3034:. The flatness of the Milky Way depends on its rate of rotation in an inertial frame of reference. If its apparent rate of rotation is attributed entirely to rotation in an inertial frame, a different "flatness" is predicted than if it is supposed that part of this rotation is actually due to rotation of the universe and should not be included in the rotation of the galaxy itself. Based upon the laws of physics, a model is set up in which one parameter is the rate of rotation of the Universe. If the laws of physics agree more accurately with observations in a model with rotation than without it, we are inclined to select the best-fit value for rotation, subject to all other pertinent experimental observations. If no value of the rotation parameter is successful and theory is not within observational error, a modification of physical law is considered, for example,
4443:, employed for navigation of seagoing vessels, finds the geometric north. It does so, not by sensing the Earth's magnetic field, but by using inertial space as its reference. The outer casing of the gyrocompass device is held in such a way that it remains aligned with the local plumb line. When the gyroscope wheel inside the gyrocompass device is spun up, the way the gyroscope wheel is suspended causes the gyroscope wheel to gradually align its spinning axis with the Earth's axis. Alignment with the Earth's axis is the only direction for which the gyroscope's spinning axis can be stationary with respect to the Earth and not be required to change direction with respect to inertial space. After being spun up, a gyrocompass can reach the direction of alignment with the Earth's axis in as little as a quarter of an hour.
1553:). Another approach is to identify all real sources for real forces and account for them. A possible issue with this approach is the possibility of missing something, or accounting inappropriately for their influence, perhaps, again, due to Mach's principle and an incomplete understanding of the universe. A third approach is to look at the way the forces transform when shifting reference frames. Fictitious forces, those that arise due to the acceleration of a frame, disappear in inertial frames and have complicated rules of transformation in general cases. Based on the universality of physical law and the request for frames where the laws are most simply expressed, inertial frames are distinguished by the absence of such fictitious forces.
739:
4383:
stationary spheres from a rotating frame), the zero tension in the string is accounted for by observing that the centripetal force is supplied by the centrifugal and
Coriolis forces in combination, so no tension is needed. If the spheres really are rotating, the tension observed is exactly the centripetal force required by the circular motion. Thus, measurement of the tension in the string identifies the inertial frame: it is the one where the tension in the string provides exactly the centripetal force demanded by the motion as it is observed in that frame, and not a different value. That is, the inertial frame is the one where the fictitious forces vanish.
4276:
752:
1650:
2211:
suppose that your watch is running five minutes fast compared to the local standard time. If you know that this is the case, when somebody asks you what time it is, you can deduct five minutes from the time displayed on your watch to obtain the correct time. The measurements that an observer makes about a system depend therefore on the observer's frame of reference (you might say that the bus arrived at 5 past three, when in fact it arrived at three).
4265:
4452:
1389:
4379:, no originating bodies. A second approach is to look at a variety of frames of reference. For any inertial frame, the Coriolis force and the centrifugal force disappear, so application of the principle of special relativity would identify these frames where the forces disappear as sharing the same and the simplest physical laws, and hence rule that the rotating frame is not an inertial frame.
3653:
3507:
4224:
2481:, which determines whether the ratio of inertial to gravitational mass is the same for all bodies, regardless of size or composition. To date no difference has been found to a few parts in 10. For some discussion of the subtleties of the Eötvös experiment, such as the local mass distribution around the experimental site (including a quip about the mass of Eötvös himself), see Franklin.
2853:
3872:
2203:, that is, 25 seconds, as before. Note how much easier the problem becomes by choosing a suitable frame of reference. The third possible frame of reference would be attached to the second car. That example resembles the case just discussed, except the second car is stationary and the first car moves backward towards it at
4374:
For example, consider a stationary object in an inertial frame. Being at rest, no net force is applied. But in a frame rotating about a fixed axis, the object appears to move in a circle, and is subject to centripetal force. How can it be decided that the rotating frame is a non-inertial frame? There
3518:
3372:
2230:
For a simple example involving only the orientation of two observers, consider two people standing, facing each other on either side of a north-south street. See Figure 2. A car drives past them heading south. For the person facing east, the car was moving to the right. However, for the person facing
6067:
That is, the universality of the laws of physics requires the same tension to be seen by everybody. For example, it cannot happen that the string breaks under extreme tension in one frame of reference and remains intact in another frame of reference, just because we choose to look at the string from
4431:
and accelerometers to determine accelerations relative to inertial space. After a gyroscope is spun up in a particular orientation in inertial space, the law of conservation of angular momentum requires that it retain that orientation as long as no external forces are applied to it. Three orthogonal
4415:
For these ideas to apply, everything observed in the frame has to be subject to a base-line, common acceleration shared by the frame itself. That situation would apply, for example, to the elevator example, where all objects are subject to the same gravitational acceleration, and the elevator itself
4411:
This principle generalizes the notion of an inertial frame. For example, an observer confined in a free-falling lift will assert that he himself is a valid inertial frame, even if he is accelerating under gravity, so long as he has no knowledge about anything outside the lift. So, strictly speaking,
2210:
It would have been possible to choose a rotating, accelerating frame of reference, moving in a complicated manner, but this would have served to complicate the problem unnecessarily. It is also necessary to note that one can convert measurements made in one coordinate system to another. For example,
1668:
Consider a situation common in everyday life. Two cars travel along a road, both moving at constant velocities. See Figure 1. At some particular moment, they are separated by 200 meters. The car in front is traveling at 22 meters per second and the car behind is traveling at 30 meters per second. If
3347:
