5390:
4010:
1229:
3506:
3371:
1729:
is the vector sum of the physical forces applied to the particle and
1496:
with respect to the stationary frame is related to by the equation:
1025:
1021:
941:
506:
5407:
An elementary treatise on analytic mechanics: with numerous examples
5158:
5108:
4713:(Reprint of 1970 University of Toronto ed.). Dover. p. 1.
4223:
881:
This fictitious force is often applied to rotating devices, such as
4044:
3435:
1855:{\textstyle {\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}}
425:
308:
283:
4771:
Cartesian
Impedance Control of Redundant and Flexible-Joint Robots
4624:
4097:. Sausalito CA: University Science Books. Chapter 9, pp. 344 ff.
3458:
used in many automobile seat belts operate on the same principle.
1247:
1166:
398:
251:
168:
5286:(2nd ed.). New Delhi: Prentice-Hall of India. p. 121.
4257:
3927:
1932:), the absolute acceleration of the particle can be written as:
1165:
where the magnitude of the apparent force is often reported in "
833:
from the axis of rotation of a frame of reference rotating with
5474:
3968:. Ingrid V. Eriksson. New York: Nova Science Publishers. 2008.
3931:
Mach's principle : from Newton's bucket to quantum gravity
3885:(in French). Vol. 7. The Hague: M. Nijhoff. 1897. p.
1651:{\displaystyle {\boldsymbol {\omega }}\times {\boldsymbol {P}}}
457:
303:
213:
4449:(Third ed.). Oxford: Butterworth-Heinemann. p. 128.
4406:
3522:
While the majority of the scientific literature uses the term
1111:. It does not exist when a system is described relative to an
4795:
Shuzhi S. Ge; Tong Heng Lee; Christopher John Harris (1998).
3621:
1658:
attributable to the motion of the rotating frame. The vector
1206:
293:
288:
230:
5047:"Effects of an intrinsic metric of molecular internal space"
4025:
5220:. Princeton, N.J.: Princeton University Press. p. 47.
4597:
4469:
4013:
Mechanics, mechanical waves, kinetic theory, thermodynamics
3470:
916:
Confusingly, the term has sometimes also been used for the
823:
298:
261:
4300:
3473:-level gravity on mice with gravity simulated in this way.
3465:, as in proposed designs for rotating space stations. The
1209:
constitutes a rotating reference frame because it rotates
1189:. In order to keep the stone moving in a circular path, a
5253:. Vol. 25. American Journal of Physics. p. 325.
5017:
3549:}, which can be as simple as the usual polar coordinates
3294:
is the component of the position vector perpendicular to
1223:
91:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
3538:. Lagrangian mechanics formulates mechanics in terms of
4798:
Adaptive Neural
Network Control of Robotic Manipulators
1925:{\textstyle {\frac {\mathrm {d} }{\mathrm {d} t}}\left}
1716:{\displaystyle {\boldsymbol {F}}=m{\boldsymbol {a}}\ ,}
1299:
1059:
Centrifugal force has also played a role in debates in
5410:(25th ed.). D. Van Nostrand Company. p. 357.
3170:{\displaystyle -2m{\boldsymbol {\omega }}\times \left}
1868:
1825:
1414:
with respect to the rotating frame is, by definition,
5071:
4986:
4923:
4874:
4852:
4823:
4743:(2 ed.). Cambridge University Press. p. 90
3555:
3322:
3300:
3273:
3233:
3183:
3116:
3059:
2847:
2790:
2725:
1938:
1745:
1690:
1634:
1604:
1502:
846:
55:
5403:
5364:
5157:
Donato Bini; Paolo Carini; Robert T Jantzen (1997).
5107:
Donato Bini; Paolo Carini; Robert T Jantzen (1997).
4442:
3677:
1362:
directed along the axes of the rotating frame (i.e.
1107:
Centrifugal force is an outward force apparent in a
4737:"Generalized coordinates and kinematic constraints"
2719:The apparent acceleration in the rotating frame is
1230:
Weight of an object at the poles and on the equator
5449:
5213:
5086:
5044:
4994:
4964:
4905:
4860:
4838:
4733:For a description of generalized coordinates, see
4674:
4090:
3576:
3342:
3308:
3286:
3259:
3219:
3169:
3099:
3039:
2833:
2776:
2704:
1924:
1854:
1802:
1715:
1650:
1610:
1590:
871:
90:
5424:Robotics: a reference guide to the new technology
4706:
4536:
4382:. Arlington, Texas: S.A.W.E., Inc. Archived from
3928:Julian B. Barbour; Herbert Pfister, eds. (1995).
5487:
5420:
5251:"Centrifugal Forces and Newton's Laws of Motion"
4734:
4567:Contemporary Physics and the Limits of Knowledge
4500:
3655:This reaction force is sometimes described as a
3505:make use of centrifugal forces. For instance, a
1151:
4234:Theoretical Mechanics of Particles and Continua
4028:"Photon Bunching in a Rotating Reference Frame"
4011:Richard T. Weidner and Robert L. Sells (1973).
5248:
4237:. Courier Dover Publications. pp. 38–39.
4160:
1680:Newton's law of motion for a particle of mass
5447:
4767:
4651:
4625:I. Bernard Cohen; George Edwin Smith (2002).
4307:Knight, Judson (2016). Schlager, Neil (ed.).
3855:. Ames: Iowa State University Press. p.
1016:, which speculation may prove of good use in
936:History of centrifugal and centripetal forces
780:
4965:{\displaystyle {\dot {q}}_{i}{\dot {q}}_{j}}
4917:while those involving a product of the type
4563:
4504:A universe of atoms, an atom in the universe
3904:Philosophiae naturalis principia mathematica
3900:
5265:"Acceleration and force in circular motion"
4604:. Cambridge University Press. p. 324.
4258:Jerrold E. Marsden; Tudor S. Ratiu (1999).
4015:(2 ed.). Allyn and Bacon. p. 123.
3628:. A body undergoing curved motion, such as
3617:In another instance the term refers to the
3461:Centrifugal forces can be used to generate
3343:{\displaystyle ({\boldsymbol {\omega }}=0)}
1218:: the strength and direction of the local "
4631:. Cambridge University Press. p. 43.
3529:
787:
773:
5174:
5163:International Journal of Modern Physics D
5124:
5113:International Journal of Modern Physics D
4530:
4494:
4436:
4407:John L. Synge; Byron A. Griffith (2007).
4361:, Cornell University, retrieved June 2007
4288:. Encyclopædia Britannica. 17 August 2016
4219:
4217:
4117:
4043:
3848:
3517:
952:' notes and letters. Note, that in Latin
31:centrifugal forces present in this frame.