When there is accelerated motion due to a force being exerted there is manifestation of inertia. If an electric car designed to recharge its battery system when decelerating is switched to braking, the batteries are recharged, illustrating the physical strength of manifestation of inertia. However,
3054:
rotation. However, if rotation were found, interpretation of observations in a frame tied to the universe would have to be corrected for the fictitious forces inherent in such rotation in classical physics and special relativity, or interpreted as the curvature of spacetime and the motion of matter
1524:
is an indication of zero net force, the rule does not identify inertial reference frames because straight-line motion can be observed in a variety of frames. If the rule is interpreted as defining an inertial frame, then being able to determine when zero net force is applied is crucial. The problem
1008:
The laws of
Newtonian mechanics do not always hold in their simplest form...If, for instance, an observer is placed on a disc rotating relative to the earth, he/she will sense a 'force' pushing him/her toward the periphery of the disc, which is not caused by any interaction with other bodies. Here,
3010:
In practice, using a frame of reference based upon the fixed stars as though it were an inertial frame of reference introduces little discrepancy. For example, the centrifugal acceleration of the Earth because of its rotation about the Sun is about thirty million times greater than that of the Sun
1548:
There are several approaches to this issue. One approach is to argue that all real forces drop off with distance from their sources in a known manner, so it is only needed that a body is far enough away from all sources to ensure that no force is present. A possible issue with this approach is the
1033:
In practical terms, the equivalence of inertial reference frames means that scientists within a box moving with a constant absolute velocity cannot determine this velocity by any experiment. Otherwise, the differences would set up an absolute standard reference frame. According to this definition,
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1580:
in two ways: first, it is restricted to mechanics, and second, it makes no mention of simplicity. It shares the special principle of the invariance of the form of the description among mutually translating reference frames. The role of fictitious forces in classifying reference frames is pursued
3006:
at a speed of 117 km/s. The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space. Rather, the identification of an inertial frame is based on the simplicity of the laws of physics in the frame. The laws of nature take a simpler form in
4382:
Newton examined this problem himself using rotating spheres, as shown in Figure 2 and Figure 3. He pointed out that if the spheres are not rotating, the tension in the tying string is measured as zero in every frame of reference. If the spheres only appear to rotate (that is, we are watching
2524:
of all observed double star systems remains fixed with respect to the direction of the angular momentum of the Solar System. These observations allowed him to conclude that inertial frames inside the galaxy do not rotate with respect to one another, and that the space of the Milky Way is
3348:
the manifestation of inertia does not prevent acceleration (or deceleration), for manifestation of inertia occurs in response to change in velocity due to a force. Seen from the perspective of a rotating frame of reference the manifestation of inertia appears to exert a force (either in
2705:
2220:
2234:
For a more complex example involving observers in relative motion, consider Alfred, who is standing on the side of a road watching a car drive past him from left to right. In his frame of reference, Alfred defines the spot where he is standing as the origin, the road as the
1009:
the acceleration is not the consequence of the usual force, but of the so-called inertial force. Newton's laws hold in their simplest form only in a family of reference frames, called inertial frames. This fact represents the essence of the
Galilean principle of relativity:
4412:
inertial frame is a relative concept. With this in mind, inertial frames can collectively be defined as a set of frames which are stationary or moving at constant velocity with respect to each other, so that a single inertial frame is defined as an element of this set.
1530:
The weakness of the principle of inertia lies in this, that it involves an argument in a circle: a mass moves without acceleration if it is sufficiently far from other bodies; we know that it is sufficiently far from other bodies only by the fact that it moves without
2496:, whereby objects move in a way dictated by the curvature of spacetime. As a consequence of this curvature, it is not a given in general relativity that inertial objects moving at a particular rate with respect to each other will continue to do so. This phenomenon of
983:
Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to
2953:
were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, an important case being frames rotating relative to the fixed stars, the laws of motion did not hold in their simplest form, but had to be supplemented by the addition of
3668:
1636:. The predictions of special relativity have been extensively verified experimentally. The Lorentz transformation reduces to the Galilean transformation as the speed of light approaches infinity or as the relative velocity between frames approaches zero.
3958:
2507:, where curvature effects become less important and the earlier inertial frame arguments can come back into play. Consequently, modern special relativity is now sometimes described as only a "local theory". "Local" can encompass, for example, the entire
4049:
4432:
gyroscopes establish an inertial reference frame, and the accelerators measure acceleration relative to that frame. The accelerations, along with a clock, can then be used to calculate the change in position. Thus, inertial navigation is a form of
2515:
observed the motion of pairs of stars orbiting each other. He found that the two orbits of the stars of such a system lie in a plane, and the perihelion of the orbits of the two stars remains pointing in the same direction with respect to the
1140:
The original question, "relative to what frame of reference do the laws of motion hold?" is revealed to be wrongly posed. The laws of motion essentially determine a class of reference frames, and (in principle) a procedure for constructing
3648:{\displaystyle \mathbf {a} '=\mathbf {a} -{\dot {\boldsymbol {\omega }}}\times \mathbf {r} '-2{\boldsymbol {\omega }}\times \mathbf {v} '-{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times \mathbf {r} ')-\mathbf {A} _{0}.}
3502:{\displaystyle \mathbf {a} =\mathbf {a} '+{\dot {\boldsymbol {\omega }}}\times \mathbf {r} '+2{\boldsymbol {\omega }}\times \mathbf {v} '+{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times \mathbf {r} ')+\mathbf {A} _{0},}
4219:{\displaystyle \mathbf {F} '_{\mathrm {centrifugal} }=-m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times \mathbf {r} ')=m(\omega ^{2}\mathbf {r} '-({\boldsymbol {\omega }}\cdot \mathbf {r} '){\boldsymbol {\omega }})}
1281:
1069:. An inertial frame was then one in uniform translation relative to absolute space. However, some "relativists", even at the time of Newton, felt that absolute space was a defect of the formulation, and should be replaced.
4395:
If bodies, any how moved among themselves, are urged in the direction of parallel lines by equal accelerative forces, they will continue to move among themselves, after the same manner as if they had been urged by no such
2978:
would not work for the rotating observer without invoking centrifugal and
Coriolis forces to account for their observations (tension in the case of the spheres; parabolic water surface in the case of the rotating bucket).
4375:
are two approaches to this resolution: one approach is to look for the origin of the fictitious forces (the
Coriolis force and the centrifugal force). It will be found there are no sources for these forces, no associated
2428:
Here the relation between inertial and non-inertial observational frames of reference is considered. The basic difference between these frames is the need in non-inertial frames for fictitious forces, as described below.
3342:
2848:{\displaystyle \mathbf {F} '=\mathbf {F} -2m\mathbf {\Omega } \times \mathbf {v} _{B}-m\mathbf {\Omega } \times (\mathbf {\Omega } \times \mathbf {x} _{B})-m{\frac {d\mathbf {\Omega } }{dt}}\times \mathbf {x} _{B}\ ,}
2966:. Two experiments were devised by Newton to demonstrate how these forces could be discovered, thereby revealing to an observer that they were not in an inertial frame: the example of the tension in the cord linking
1888:
4319:
The equations of motion in a non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a
3250:
3203:
3151:
1134:
The utility of operational definitions was carried much further in the special theory of relativity. Some historical background including Lange's definition is provided by DiSalle, who says in summary:
2915:= 0; that is, they are zero for an inertial frame (which, of course, does not rotate); they take on a different magnitude and direction in every rotating frame, depending upon its particular value of
93:
5652:
3359:
A common sort of accelerated reference frame is a frame that is both rotating and translating (an example is a frame of reference attached to a CD which is playing while the player is carried).
2686:
5467:
3867:{\displaystyle \mathbf {F} '=\mathbf {F} _{\mathrm {physical} }+\mathbf {F} '_{\mathrm {Euler} }+\mathbf {F} '_{\mathrm {Coriolis} }+\mathbf {F} '_{\mathrm {centripetal} }-m\mathbf {A} _{0},}
1108:
The existence of absolute space contradicts the internal logic of classical mechanics since, according to the
Galilean principle of relativity, none of the inertial frames can be singled out.
1097:
A reference frame in which a mass point thrown from the same point in three different (non co-planar) directions follows rectilinear paths each time it is thrown, is called an inertial frame.
2589:
2283:-axis. In this frame of reference, it is Betsy who is stationary and the world around her that is moving – for instance, as she drives past Alfred, she observes him moving with velocity
2128:
1430:
1215:
2919:; they are ubiquitous in the rotating frame (affect every particle, regardless of circumstance); and they have no apparent source in identifiable physical sources, in particular,
1330:
117:
6212:
2462:
There is no experiment observers can perform to distinguish whether an acceleration arises because of a gravitational force or because their reference frame is accelerating.
3883:
2039:
1186:
2271:
Now consider Betsy, the person driving the car. Betsy, in choosing her frame of reference, defines her location as the origin, the direction to her right as the positive
1975:
1935:
3969:
1757:
1717:
2477:
This idea was introduced in
Einstein's 1907 article "Principle of Relativity and Gravitation" and later developed in 1911. Support for this principle is found in the
2072:
3074:
An accelerated frame of reference is often delineated as being the "primed" frame, and all variables that are dependent on that frame are notated with primes, e.g.
1676:
as follows. We stand on the side of the road and start a stop-clock at the exact moment that the second car passes us, which happens to be when they are a distance
4282:: Exploded view of rotating spheres in an inertial frame of reference showing the centripetal forces on the spheres provided by the tension in the tying string.
1995:
2268:-direction. Alfred's frame of reference is considered an inertial frame because he is not accelerating, ignoring effects such as Earth's rotation and gravity.
2231:
west, the car was moving to the left. This discrepancy is because the two people used two different frames of reference from which to investigate this system.
1561:
The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line.
4842:
4371:
To apply the
Newtonian definition of an inertial frame, the understanding of separation between "fictitious" forces and "real" forces must be made clear.
1669:
we want to find out how long it will take the second car to catch up with the first, there are three obvious "frames of reference" that we could choose.
1444:
provided a body not subject to forces appears to move in a straight line. If that motion is seen in one frame, it will also appear that way in the other.
2938:; only non-inertial observers need fictitious forces. The laws of physics in the inertial frame are simpler because unnecessary forces are not present.
1223:
5037:
5464:
4271:: Two spheres tied with a string and rotating at an angular rate ω. Because of the rotation, the string tying the spheres together is under tension.
2931:). For example, the centrifugal force that appears to emanate from the axis of rotation in a rotating frame increases with distance from the axis.
966:
The motion of a body can only be described relative to something else—other bodies, observers, or a set of spacetime coordinates. These are called
1166:
postulate the equivalence of all inertial reference frames. The
Galilean transformation transforms coordinates from one inertial reference frame,
1601:, like Newtonian mechanics, postulates the equivalence of all inertial reference frames. However, because special relativity postulates that the
824:, i.e., remain at rest until acted upon by external forces, and the laws of nature can be observed without the need for acceleration correction.