5099:
4839:{\displaystyle {\boldsymbol {\dot {q}}}}
4727:
3803:
3761:
3759:
3370:
3358:
1622:. In other words, the rate of change of
814:. It is directed radially away from the
25:
5279:
5257:
5011:
4988:
4854:
4827:
4710:The variational principles of mechanics
4699:
4540:The Variational Principles of Mechanics
4370:
4364:
4251:
4084:
3956:
3327:
3309:{\displaystyle {\boldsymbol {\omega }}}
3302:
3210:
3202:
3191:
3145:
3127:
3093:
3072:
3003:
2970:
2962:
2951:
2923:
2903:
2889:
2868:
2849:
2807:
2746:
2685:
2677:
2666:
2641:
2621:
2610:
2589:
2549:
2507:
2499:
2474:
2449:
2441:
2420:
2387:
2367:
2335:
2288:
2272:
2264:
2243:
2210:
2190:
2158:
2116:
2108:
2083:
2026:
1971:
1944:
1901:
1835:
1770:
1747:
1703:
1692:
1644:
1636:
1578:
1570:
1545:
1512:
1246:When the same object is weighed on the
5488:
5456:. Princeton University Press. p.
5441:
5414:
5397:
5214:Mook, Delo E.; Thomas Vargish (1987).
4681:. Greenwood Publishing Group. p.
4598:Louis N. Hand; Janet D. Finch (1998).
4470:Louis N. Hand; Janet D. Finch (1998).
4463:
4306:
4214:
3921:
3882:Œuvres complètes de Christiaan Huygens
3612:
3260:{\displaystyle m\omega ^{2}r_{\perp }}
1406:), then the first time derivative of
1234:If an object is weighed with a simple
1091:) and gravitational forces led to the
913:such as a rotating coordinate system.
5314:
5308:
5242:
4846:where the coefficients may depend on
4705:For an introduction, see for example
4672:
4557:
4507:(2 ed.). Springer. p. 249.
4400:
3965:Science education in the 21st century
3893:
3809:
3765:
3756:
3701:Centrifugal mechanism of acceleration
974:means "fleeing from the center" in a
948:("centrifugal force") is attested in
818:. The magnitude of centrifugal force
469:Newton's law of universal gravitation
5207:
5038:
5018:R. K. Mittal; I. J. Nagrath (2003).
4906:{\displaystyle {{\dot {q}}_{i}}^{2}}
4801:. World Scientific. pp. 47–48.
3771:"Christiaan Huygens' Great Treasure"
3397:The tension in a string joining two
3354:
1300:Time derivatives in a rotating frame
1172:
4761:
3899:An English translation is found at
1292:is regarded as a special case of a
1284:Mechanics of planar particle motion
1056:" arising in a rotating reference.
987:, Huygens writes (as translated by
970:) means "fleeing, avoiding". Thus,
450:Mechanics of planar particle motion
58:
13:
4788:
4658:. Harper & Brothers. pp.
4278:
3934:. Boston: Birkhäuser. p. 69.
3830:from the original on 16 March 2020
3791:from the original on 13 April 2018
3469:would have studied the effects of
3390:The shape of the surface of water
3155:
3140:
3082:
3067:
3010:
2992:
2930:
2918:
2875:
2863:
2814:
2796:
2753:
2735:
2648:
2636:
2596:
2584:
2556:
2538:
2481:
2469:
2427:
2415:
2394:
2382:
2342:
2324:
2295:
2283:
2250:
2238:
2217:
2205:
2165:
2147:
2090:
2078:
2055:
2049:
2033:
2021:
2007:
2001:
1978:
1960:
1908:
1896:
1878:
1872:
1842:
1830:
1777:
1759:
1552:
1540:
1519:
1507:
1211:once every 23 hours and 56 minutes
14:
5527:
5467:
5024:. Tata McGraw-Hill. p. 202.
4995:{\displaystyle {\boldsymbol {q}}}
4980:. The third type is functions of
4861:{\displaystyle {\boldsymbol {q}}}
4628:The Cambridge companion to Newton
4163:"Frames of Reference: The Basics"
3534:One of these instances occurs in
1288:For the following formalism, the
5473:
5427:. Greenwood Press. p. 267.
5317:"Introducing motion in a circle"
4830:
3680:
754:
753:
740:
73:
5358:
5273:
4666:
4645:
4618:
4591:
4521:
4443:LD Landau; LM Lifshitz (1976).
4427:
4345:
4203:
4185:
4154:
4111:
4019:
3421:
1675:
1102:
872:{\displaystyle F=m\omega ^{2}r}
5452:Physics for the Inquiring Mind
5367:"Physics, the pioneer science"
5315:Roche, John (September 2001).
5087:{\displaystyle {\dot {\phi }}}
4815:Euler–Lagrange equations
4313:. Thomson Learning. p. 47
4062:10.1103/physrevlett.123.110401
4004:
3873:
3849:Blackwell, Richard J. (1986).
3842:
3733:
3596:Euler–Lagrange equations
3571:
3556:
3337:
3323:
3214:
3198:
2974:
2958:
2689:
2673:
1067:can be detected: the rotating
909:, when they are analyzed in a
1:
5404:Edward Albert Bowser (1920).
5365:Lloyd William Taylor (1959).
5045:T Yanao; K Takatsuka (2005).
4741:Dynamics of Multibody Systems
4373:"Precise Measurement of Mass"
3810:Yoder, Joella (17 May 2013).
3750:
3657:centrifugal inertial reaction
3577:{\displaystyle (r,\ \theta )}
3448:Inertial drum brake ascenders
1342:with respect to unit vectors
1267:
1159:Newton's second law of motion
1152:Vehicle driving round a curve
376:Koopman–von Neumann mechanics
4167:From Stargazers to Starships
3696:Balancing of rotating masses
3638:Newton's third law of motion
3177:, and the centrifugal force
1294:non-inertial reference frame
1187:Newton's first law of motion
911:non–inertial reference frame
444:Non-inertial reference frame
7:
5371:American Journal of Physics
4120:European Journal of Physics
4091:John Robert Taylor (2004).
3673:
3624:to a centripetal force, or
1684:written in vector form is:
1290:rotating frame of reference
1183:inertial frame of reference
1146:
1113:inertial frame of reference
812:rotating frame of reference
371:Appell's equation of motion
241:Inertial frame of reference
10:
5532:
5344:10.1088/0031-9120/36/5/305
4707:Cornelius Lanczos (1986).
4537:Cornelius Lanczos (1986).
4478:Cambridge University Press
4352:"Curious About Astronomy?"
4140:10.1088/0143-0807/29/3/019
3648:the body in curved motion
3626:reactive centrifugal force
3414:shape reflects, following
3378:
3287:{\displaystyle r_{\perp }}
1277:
1271:
1037:, Newton further develops
1008:received Huygens work via
933:
929:
919:reactive centrifugal force
18:
5421:Joseph A. Angelo (2007).