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5975:
5801:
4912:
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is constant, she is in an inertial frame of reference, and she will find the acceleration to be the same as Alfred in her frame of reference,
5774:
3007:
inertial frames of reference because in these frames one did not have to introduce inertial forces when writing down Newton's law of motion.
783:
4664:
999:
This simplicity manifests itself in that inertial frames have self-contained physics without the need for external causes, while physics in
5002:
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2904:
5748:
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showing scenes as viewed from both an inertial frame and a rotating frame of reference, visualizing the
Coriolis and centrifugal forces.
2990:. Those that are outside our galaxy (such as nebulae once mistaken to be stars) participate in their own motion as well, partly due to
491:
5855:
5672:
4975:
4764:
1488:
An inertial frame of reference is one in which the motion of a particle not subject to forces is in a straight line at constant speed.
1463:
Newton viewed the first law as valid in any reference frame that is in uniform motion (neither rotating nor accelerating) relative to
1111:
Absolute space does not explain inertial forces since they are related to acceleration with respect to any one of the inertial frames.
5251:
4815:
5153:
2310:
Finally, as an example of non-inertial observers, assume Candace is accelerating her car. As she passes by him, Alfred measures her
974:, all physical laws take their simplest form in an inertial frame, and there exist multiple inertial frames interrelated by uniform
5828:
5438:
5224:
5094:
4295:
The effect of this being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations…
464:
6355:
2949:. In reference frames that were either at rest with respect to the fixed stars or in uniform translation relative to these stars,
2492:
with a metric that produces non-zero curvature. In general relativity, the principle of inertia is replaced with the principle of
3089:
The vector from the origin of an inertial reference frame to the origin of an accelerated reference frame is commonly notated as
2137:
situated in the first car. In this case, the first car is stationary and the second car is approaching from behind at a speed of
855:
2899:′ are the "fictitious" forces for this frame, whose causes are external to the system in the frame. The first extra term is the
1897:= 0 s the first car is 200m down the road and the second car is right beside us, as expected. We want to find the time at which
1034:
supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the
6255:
5634:
5295:
However, in the Newtonian system the Galilean transformation connects these frames and in the special theory of relativity the
49:
4549:
3209:
3162:
3110:
1453:
840:
6043:
5682:
5526:
5448:
5418:
5377:
5352:
5324:
3275:
5516:
5489:
2699:, but also additional terms (the paragraph following this equation presents the main points without detailed mathematics):
2488:
modifies the distinction between nominally "inertial" and "non-inertial" effects by replacing special relativity's "flat"
4948:
446:
2500:
means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity.
1003:
has external causes. The principle of simplicity can be used within Newtonian physics as well as in special relativity:
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3003:
1509:
will remain at rest and a body in motion will continue to move uniformly—that is, in a straight line and at constant
776:
4481:
2647:
1683:
apart. Since neither of the cars is accelerating, we can determine their positions by the following formulas, where
6271:
4310:
The presence of fictitious forces indicates the physical laws are not the simplest laws available, in terms of the
3093:. Given a point of interest that exists in both frames, the vector from the inertial origin to the point is called
3014:
To illustrate further, consider the question: "Does the Universe rotate?" An answer might explain the shape of the
2555:
2326:-direction. Assuming Candace's acceleration is constant, what acceleration does Betsy measure? If Betsy's velocity
899:
vary depending on the acceleration of that frame with respect to an inertial frame. Viewed from the perspective of
738:
1114:
Absolute space acts on physical objects by inducing their resistance to acceleration but it cannot be acted upon.
1065:
Newton posited an absolute space considered well-approximated by a frame of reference stationary relative to the
112:
3018:
galaxy using the laws of physics, although other observations might be more definitive; that is, provide larger
5583:
5553:
4477:
4357:
3027:
2078:
367:
107:
17:
1398:
866:
of objects in one inertial frame can be converted to measurements in another by a simple transformation — the
6418:
4666:
The Principle of Relativity: a collection of original memoirs on the special and general theory of relativity
2493:
924:
851:. However, this is not required for the definition, and it is now known that those stars are in fact moving.
5029:
2862:
pointing in the direction of the axis of rotation, and with magnitude equal to the angular rate of rotation
1191:
1147:
6413:
6408:
6336:
4436:
that requires no external input, and therefore cannot be jammed by any external or internal signal source.
4341:
891:
769:
756:
517:
440:
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205:
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of the body according to a rotating observer (different from the velocity seen by the inertial observer).
882:; these approximately match when the relative speed of the frames is low, but differ as it approaches the
4587:
2630:
2423:
1460:
generalizes the notion of an inertial frame to include all physical laws, not simply Newton's first law.
1289:
5284:
1353:
is the relative velocity of the two inertial reference frames. Under Galilean transformations, the time
215:
6370:
4424:
2950:
2614:
of the particle (also a vector) which would be measured by an observer at rest in the frame. The force
1633:
1502:
1102:
The inadequacy of the notion of "absolute space" in Newtonian mechanics is spelled out by Blagojevich:
1089:
656:
545:
471:
331:
264:
1556:
Newton enunciated a principle of relativity himself in one of his corollaries to the laws of motion:
5700:"Constraints on the proper motion of the Andromeda Galaxy based on the survival of its satellite M33"
3953:{\displaystyle \mathbf {F} '_{\mathrm {Euler} }=-m{\dot {\boldsymbol {\omega }}}\times \mathbf {r} '}
2991:
1539:
410:
6320:
5937:
5545:
Information Theory and Quantum Physics: Physical Foundations for Understanding the Conscious Process
3263:
are the velocity and acceleration of the accelerated system with respect to the inertial system and
5883:
Wlodzimierz Godlowski; Marek Szydlowski (2003). "Dark energy and global rotation of the Universe".
4462:
4365:
3031:
1672:
First, we could observe the two cars from the side of the road. We define our "frame of reference"
1085:
686:
530:
4044:{\displaystyle \mathbf {F} '_{\mathrm {Coriolis} }=-2m{\boldsymbol {\omega }}\times \mathbf {v} '}
2003:
1169:
862:
look the same in all inertial reference frames, and no inertial frame is privileged over another.
6387:
4875:
4797:
4554:
4466:
4356:
itself and not from any physical force acting on the body. Examples of fictitious forces are the
3063:
3042:. So far, observations show any rotation of the universe is very slow, no faster than once every
3039:
3023:
1940:
1900:
1618:
1514:
1163:
1060:
867:
636:
400:
4892:
Lange, Ludwig (1885). "Über die wissenschaftliche Fassung des Galileischen Beharrungsgesetzes".
676:
6340:
An example of a new type of cosmological solutions of Einstein's field equations of gravitation
6153:
6033:
5296:
5207:
3271:
are the velocity and acceleration of the point of interest with respect to the inertial frame.
2975:
2542:
2478:
2452:
2376:-direction—a smaller value than Alfred has measured. Similarly, if she is accelerating at rate
1656:: Two cars moving at different but constant velocities observed from stationary inertial frame
1614:
1039:
875:
681:
498:
6233:
5699:
5620:
5590:
5560:
5410:
4691:
4626:
4390:, Newton expressed the idea of undetectability of straight-line accelerations held in common:
4286:
Inertial and non-inertial reference frames can be distinguished by the absence or presence of
1726:
1686:
6128:
5331:
4539:
2970:
about their center of gravity, and the example of the curvature of the surface of water in a
2534:
2503:
However, the general theory reduces to the special theory over sufficiently small regions of
2448:
2045:
975:
691:
666:
352:
170:
6012:
5951:
5902:
5724:
4697:
2867:
1521:
711:
671:
579:
575:
567:
557:
347:
340:
96:
5299:
connects them. The two transformations agree for speeds of translation much less than the
706:
8:
4529:
4387:
3019:
1610:
1550:
1480:
931:
900:
847:, originally thought that one of these frames was absolute — the one approximated by the
831:(straight-line motion) with respect to one another. In such a frame, an object with zero
486:
427:
405:
150:
145:
140:
40:
6016:
5955:
5906:
5728:
4869:
4791:
4701:
1042:
are a subgroup. In Newtonian mechanics, inertial frames of reference are related by the
6352:
6002:
5967:
5918:
5892:
5740:
5714:
4580:
4544:
4534:
4353:
4251:
3274:
These equations allow transformations between the two coordinate systems; for example,
2512:
2497:
2485:
2438:
2419:
1980:
1629:
1598:
1590:
1027:
971:
967:
920:
908:
904:
879:
828:
817:
801:
616:
357:
232:
200:
160:
5697:
2356:-direction (in other words, slowing down), she will find Candace's acceleration to be
6239:
6218:
6108:
6083:
6039:
5922:
5863:
5834:
5807:
5780:
5678:
5609:
5579:
5549:
5522:
5495:
5444:
5414:
5403:
5383:
5373:
5348:
5320:
5257:
5230:
5186:
5159:
5129:
5122:
5100:
5074:
5064:
5008:
4981:
4954:
4922:
4848:
4821:
4770:
4743:
4705:
4670:
4656:
4630:
4619:
4591:
4519:
3059:
2995:
2963:
2955:
1011: The laws of mechanics have the same form in all inertial frames.
943:
871:
797:
626:
583:
540:
535:
476:
252:
242:
135:
6252:
6174:
5744:
5631:
1035:
6311:
5971:
5959:
5942:
5910:
5732:
4287:
4255:
4245:
3363:
3062:
effects are important, there are additional conceptual complications that arise in
2999:
2967:
2928:
2599:
2521:
2508:
2415:
1624:
The invariance of the speed of light leads to counter-intuitive phenomena, such as
1476:
912:
721:
701:
646:
641:
587:
562:
417:
275:
220:
195:
1276:{\displaystyle \mathbf {r} ^{\prime }=\mathbf {r} -\mathbf {r} _{0}-\mathbf {v} t}
1088:
in 1885, to replace Newton's definitions of "absolute space and time" with a more
6423:
6359:
6327:
6300:
6275:
6259:
6189:
6163:
6149:
6058:
For example, there is no body providing a gravitational or electrical attraction.
6029:
5638:
5603:
5573:
5543:
5471:
5314:
5180:
4652:
4648:
4326:
4259:
3353:
2971:
2489:
1595:
1077:
935:
896:
716:
661:
611:
606:
525:
2520:. Schwarzschild pointed out that that was invariably seen: the direction of the
6382:
5300:
4524:
4433:
4361:
4052:
2959:
2946:
2900:
2546:
1602:
1506:
1472:
1464:
1043:
883:
743:
651:
552:
269:
6377:
6364:
6315:
5914:
2923:. Also, fictitious forces do not drop off with distance (unlike, for example,
1371:
between two simultaneous events (or, equivalently, the length of any object, |
6402:
5387:
5078:
4376:
2987:
2924:
2623:
1625:
1549:
historically long-lived view that the distant universe might affect matters (
955:
859:
631:
458:
5119:
6293:
6284:
4660:
2611:
2517:
2311:
1494:
844:
696:
621:
310:
190:
6304:
Effect of the Global Rotation of the Universe on the Formation of Galaxies
1026:
However, this definition of inertial frames is understood to apply in the
827:
All frames of reference with zero acceleration are in a state of constant
5897:
5719:
4440:
4275:
4234:
3961:
3035:
2942:
2908:
1468:
1066:
863:
848:
6268:
6007:
4693:
Einstein's Space-Time: An Introduction to Special and General Relativity
4314:, a frame where fictitious forces are present is not an inertial frame:
3337:{\displaystyle \mathbf {F} =m\mathbf {a} =m\mathbf {A} +m\mathbf {a} '.}
2541:, is satisfied: Any free motion has a constant magnitude and direction.