5193:10.1142/S021827189700011X
5155:. The companion paper is
5143:10.1142/S021827189700011X
4735:Ahmed A. Shabana (2003).
4501:Mark P Silverman (2002).
4371:Boynton, Richard (2001).
4357:January 17, 2015, at the
4264:. Springer. p. 251.
3467:Mars Gravity Biosatellite
1469:of the rotating frame is
1043:Gottfried Wilhelm Leibniz
5165:(Submitted manuscript).
5115:(Submitted manuscript).
4774:. Springer. p. 23.
4673:Myers, Rusty L. (2006).
4572:Rutgers University Press
3726:
3634:centripetal acceleration
2714:
1274:Rotating reference frame
1200:
1109:rotating reference frame
984:Horologium Oscillatorium
534:Rotating reference frame
366:Hamilton–Jacobi equation
19:Not to be confused with
5280:Mohanty, A. K. (1994).
5263:Signell, Peter (2002).
5249:G. David Scott (1957).
4410:Principles of Mechanics
4197:Encyclopædia Britannica
4161:David P. Stern (2006).
4032:Physical Review Letters
3540:generalized coordinates
3530:In Lagrangian mechanics
1611:{\displaystyle \times }
475:Newton's laws of motion
335:Newton's laws of motion
5448:Eric M Rogers (1960).
5088:
4996:
4966:
4907:
4862:
4840:
4768:Christian Ott (2008).
4652:Simon Newcomb (1878).
4527:Taylor (2005). p. 329.
4433:Taylor (2005). p. 342.
3996:: CS1 maint: others (
3578:
3518:Other uses of the term
3376:
3368:
3344:
3310:
3288:
3261:
3221:
3171:
3101:
3041:
2835:
2778:
2706:
1926:
1856:
1804:
1717:
1652:
1612:
1592:
1334:are the components of
1002:
965:
959:
953:
873:
502:Simple harmonic motion
415:Euler's laws of motion
209:D'Alembert's principle
92:
32:
16:Type of inertial force
5089:
5053:. Wiley. p. 98.
4997:
4967:
4908:
4863:
4841:
4677:The basics of physics
4564:Morton Tavel (2002).
3901:Isaac Newton (1934).
3706:Equivalence principle
3579:
3496:Archimedes' principle
3374:
3363:The interface of two
3362:
3345:
3311:
3289:
3262:
3222:
3172:
3102:
3042:
2836:
2779:
2777:{\displaystyle \left}
2707:
1927:
1857:
1805:
1718:
1653:
1613:
1593:
1093:equivalence principle
993:
891:centrifugal governors
874:
356:Hamiltonian mechanics
174:Statistical mechanics
93:
29:
5482:at Wikimedia Commons
5069:
5021:Robotics and Control
5004:gravitational forces
5002:only and are called
4984:
4921:
4872:
4850:
4821:
4601:Analytical Mechanics
4473:Analytical Mechanics
3590:, using in place of
3553:
3536:Lagrangian mechanics
3432:centrifugal governor
3392:rotating in a bucket
3320:
3298:
3271:
3231:
3181:
3114:
3057:
2845:
2788:
2723:
1936:
1866:
1823:
1743:
1688:
1632:
1620:vector cross product
1602:
1500:
1475:then the derivative
1260:not a perfect sphere
989:Richard J. Blackwell
899:centrifugal railways
895:centrifugal clutches
844:
579:Angular acceleration
571:Rotational frequency
351:Lagrangian mechanics
344:Analytical mechanics
100:Second law of motion
53:
5383:1961AmJPh..29..563T
5336:2001PhyEd..36..399R
5185:1997IJMPD...6..143B
5135:1997IJMPD...6..143B
4380:Sawe Paper No. 3147
4286:"Centrifugal force"
4225:Alexander L. Fetter
4132:2008EJPh...29..599K
4094:Classical Mechanics
4054:2019PhRvL.123k0401R
3613:As a reactive force
3481:centrifugal casting
1465:. If the absolute
1216:gravitational force
1061:classical mechanics
976:literal translation
958:means "center" and
808:Newtonian mechanics
431:Harmonic oscillator
409:Equations of motion
44:Classical mechanics
38:Part of a series on
5084:
4992:
4962:
4915:centrifugal forces
4903:
4858:
4836:
3587:generalized forces
3574:
3463:artificial gravity
3443:centrifugal clutch
3416:Clairaut's theorem
3377:
3369:
3340:
3306:
3284:
3257:
3217:
3167:
3097:
3037:
2831:
2774:
2702:
2700:
1922:
1852:
1800:
1713:
1648:
1608:
1588:
1127:the square of the
1097:general relativity
1089:artificial gravity
1018:natural philosophy
950:Christiaan Huygens
869:
747:Physics portal
361:Routhian mechanics
236:Frame of reference
88:
33:
5501:Fictitious forces
5480:Centrifugal force
5478:Media related to
5434:978-1-57356-337-6
5391:10.1119/1.1937847
5324:Physics Education
5217:Inside relativity
5081:
5060:978-0-471-71157-5
5031:978-0-07-048293-7
4953:
4934:
4887:
4833:
4808:978-981-02-3452-2
4781:978-3-540-69253-9
4754:978-0-521-54411-5
4720:978-0-486-65067-8
4692:978-0-313-32857-2
4655:Popular astronomy
4638:978-0-521-65696-2
4611:978-0-521-57572-0
4581:978-0-8135-3077-2
4550:978-0-486-65067-8
4514:978-0-387-95437-0
4487:978-0-521-57572-0
4456:978-0-7506-2896-9
4420:978-1-4067-4670-9
4310:Centripetal Force
4271:978-0-387-98643-2
4244:978-0-486-43261-8
4229:John Dirk Walecka
4199:. April 30, 2015.