1513:. Newtonian inertial frames transform among each other according to the
5253:
Six not-so-easy pieces: Einstein's relativity, symmetry, and space-time
4817:
Six not-so-easy pieces: Einstein's relativity, symmetry, and space-time
4634:
2619:
1649:
1606:
481:
155:
5370:
Special relativity and classical field theory: the theoretical minimum
2982:
As now known, the fixed stars are not fixed. Those that reside in the
5963:
5882:
5698:
Abraham Loeb; Mark J. Reid; Andreas Brunthaler; Heino Falcke (2005).
4428:
3156:
Taking the first and second derivatives of this with respect to time
3015:
2983:
2504:
2386:-direction (speeding up), she will observe Candace's acceleration as
895:
has non-zero acceleration. In such a frame, the interactions between
832:
503:
6288:
On physical foundations and observational effects of cosmic rotation
4616:
4451:
3097:, and the vector from the accelerated origin to the point is called
1883:{\displaystyle x_{1}(t)=d+v_{1}t=200+22t,\quad x_{2}(t)=v_{2}t=30t.}
5736:
4264:
3352:
direction, or in a direction orthogonal to an object's motion, the
2889:
2858:
where the angular rotation of the frame is expressed by the vector
2254:
1467:; as a practical matter, "absolute space" was considered to be the
1368:
836:
422:
305:
280:
5347:(4th Revised English ed.). Pergamon Press. pp. 273–274.
5063:(Second ed.). Oxford UK: Oxford University Press. p. 1.
3050:
years (10 rad/yr), and debate persists over whether there is
2945:
were invoked as a reference frame, supposedly at rest relative to
1388:
6391:
6265:
Rom. Journ. Phys., Vol. 53, Nos. 1–2, P. 405–415, Bucharest, 2008
1452:
frame of reference, or inertial reference frame, is one in which
1449:
951:
947:
916:
821:
395:
248:
165:
6263:
Modeling the electric and magnetic fields in a rotating universe
6210:
2691:
which looks the same as in an inertial frame, but now the force
2295:-direction. If she is driving north, then north is the positive
1367:
between two events is the same for all reference frames and the
911:
caused by the interaction of objects have to be supplemented by
843:
holds. Such frames are known as inertial. Some physicists, like
4582:
Discovering the Natural Laws: The Experimental Basis of Physics
2920:
2457:
General relativity is based upon the principle of equivalence:
2219:
954:. Nevertheless, for many applications the Earth is an adequate
454:
300:
210:
5487:
5222:
6080:
Fundamentals of High Accuracy Inertial Navigation, Volume 174
4941:
L. Lange (1885) as quoted by Max von Laue in his book (1921)
4349:
1510:
1498:
939:
290:
285:
227:
6177:(1900). "La théorie de Lorentz et le Principe de Réaction".
6107:(pbk. ed.). Hoboken: Taylor & Francis. p. 95.
4647:
3512:
or, to solve for the acceleration in the accelerated frame,
1493:
Hence, with respect to an inertial frame, an object or body
5641:
Section 3: The Work of Karl Schwarzschild (2.2 MB PDF-file)
5465:
On the influence of gravitation on the propagation of light
4840:
4696:, Springer Science & Business Media, pp. 209–210,
295:
258:
2911:. These terms all have these properties: they vanish when
1436:
has an arbitrary but fixed rotation with respect to frame
923:, the fictitious (i.e. inertial) forces are attributed to
6214:
Mach's Principle: From Newton's Bucket to Quantum Gravity
5799:
5120:
Robert Resnick; David Halliday; Kenneth S. Krane (2001).
2301:-direction; if she turns east, east becomes the positive
2277:-axis, and the direction in front of her as the positive
2241:-axis, and the direction in front of him as the positive
934:, its surface is not an inertial frame of reference. The
88:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
5440:
Physics for Scientists and Engineers with Modern Physics
5249:
4813:
3245:{\displaystyle \mathbf {a} =\mathbf {A} +\mathbf {a} '.}
3198:{\displaystyle \mathbf {v} =\mathbf {V} +\mathbf {v} ',}
3146:{\displaystyle \mathbf {r} =\mathbf {R} +\mathbf {r} '.}
2470:
Physics for Scientists and Engineers with Modern Physics
1395:: Two frames of reference moving with relative velocity
5319:(reprinted ed.). Courier Corporation. p. 27.
4921: ed.). Oxford University Press. pp. 645–646.
2154:. To catch up to the first car, it will take a time of
1049:
4235:
Separating non-inertial from inertial reference frames
2626:, electromagnetic, gravitational, and nuclear forces.
1349:
represent shifts in the origin of space and time, and
5518:
No Easy Answers: Science and the Pursuit of Knowledge
4063:
3972:
3886:
3671:
3521:
3375:
3287:
3212:
3165:
3113:
2708:
2650:
2558:
2406:-direction—a larger value than Alfred's measurement.
2081:
2048:
2006:
1983:
1943:
1903:
1772:
1729:
1689:
1401:
1292:
1226:
1194:
1172:
820:. Observed relative to such a frame, objects exhibit
52:
5367:
5342:
2344:-direction. However, if she is accelerating at rate
2133:
Alternatively, we could choose a frame of reference
1613:, the transformation between inertial frames is the
1479:
is abandoned, and an inertial frame in the field of
1217:, by simple addition or subtraction of coordinates:
5436:
835:acting on it, is perceived to move with a constant
6390:from the original on 13 November 2021 – via
5402:
5121:
4973:
4762:
4618:
4579:
4218:
4043:
3952:
3866:
3647:
3501:
3336:
3244:
3197:
3145:
2847:
2680:
2583:
2122:
2066:
2033:
1989:
1969:
1929:
1882:
1751:
1711:
1424:
1324:
1275:
1209:
1180:
992:The foundation of the general theory of relativity
87:
6028:
5091:For a discussion of the role of fixed stars, see
5036:. Metaphysics Research Lab, Stanford University.
4910:
4577:
938:can deflect certain forms of motion as seen from
6400:
6269:Yuri N. Obukhov, Thoralf Chrobok, Mike Scherfner
6168:Relativity, the special and the general theories
5853:
5605:Cosmological Inflation and Large-Scale Structure
4406:Corollary VI, p. 89, in Andrew Motte translation
1719:is the position in meters of car one after time
1571:, Corollary V, p. 88 in Andrew Motte translation
5772:
5644:
5491:Physics Through the Nineteen Nineties: Overview
4789:
4617:Sidney Borowitz; Lawrence A. Bornstein (1968).
2528:
1660:attached to the road and moving inertial frame
5650:
5521:. University of Pittsburgh Press. p. 66.
5514:
5457:
5027:
2681:{\displaystyle \mathbf {F} '=m\mathbf {a} \ ,}
2622:of all "real" forces on the particle, such as
5571:
5178:
5000:
4891:
2584:{\displaystyle \mathbf {F} =m\mathbf {a} \ ,}
777:
6342:Rev. Mod. Phys., Vol. 21, p. 447, 1949.
6102:
5826:
5670:
5275:
5273:
5128:(5th ed.). Wiley. Volume 1, Chapter 3.
5092:
4735:
4301:Sidney Borowitz and Lawrence A Bornstein in
3362:This arrangement leads to the equation (see
1505:), in the absence of a net force, a body at
1448:Within the realm of Newtonian mechanics, an
6211:Julian B. Barbour; Herbert Pfister (1998).
6035:Mathematical Methods of Classical Mechanics
5608:. Cambridge University Press. p. 329.
5400:
5158:. New Delhi: Tata McGraw-Hill. p. 70.
4967:
4880:rotating sphere Mach cord OR string OR rod.
4669:. Courier Dover Publications. p. 111.
4480:. Unsourced material may be challenged and
4332:Mathematical Methods of Classical Mechanics
3055:along the geodesics in general relativity.
1520:If this rule is interpreted as saying that
5876:
5862:. Imperial College Press. p. 32, §9.
5632:In the Shadow of the Relativity Revolution
5602:Liddle, Andrew R.; Lyth, David H. (2000).
5601:
5205:
5151:
4994:
4946:
4867:
4793:Relativity: The Special and General Theory
4612:
4610:
2226:: Simple-minded frame-of-reference example
1471:In the theory of relativity the notion of
1038:of symmetry transformations, of which the
784:
770:
27:Fundamental concept of classical mechanics
6353:Stanford Encyclopedia of Philosophy entry
6129:"The gyroscope pilots ships & planes"
6103:Kennie, T.J.M.; Petrie, G., eds. (1993).
6077:
6006:
5896:
5718:
5270:
5212:. Princeton University Press. p. 58.
5199:
5172:
4756:
4621:A Contemporary View of Elementary Physics
4573:
4571:
4500:Learn how and when to remove this message
4352:that result from the acceleration of the
4303:A Contemporary View of Elementary Physics
2123:{\displaystyle t=25\ \mathrm {seconds} .}
6231:
6173:
5847:
5508:
5494:. National Academies Press. p. 15.
5430:
5368:Susskind, Leonard; Art Friedman (2017).
5243:
5058:
4950:A Modern Approach to Classical Mechanics
4874:. The Open Court Publishing Co. p.
4783:
4274:
4263:
2934:All observers agree on the real forces,
2218:
1648:
1425:{\displaystyle {\stackrel {\vec {v}}{}}}
1387:
1030:realm and ignores relativistic effects.
6194:On the Electrodynamics of Moving Bodies
6061:
6022:
5793:
5766:
5651:Landau, L. D.; Lifshitz, E. M. (1960).
5488:National Research Council (US) (1986).
5316:Relativity for Scientists and Engineers
5312:
5223:William Geraint Vaughan Rosser (1991).
5145:
5113:
5096:Nothingness: The Science of Empty Space
5052:
5034:The Stanford Encyclopedia of Philosophy
5021:
4904:
4689:
4641:
4607:
4209:
4188:
4132:
4121:
4024:
3928:
3607:
3596:
3575:
3546:
3461:
3450:
3429:
3400:
2525:approximately Galilean or Minkowskian.
2247:-axis. To him, the car moves along the
14:
6401:
6238:. Springer. p. 369; Footnote 12.
5996:
5443:. Pearson Prentice Hall. p. 155.
5409:. Cambridge University Press. p.
5336:
5216:
5185:. London/Berlin: Springer. p. 6.
4841:Armin Wachter; Henning Hoeber (2006).