4104:978-1-891389-22-1
3975:978-1-60021-951-1
3866:978-0-8138-0933-5
3664:centrifugal force
3644:force is exerted
3567:
3524:centrifugal force
3381:Absolute rotation
3355:Absolute rotation
3033:
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2015:
1993:
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1850:
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1792:
1709:
1584:
1560:
1527:
1264:
1191:centripetal force
1173:Stone on a string
1065:absolute rotation
998:centrifugal force
924:centripetal force
887:centrifugal pumps
800:Centrifugal force
797:
796:
544:Centrifugal force
539:Centripetal force
495:Euler's equations
480:Relative velocity
256:Moment of inertia
86:
60:
21:Centripetal force
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2552:
2547:
2546:
2541:
2534:
2522:
2518:
2514:
2511:
2510:
2502:
2494:
2490:
2488:
2484:
2478:
2477:
2472:
2466:
2452:
2444:
2436:
2434:
2430:
2424:
2423:
2418:
2412:
2407:
2403:
2401:
2397:
2391:
2390:
2385:
2379:
2370:
2362:
2358:
2356:
2355:
2354:
2345:
2339:
2338:
2333:
2332:
2327:
2320:
2308:
2304:
2302:
2298:
2292:
2291:
2286:
2280:
2275:
2267:
2259:
2257:
2253:
2247:
2246:
2241:
2235:
2230:
2226:
2224:
2220:
2214:
2213:
2208:
2202:
2193:
2185:
2181:
2179:
2178:
2177:
2168:
2162:
2161:
2156:
2155:
2150:
2143:
2131:
2127:
2123:
2120:
2119:
2111:
2103:
2099:
2097:
2093:
2087:
2086:
2081:
2075:
2064:
2062:
2058:
2052:
2047:
2042:
2040:
2036:
2030:
2029:
2024:
2018:
2016:
2014:
2010:
2004:
1999:
1994:
1992:
1991:
1990:
1981:
1975:
1974:
1969:
1968:
1963:
1956:
1947:
1931:
1929:
1928:
1923:
1921:
1917:
1915:
1911:
1905:
1904:
1899:
1893:
1887:
1885:
1881:
1875:
1870:
1861:
1859:
1858:
1853:
1851:
1849:
1845:
1839:
1838:
1833:
1827:
1815:
1809:
1807:
1806:
1801:
1794:
1793:
1791:
1790:
1789:
1780:
1774:
1773:
1768:
1767:
1762:
1755:
1750:
1735:is the absolute
1734:
1728:
1722:
1720:
1719:
1714:
1707:
1706:
1695:
1683:
1667:
1663:
1657:
1655:
1654:
1649:
1647:
1639:
1627:
1617:
1615:
1614:
1609:
1597:
1595:
1594:
1589:
1582:
1581:
1573:
1565:
1561:
1559:
1555:
1549:
1548:
1543:
1537:
1528:
1526:
1522:
1516:
1515:
1510:
1504:
1495:
1487:
1474:
1467:angular velocity
1464:
1413:
1405:
1361:
1341:
1333:
1311:
1280:Fictitious force
1253:
1129:angular velocity
1081:Mach's principle
1073:rotating spheres
1054:fictitious force
903:planetary orbits
878:
876:
875:
870:
865:
864:
839:
835:angular velocity
829:at the distance
822:on an object of
816:axis of rotation
804:fictitious force
789:
782:
775:
762:
757:
756:
749:
745:
744:
650:Johann Bernoulli
645:Daniel Bernoulli
566:Tangential speed
470:
446:
421:Fictitious force
416:
268:Mechanical power
258:
199:Angular momentum
97:
95:
94:
89:
87:
85:
77:
76:
67:
62:
61:
35:
34:
5531:
5530:
5526:
5525:
5524:
5522:
5521:
5520:
5486:
5485:
5470:
5465:
5446:
5442:
5435:
5419:
5415:
5402:
5398:
5363:
5359:
5319:
5313:
5309:
5294:
5283:Fluid mechanics
5278:
5274:
5262:
5258:
5247:
5243:
5228:
5212:
5208:
5176:gr-qc/0106014v1
5126:gr-qc/0106014v1
5104:
5100:
5073:
5072:
5070:
5067:
5066:
5061:
5043:
5039:
5032:
5016:
5012:
4987:
4985:
4982:
4981:
4978:Coriolis forces
4956:
4945:
4944:
4943:
4937:
4926:
4925:
4924:
4922:
4919:
4918:
4897:
4890:
4879:
4878:
4877:
4876:
4875:
4873:
4870:
4869:
4853:
4851:
4848:
4847:
4825:
4824:
4822:
4819:
4818:
4809:
4793:
4789:
4782:
4766:
4762:
4755:
4732:
4728:
4721:
4704:
4700:
4693:
4671:
4667:
4650:
4646:
4639:
4623:
4619:
4612:
4596:
4592:
4582:
4562:
4558:
4551:
4535:
4531:
4526:
4522:
4515:
4499:
4495:
4488:
4480:. p. 267.
4468:
4464:
4457:
4441:
4437:
4432:
4428:
4421:
4405:
4401:
4392:
4390:
4386:
4375:
4369:
4365:
4359:Wayback Machine
4350:
4346:
4334:
4333:
4324:
4323:
4316:
4314:
4305:
4301:
4291:
4289:
4284:
4283:
4279:
4272:
4256:
4252:
4245:
4222:
4215:
4208:
4204:
4191:
4190:
4186:
4176:
4174:
4173:on 6 April 2020
4159:
4155:
4116:
4112:
4105:
4089:
4085:
4024:
4020:
4009:
4005:
3989:
3988:
3976:
3962:
3961:
3957:
3942:
3926:
3922:
3915:
3898:
3894:
3879:
3878:
3874:
3867:
3847:
3843:
3833:
3831:
3824:
3808:
3804:
3794:
3792:
3788:
3773:
3764:
3757:
3753:
3748:
3747:
3741:vim centrifugam
3738:
3734:
3729:
3686:
3679:
3676:
3666:rather than as
3630:circular motion
3615:
3603:
3554:
3551:
3550:
3547:
3532:
3520:
3503:amusement rides
3424:
3412:oblate spheroid
3383:
3357:
3326:
3321:
3318:
3317:
3301:
3299:
3296:
3295:
3278:
3274:
3272:
3269:
3268:
3251:
3247:
3241:
3237:
3232:
3229:
3228:
3209:
3201:
3190:
3182:
3179:
3178:
3154:
3149:
3144:
3139:
3138:
3134:
3126:
3115:
3112:
3111:
3092:
3081:
3076:
3071:
3066:
3058:
3055:
3054:
3018:
3014:
3009:
3008:
3002:
2996:
2991:
2990:
2989:
2987:
2983:
2969:
2961:
2950:
2929:
2928:
2922:
2917:
2916:
2914:
2910:
2902:
2888:
2874:
2873:
2867:
2862:
2861:
2859:
2848:
2846:
2843:
2842:
2822:
2818:
2813:
2812:
2806:
2800:
2795:
2794:
2793:
2791:
2789:
2786:
2785:
2761:
2757:
2752:
2751:
2745:
2739:
2734:
2733:
2732:
2730:
2726:
2724:
2721:
2720:
2717:
2699:
2698:
2684:
2676:
2665:
2647:
2646:
2640:
2635:
2634:
2632:
2628:
2620:
2609:
2595:
2594:
2588:
2583:
2582:
2580:
2564:
2560:
2555:
2554:
2548:
2542:
2537:
2536:
2535:
2533:
2529:
2520:
2519:
2506:
2498:
2480:
2479:
2473:
2468:
2467:
2465:
2461:
2460:
2456:
2448:
2440:
2426:
2425:
2419:
2414:
2413:
2411:
2393:
2392:
2386:
2381:
2380:
2378:
2374:
2366:
2350:
2346:
2341:
2340:
2334:
2328:
2323:
2322:
2321:
2319:
2315:
2306:
2305:
2294:
2293:
2287:
2282:
2281:
2279:
2271:
2263:
2249:
2248:
2242:
2237:
2236:
2234:
2216:
2215:
2209:
2204:
2203:
2201:
2197:
2189:
2173:
2169:
2164:
2163:
2157:
2151:
2146:
2145:
2144:
2142:
2138:
2129:
2128:
2115:
2107:
2089:
2088:
2082:
2077:
2076:
2074:
2070:
2069:
2065:
2054:
2053:
2048:
2046:
2032:
2031:
2025:
2020:
2019:
2017:
2006:
2005:
2000:
1998:
1986:
1982:
1977:
1976:
1970:
1964:
1959:
1958:
1957:
1955:
1948:
1943:
1939:
1937:
1934:
1933:
1907:
1906:
1900:
1895:
1894:
1892:
1888:
1877:
1876:
1871:
1869:
1867:
1864:
1863:
1841:
1840:
1834:
1829:
1828:
1826:
1824:
1821:
1820:
1811:
1785:
1781:
1776:
1775:
1769:
1763:
1758:
1757:
1756:
1754:
1746:
1744:
1741:
1740:
1730:
1724:
1702:
1691:
1689:
1686:
1685:
1681:
1678:
1670:right-hand rule
1665:
1659:
1643:
1635:
1633:
1630:
1629:
1623:
1603:
1600:
1599:
1577:
1569:
1551:
1550:
1544:
1539:
1538:
1536:
1532:
1518:
1517:
1511:
1506:
1505:
1503:
1501:
1498:
1497:
1489:
1476:
1470:
1454:
1438:
1422:
1415:
1407:
1399:
1387:
1375:
1363:
1343:
1335:
1332:
1325:
1319:
1313:
1305:
1302:
1286:
1276:
1270:
1240:restoring force
1232:
1203:
1175:
1163:roller coasters
1154:
1149:
1105:
1069:bucket argument
1010:Henry Oldenburg
1004:The same year,
940:From 1659, the
938:
932:
860:
856:
845:
842:
841:
837:
793:
752:
739:
738:
731:
730:
729:
604:
596:
595:
575:
529:Circular motion
523:
513:
512:
511:
468:
438:
435:
414:
393:
385:
384:
381:
380:
338:
328:
320:
319:
318:
277:
273:Mechanical work
266:
250:
188:
180:
179:
178:
133:
125:
102:
78:
72:
68:
66:
57:
56:
54:
51:
50:
24:
17:
12:
11:
5:
5529:
5519:
5518:
5513:
5508:
5503:
5498:
5484:
5483:
5469:
5468:External links
5466:
5464:
5463:
5440:
5433:
5413:
5396:
5357:
5330:(5): 399–405.
5307:
5292:
5272:
5256:
5241:
5226:
5206:
5169:(1): 143–198.
5119:(1): 143–198.
5098:
5080:
5077:
5059:
5037:
5030:
5010:
4990:
4959:
4952:
4949:
4940:
4933:
4930:
4900:
4893:
4886:
4883:
4856:
4832:
4829:
4807:
4787:
4780:
4760:
4753:
4726:
4719:
4698:
4691:
4665:
4644:
4637:
4617:
4610:
4590:
4580:
4574:. p. 93.
4556:
4549:
4529:
4520:
4513:
4493:
4486:
4462:
4455:
4435:
4426:
4419:
4399:
4363:
4344:
4299:
4277:
4270:
4250:
4243:
4213:
4202:
4184:
4153:
4126:(3): 599–606.
4110:
4103:
4083:
4038:(11): 110401.
4018:
4003:
3974:
3955:
3940:
3920:
3913:
3892:
3872:
3865:
3841:
3822:
3802:
3754:
3752:
3749:
3746:
3745:
3731:
3730:
3728:
3725:
3724:
3723:
3718:
3713:
3708:
3703:
3698:
3692:
3691:
3688:Physics portal
3675:
3672:
3614:
3611:
3601:
3573:
3570:
3564:
3561:
3558:
3545:
3531:
3528:
3519:
3516:
3511:
3510:
3499:
3492:buoyant forces
3484:
3474:
3459:
3439:
3423:
3420:
3403:
3402:
3395:
3379:Main article:
3356:
3353:
3339:
3336:
3333:
3329:
3325:
3304:
3281:
3277:
3254:
3250:
3244:
3240:
3236:
3216:
3212:
3208:
3204:
3200:
3197:
3193:
3189:
3186:
3165:
3161:
3157:
3152:
3147:
3142:
3137:
3133:
3129:
3125:
3122:
3119:
3109:Coriolis force
3095:
3091:
3088:
3084:
3079:
3074:
3069:
3065:
3062:
3036:
3029:
3021:
3017:
3012:
3005:
2999:
2994:
2986:
2982:
2979:
2976:
2972:
2968:
2964:
2960:
2957:
2953:
2949:
2946:
2942:
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2913:
2909:
2905:
2901:
2898:
2895:
2891:
2887:
2881:
2877:
2870:
2865:
2858:
2855:
2851:
2825:
2821:
2816:
2809:
2803:
2798:
2772:
2764:
2760:
2755:
2748:
2742:
2737:
2729:
2716:
2713:
2697:
2691:
2687:
2683:
2679:
2675:
2672:
2668:
2664:
2660:
2654:
2650:
2643:
2638:
2631:
2627:
2623:
2619:
2616:
2612:
2608:
2602:
2598:
2591:
2586:
2579:
2575:
2567:
2563:
2558:
2551:
2545:
2540:
2532:
2528:
2525:
2523:
2521:
2517:
2509:
2505:
2501:
2497:
2493:
2487:
2483:
2476:
2471:
2464:
2459:
2455:
2451:
2447:
2443:
2439:
2433:
2429:
2422:
2417:
2410:
2406:
2400:
2396:
2389:
2384:
2377:
2373:
2369:
2365:
2361:
2353:
2349:
2344:
2337:
2331:
2326:
2318:
2314:
2311:
2309:
2307:
2301:
2297:
2290:
2285:
2278:
2274:
2270:
2266:
2262:
2256:
2252:
2245:
2240:
2233:
2229:
2223:
2219:
2212:
2207:
2200:
2196:
2192:
2188:
2184:
2176:
2172:
2167:
2160:
2154:
2149:
2141:
2137:
2134:
2132:
2130:
2126:
2118:
2114:
2110:
2106:
2102:
2096:
2092:
2085:
2080:
2073:
2068:
2061:
2057:
2051:
2045:
2039:
2035:
2028:
2023:
2013:
2009:
2003:
1997:
1989:
1985:
1980:
1973:
1967:
1962:
1954:
1951:
1949:
1946:
1942:
1941:
1920:
1914:
1910:
1903:
1898:
1891:
1884:
1880:
1874:
1848:
1844:
1837:
1832:
1799:
1788:
1784:
1779:
1772:
1766:
1761:
1753:
1749:
1712:
1705:
1701:
1698:
1694:
1677:
1674:
1664:has magnitude
1646:
1642:
1638:
1607:
1587:
1580:
1576:
1572:
1568:
1564:
1558:
1554:
1547:
1542:
1535:
1531:
1525:
1521:
1514:
1509:
1452:
1436:
1420:
1397:
1385:
1373:
1330:
1323:
1317:
1301:
1298:
1272:Main article:
1269:
1266:
1236:spring balance
1231:
1228:
1202:
1199:
1174:
1171:
1153:
1150:
1148:
1145:
1137:Coriolis force
1104:
1101:
1039:vis centrifuga
1014:vis centrifuga
934:Main article:
931:
928:
868:
863:
859:
855:
852:
849:
795:
794:
792:
791:
784:
777:
769:
766:
765:
764:
763:
750:
733:
732:
728:
727:
722:
717:
712:
707:
702:
697:
692:
687:
682:
677:
672:
667:
662:
657:
652:
647:
642:
637:
632:
627:
622:
617:
612:
606:
605:
602:
601:
598:
597:
594:
593:
574:
573:
568:
563:
558:
556:Coriolis force
553:
552:
551:
541:
536:
531:
525:
524:
519:
518:
515:
514:
510:
509:
504:
499:
498:
497:
492:
482:
477:
472:
465:
454:
453:
452:
447:
434:
433:
428:
423:
418:
411:
406:
401:
395:
394:
391:
390:
387:
386:
383:
382:
379:
378:
373:
368:
363:
358:
353:
347:
341:
339:
332:
329:
326:
325:
322:
321:
317:
316:
311:
306:
301:
296:
291:
286:
281:
275:
270:
264:
259:
248:
243:
238:
233:
228:
227:
226:
221:
211:
206:
201:
196:
190:
189:
186:
185:
182:
181:
177:
176:
171:
166:
161:
156:
151:
146:
141:
135:
134:
131:
130:
127:
126:
124:
123:
118:
113:
107:
104:
103:
98:
84:
81:
75:
71:
65:
47:
46:
40:
39:
15:
9:
6:
4:
3:
2:
5528:
5517:
5514:
5512:
5509:
5507:
5504:
5502:
5499:
5497:
5494:
5493:
5491:
5481:
5476:
5472:
5471:
5459:
5454:
5453:
5444:
5436:
5430:
5426:
5425:
5417:
5409:
5408:
5400:
5392:
5388:
5384:
5380:
5376:
5372:
5368:
5361:
5353:
5349:
5345:
5341:
5337:
5333:
5329:
5325:
5318:
5311:
5303:
5299:
5295:
5293:81-203-0894-8
5289:
5285:
5284:
5276:
5269:
5266:
5260:
5252:
5245:
5237:
5233:
5229:
5227:0-691-08472-6
5223:
5219:
5218:
5210:
5202:
5198:
5194:
5190:
5186:
5182:
5177:
5172:
5168:
5164:
5160:
5152:
5148:
5144:
5140:
5136:
5132:
5127:
5122:
5118:
5114:
5110:
5102:
5095:
5078:
5075:
5062:
5056:
5052:
5048:
5041:
5033:
5027:
5023:
5022:
5014:
5007:
5005:
4979:
4975:
4957:
4950:
4947:
4938:
4931:
4928:
4916:
4898:
4891:
4884:
4881:
4816:
4813:In the above
4810:
4804:
4800:
4799:
4791:
4783:
4777:
4773:
4772:
4764:
4756:
4750:
4746:
4742:
4738:
4730:
4722:
4716:
4712:
4711:
4702:
4694:
4688:
4684:
4679:
4678:
4669:
4661:
4657:
4656:
4648:
4640:
4634:
4630:
4629:
4621:
4613:
4607:
4603:
4602:
4594:
4587:
4583:
4577:
4573:
4569:
4568:
4560:
4552:
4546:
4542:
4541:
4533:
4524:
4516:
4510:
4506:
4505:
4497:
4489:
4483:
4479:
4475:
4474:
4466:
4458:
4452:
4448:
4447:
4439:
4430:
4422:
4416:
4412:
4411:
4403:
4389:on 2007-02-27
4385:
4381:
4374:
4367:
4360:
4356:
4353:
4348:
4340:
4328:
4312:
4311:
4303:
4287:
4281:
4273:
4267:
4263:
4262:
4254:
4246:
4240:
4236:
4235:
4230:
4226:
4220:
4218:
4211:
4206:
4198:
4194:
4188:
4172:
4168:
4164:
4157:
4149:
4145:
4141:
4137:
4133:
4129:
4125:
4121:
4114:
4106:
4100:
4096:
4095:
4087:
4079:
4075:
4071:
4067:
4063:
4059:
4055:
4051:
4046:
4041:
4037:
4033:
4029:
4022:
4014:
4007:
3999:
3993:
3985:
3981:
3977:
3971:
3967:
3966:
3959:
3951:
3947:
3943:
3941:0-8176-3823-7
3937:
3933:
3932:
3924:
3916:
3914:9780520009271
3910:
3906:
3905:
3896:
3888:
3884:
3883:
3876:
3868:
3862:
3858:
3854:
3853:
3845:
3829:
3825:
3823:9789004235656
3819:
3815:
3814:
3806:
3787:
3783:
3779:
3772:
3768:
3767:Yoder, Joella
3762:
3760:
3755:
3742:
3736:
3732:
3722:
3721:Lamm equation
3719:
3717:
3714:
3712:
3709:
3707:
3704:
3702:
3699:
3697:
3694:
3693:
3689:
3683:
3678:
3671:
3669:
3665:
3660:
3658:
3653:
3651:
3647:
3643:
3639:
3635:
3631:
3627:
3623:
3620:
3610:
3608:
3604:
3597:
3593:
3592:Newton's laws
3589:
3588:
3568:
3562:
3559:
3548:
3541:
3537:
3527:
3525:
3515:
3508:
3504:
3500:
3497:
3493:
3488:
3485:
3482:
3478:
3475:
3472:
3468:
3464:
3460:
3457:
3456:inertia reels
3453:
3452:rock climbing
3449:
3444:
3440:
3437:
3433:
3429:
3428:
3427:
3419:
3417:
3413:
3407:
3400:
3396:
3393:
3389:
3388:
3387:
3382:
3373:
3366:
3361:
3352:
3334:
3331:
3279:
3275:
3252:
3248:
3242:
3238:
3234:
3206:
3195:
3187:
3184:
3163:
3159:
3150:
3135:
3131:
3123:
3120:
3117:
3110:
3089:
3086:
3077:
3063:
3060:
3053:
3047:
3034:
3027:
3019:
3015:
2997:
2984:
2980:
2977:
2966:
2955:
2947:
2944:
2940:
2934:
2911:
2907:
2899:
2896:
2893:
2885:
2879:
2856:
2853:
2823:
2819:
2801:
2770:
2762:
2758:
2740:
2727:
2712:
2695:
2681:
2670:
2662:
2658:
2652:
2629:
2625:
2617:
2614:
2606:
2600:
2577:
2573:
2565:
2561:
2543:
2530:
2526:
2524:
2515:
2503:
2495:
2491:
2485:
2462:
2457:
2453:
2445:
2437:
2431:
2408:
2404:
2398:
2375:
2371:
2363:
2359:
2351:
2347:
2329:
2316:
2312:
2310:
2299:
2276:
2268:
2260:
2254:
2231:
2227:
2221:
2198:
2194:
2186:
2182:
2174:
2170:
2152:
2139:
2135:
2133:
2124:
2112:
2104:
2100:
2094:
2071:
2066:
2059:
2043:
2037:
2011:
1995:
1987:
1983:
1965:
1952:
1950:
1918:
1912:
1889:
1882:
1846:
1817:
1814:
1797:
1786:
1782:
1764:
1751:
1738:
1733:
1727:
1710:
1699:
1696:
1673:
1671:
1662:
1640:
1626:
1621:
1605:
1585:
1574:
1566:
1562:
1556:
1533:
1529:
1523:
1494:
1493:
1486:
1482:
1481:
1473:
1468:
1463:
1462:
1458:
1451:
1447:
1446:
1442:
1435:
1431:
1430:
1426:
1419:
1412:
1411:
1404:
1403:
1396:
1392:
1391:
1384:
1380:
1379:
1372:
1368:
1367:
1360:
1359:
1354:
1353:
1348:
1347:
1340:
1339:
1329:
1322:
1316:
1310:
1309:
1297:
1295:
1291:
1285:
1281:
1275:
1265:
1263:
1261:
1256:
1251:
1249:
1244:
1241:
1237:
1227:
1225:
1221:
1217:
1212:
1208:
1198:
1194:
1192:
1188:
1184:
1179:
1170:
1168:
1164:
1160:
1144:
1142:
1138:
1133:
1130:
1124:
1122:
1116:
1114:
1110:
1100:
1098:
1094:
1090:
1085:
1082:
1079:Around 1883,
1077:
1074:
1070:
1066:
1062:
1057:
1055:
1050:
1048:
1044:
1040:
1036:
1035:
1029:
1027:
1024:, as well as
1023:
1019:
1015:
1011:
1007:
1001:
999:
992:
990:
986:
985:
979:
977:
973:
969:
968:
963:
962:
957:
956:
951:
947:
946:vi centrifuga
943:
937:
927:
925:
921:
920:
914:
912:
908:
907:banked curves
904:
900:
896:
892:
888:
884:
879:
866:
861:
857:
853:
850:
847:
836:
832:
828:
825:
821:
817:
813:
809:
805:
801:
790:
785:
783:
778:
776:
771:
770:
768:
767:
761:
751:
748:
743:
737:
736:
735:
734:
726:
723:
721:
718:
716:
713:
711:
708:
706:
703:
701:
698:
696:
693:
691:
688:
686:
683:
681:
678:
676:
673:
671:
668:
666:
663:
661:
658:
656:
653:
651:
648:
646:
643:
641:
638:
636:
633:
631:
628:
626:
623:
621:
618:
616:
613:
611:
608:
607:
600:
599:
592:
588:
584:
580:
577:
576:
572:
569:
567:
564:
562:
559:
557:
554:
550:
547:
546:
545:
542:
540:
537:
535:
532:
530:
527:
526:
522:
517:
516:
508:
505:
503:
500:
496:
493:
491:
488:
487:
486:
483:
481:
478:
476:
473:
471:
466:
463:
459:
456:
455:
451:
448:
445:
441:
437:
436:
432:
429:
427:
424:
422:
419:
417:
412:
410:
407:
405:
402:
400:
397:
396:
389:
388:
377:
374:
372:
369:
367:
364:
362:
359:
357:
354:
352:
349:
348:
346:
345:
340:
337:
336:
331:
330:
324:
323:
315:
312:
310:
307:
305:
302:
300:
297:
295:
292:
290:
287:
285:
282:
280:
276:
274:
271:
269:
265:
263:
260:
257:
253:
249:
247:
244:
242:
239:
237:
234:
232:
229:
225:
222:
220:
217:
216:
215:
212:
210:
207:
205:
202:
200:
197:
195:
192:
191:
184:
183:
175:
172:
170:
167:
165:
162:
160:
157:
155:
152:
150:
147:
145:
142:
140:
137:
136:
129:
128:
122:
119:
117:
114:
112:
109:
108:
106:
105:
101:
82:
79:
69:
63:
49:
48:
45:
42:
41:
37:
36:
28:
22:
5496:Acceleration
5451:
5443:
5423:
5416:
5406:
5399:
5374:
5370:
5360:
5327:
5323:
5310:
5282:
5275:
5267:
5259:
5244:
5216:
5209:
5166:
5162:
5116:
5112:
5105:See p. 5 in
5101:
5064:
5050:
5040:
5020:
5013:
5003:
4977:
4973:
4914:
4812:
4797:
4790:
4770:
4763:
4744:
4740:
4729:
4709:
4701:
4676:
4668:
4654:
4647:
4627:
4620:
4600:
4593:
4585:
4566:
4559:
4539:
4532:
4523:
4503:
4496:
4472:
4465:
4445:
4438:
4429:
4409:
4402:
4391:. Retrieved
4384:the original
4379:
4366:
4347:
4315:. Retrieved
4309:
4302:
4290:. Retrieved
4280:
4260:
4253:
4233:
4205:
4196:
4193:"Centrifuge"
4187:
4175:. Retrieved
4171:the original
4166:
4156:
4123:
4119:
4113:
4093:
4086:
4035:
4031:
4021:
4012:
4006:
3964:
3958:
3930:
3923:
3903:
3895:
3881:
3875:
3851:
3844:
3832:. Retrieved
3812:
3805:
3793:. Retrieved
3781:
3777:
3740:
3735:
3711:Folk physics
3667:
3663:
3661:
3656:
3654:
3649:
3645:
3616:
3606:
3599:
3585:
3543:
3533:
3523:
3521:
3512:
3477:Spin casting
3425:
3422:Applications
3408:
3404:
3384:
3048:
2718:
1862:and once to
1818:
1812:
1737:acceleration
1731:
1725:
1679:
1676:Acceleration
1660:
1624:
1618:denotes the
1491:
1490:
1484:
1479:
1478:
1471:
1460:
1459:
1456:
1449:
1444:
1443:
1440:
1433:
1428:
1427:
1424:
1417:
1409:
1408:
1401:
1400:
1394:
1389:
1388:
1382:
1377:
1376:
1370:
1365:
1364:
1357:
1356:
1351:
1350:
1345:
1344:
1337:
1336:
1327:
1320:
1314:
1307:
1306:
1303:
1287:
1257:
1254:
1252:
1245:
1233:
1204:
1195:
1180:
1176:
1155:
1134:
1125:
1117:
1106:
1103:Introduction
1086:
1078:
1058:
1051:
1047:Robert Hooke
1038:
1032:
1031:In 1687, in
1030:
1013:
1006:Isaac Newton
1003:
997:
994:
982:
981:In 1673, in
980:
971:
945:
939:
917:
915:
880:
830:
826:
819:
799:
798:
589: /
585: /
583:displacement
581: /
543:
442: /
404:Displacement
342:
333:
327:Formulations
314:Virtual work
254: /
194:Acceleration
187:Fundamentals
4976:are called
4913:are called
4335:|work=
3487:Centrifuges
3052:Euler force
1141:Euler force
1121:fixed stars
972:centrifugus
883:centrifuges
725:von Neumann
392:Core topics
5490:Categories
5377:(8): 173.
4393:2007-01-21
4045:1906.03400
3751:References
3739:In Latin:
3365:immiscible
1278:See also:
1268:Derivation
1071:, and the
660:d'Alembert
640:Maupertuis
603:Scientists
485:Rigid body
159:Kinematics
5511:Mechanics
5352:250827660
5079:˙
5076:ϕ
4951:˙
4932:˙
4885:˙
4831:˙
4446:Mechanics
4337:ignored (
4327:cite book
4148:120947179
4078:182952610
3992:cite book
3984:165958146
3816:. BRILL.
3569:θ
3507:Gravitron
3328:ω
3303:ω
3280:⊥
3253:⊥
3239:ω
3207:×
3203:ω
3196:×
3192:ω
3185:−
3132:×
3128:ω
3118:−
3090:×
3073:ω
3061:−
2967:×
2963:ω
2956:×
2952:ω
2945:−
2908:×
2904:ω
2894:−
2886:×
2869:ω
2854:−
2682:×
2678:ω
2671:×
2667:ω
2626:×
2622:ω
2607:×
2590:ω
2504:×
2500:ω
2454:×
2450:ω
2438:×
2421:ω
2372:×
2368:ω
2277:×
2273:ω
2261:×
2244:ω
2195:×
2191:ω
2113:×
2109:ω
1641:×
1637:ω
1606:×
1575:×
1571:ω
1034:Principia
1026:mechanics
1022:astronomy
942:Neo-Latin
897:, and in
858:ω
705:Liouville
587:frequency
507:Vibration
224:potential
149:Continuum
144:Celestial
121:Textbooks
5516:Rotation
5302:44020947
5236:16089285
5201:10652293
5151:10652293
4355:Archived
4317:19 April
4292:20 April
4231:(2003).
4177:20 April
4070:31573252
3950:32664808
3834:12 April
3828:Archived
3795:12 April
3786:Archived
3784:: 1–13.
3778:Tractrix
3769:(1991).
3674:See also
3668:reactive
3642:reactive
3619:reaction
3454:and the
3450:used in
3436:throttle
3267:, where
1147:Examples
760:Category
685:Hamilton
670:Lagrange
665:Clairaut
630:Horrocks
591:velocity
561:Pendulum
549:reactive
521:Rotation
490:dynamics
440:Inertial
426:Friction
309:Velocity
284:Momentum
164:Kinetics
154:Dynamics
132:Branches
116:Timeline
5379:Bibcode
5332:Bibcode
5268:Physnet
5181:Bibcode
5131:Bibcode
4128:Bibcode
4050:Bibcode
1248:equator
1220:gravity
955:centrum
930:History
720:Koopman
680:Poisson
675:Laplace
620:Huygens
615:Galileo
460: (
399:Damping
252:Inertia
246:Impulse
219:kinetic
169:Statics
139:Applied
111:History
5431:
5350:
5300:
5290:
5234:
5224:
5199:
5149:
5057:
5028:
4805:
4778:
4751:
4717:
4689:
4635:
4608:
4578:
4547:
4511:
4484:
4453:
4417:
4268:
4241:
4146:
4101:
4076:
4068:
3982:
3972:
3948:
3938:
3911:
3863:
3820:
3566:
3107:, the
3032:
2693:
2512:
2121:
1810:where
1795:
1723:where
1708:
1598:where
1583:
1181:In an
1045:, and
964:(from
961:‑fugus
893:, and
758:
710:Appell
695:Cauchy
690:Jacobi
635:Halley
625:Newton
610:Kepler
462:linear
458:Motion
304:Torque
279:Moment
214:Energy
204:Couple
5506:Force
5348:S2CID
5320:(PDF)
5197:S2CID
5171:arXiv
5147:S2CID
5121:arXiv
4974:i ≠ j
4387:(PDF)
4376:(PDF)
4144:S2CID
4074:S2CID
4040:arXiv
3789:(PDF)
3774:(PDF)
3727:Notes
3622:force
3501:Some
2715:Force
1255:Note:
1207:Earth
1201:Earth
967:fugiō
944:term
802:is a
715:Gibbs
700:Routh
655:Euler
294:Speed
289:Space
231:Force
5429:ISBN
5298:OCLC
5288:ISBN
5232:OCLC
5222:ISBN
5055:ISBN
5026:ISBN
4972:for
4803:ISBN
4776:ISBN
4749:ISBN
4715:ISBN
4687:ISBN
4662:–88.
4633:ISBN
4606:ISBN
4576:ISBN
4545:ISBN
4509:ISBN
4482:ISBN
4451:ISBN
4415:ISBN
4339:help
4319:2017
4294:2017
4266:ISBN
4239:ISBN
4179:2017
4099:ISBN
4066:PMID
3998:link
3980:OCLC
3970:ISBN
3946:OCLC
3936:ISBN
3909:ISBN
3861:ISBN
3836:2018
3818:ISBN
3797:2018
3594:the
3479:and
3471:Mars
1282:and
1205:The
1020:and
905:and
840:is:
824:mass
299:Time
262:Mass
5458:302
5387:doi
5340:doi
5189:doi
5139:doi
4136:doi
4058:doi
4036:123
3887:325
3857:173
3605:⁄ d
1488:of
1448:+ d
1432:+ d
1224:Sun
1169:".
1167:G's
1095:of
1028:".
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