4834:
4807:
4683:
4586:. Courier Dover Publications. p.
4568:
2629:In contrast, Newton's second law in a
2409:
1893:Notice that these formulas predict at
1759:is the position of car two after time
1621:which is used in Newtonian mechanics.
1210:{\displaystyle \mathbf {s} ^{\prime }}
1157:
970:. According to the first postulate of
816:) is a stationary or uniformly moving
6052:
5997:Gilson, James G. (1 September 2004),
5935:
5929:
5664:
5541:
5394:
5372:. New York: Hachette UK. Figure 2.1.
5289:
2432:
2214:
1584:
466:Newton's law of universal gravitation
6333:Nature 298, 451 – 454 (29 July 1982)
6306:General Relativity and Gravitation,
5820:
5800:Peter Graneau; Neal Graneau (2006).
5578:. Academic Publishers. p. 116.
4861:
4729:
4478:adding citations to reliable sources
4445:
1050:Newton's inertial frame of reference
5803:In the Grip of the Distant Universe
5754:from the original on 11 August 2017
5481:
5405:Introduction to Classical Mechanics
5155:Introduction to classical mechanics
5040:from the original on 7 January 2016
4935:
4742:. Hackett Publishing. p. 212.
3104:From the geometry of the situation
3004:collision course with the Milky Way
1325:{\displaystyle t^{\prime }=t-t_{0}}
447:Mechanics of planar particle motion
55:
24:
6143:
5885:General Relativity and Gravitation
5572:Bandyopadhyay, Nikhilendu (2000).
4102:
4099:
4096:
4093:
4090:
4087:
4084:
4081:
4078:
4075:
4072:
4002:
3999:
3996:
3993:
3990:
3987:
3984:
3981:
3907:
3904:
3901:
3898:
3895:
3834:
3831:
3828:
3825:
3822:
3819:
3816:
3813:
3810:
3807:
3804:
3784:
3781:
3778:
3775:
3772:
3769:
3766:
3763:
3743:
3740:
3737:
3734:
3731:
3714:
3711:
3708:
3705:
3702:
3699:
3696:
3693:
2443:Introduction to general relativity
2113:
2110:
2107:
2104:
2101:
2098:
2095:
1298:
1234:
1202:
919:. Viewed from the perspective of
25:
6435:
6346:
6121:
5978:from the original on 5 March 2016
5806:. World Scientific. p. 147.
5250:Richard Phillips Feynman (1998).
5030:"Space and Time: Inertial Frames"
4953:. World Scientific. p. 169.
4844:Compendium of Theoretical Physics
4814:Richard Phillips Feynman (1998).
4718:from the original on 7 March 2023
4348:forces (pseudo-forces); that is,
2986:turn with the galaxy, exhibiting
1644:
1054:
878:(combined with a translation) in
6135:. 15 March 1943. pp. 80–83.
6105:Engineering Surveying Technology
5478:, vol. 35, (1911) : 898–908
5007:. London: Springer. p. 58.
4977:Gravitation and Gauge Symmetries
4766:Gravitation and Gauge Symmetries
4450:
4197:
4173:
4141:
4066:
4033:
3975:
3942:
3889:
3851:
3798:
3757:
3725:
3687:
3674:
3658:Multiplying through by the mass
3632:
3616:
3584:
3560:
3536:
3524:
3486:
3470:
3438:
3414:
3386:
3377:
3323:
3311:
3300:
3289:
3231:
3222:
3214:
3184:
3175:
3167:
3132:
3123:
3115:
3069:
2974:. In both cases, application of
2829:
2809:
2783:
2774:
2763:
2746:
2737:
2723:
2711:
2668:
2653:
2571:
2560:
1576:This principle differs from the
1266:
1252:
1243:
1229:
1197:
1174:
1162:Classical theories that use the
1127:Gravitation and Gauge Symmetries
1019:Gravitation and Gauge Symmetries
958:of an inertial reference frame.
751:
750:
737:
70:
6281:Phys. Rev. D 66, 043518 (2002)
6096:
6071:
5990:
5691:
5660:. Pergamon Press. pp. 4–6.
5625:
5595:
5565:
5535:
5361:
5343:LD Landau; LM Lifshitz (1975).
5306:
5226:Introductory Special Relativity
5085:
4885:
4796:. H. Holt and Company. p.
4419:
4312:special principle of relativity
2695:′ is the resultant of not only
2641:about an axis, takes the form:
2635:non-inertial frame of reference
1832:
1458:principle of special relativity
1150:Space and Time: Inertial Frames
961:
856:principle of special relativity
5858:. In J. M. T. Thompson (ed.).
5833:. Da Capo Press. p. 275.
5779:. Springer. pp. 235–236.
5345:The Classical Theory of Fields
5099:. Da Capo Press. p. 150.
5028:Robert DiSalle (Summer 2002).
4416:accelerates at the same rate.
4311:
4213:
4205:
4184:
4158:
4149:
4128:
3624:
3603:
3478:
3457:
3028:microwave background radiation
2793:
2770:
1849:
1843:
1789:
1783:
1746:
1740:
1706:
1700:
1577:
1457:
1413:
13:
1:
6279:Shear-free rotating inflation
6160:, 2nd ed. (Freeman, NY, 1992)
6078:Chatfield, Averil B. (1997).
5425:acceleration azimuthal Morin.
4561:
4342:non-inertial reference frames
3026:, like the anisotropy of the
2895:The extra terms in the force
373:Koopman–von Neumann mechanics
5575:Theory of Special Relativity
5437:Douglas C. Giancoli (2007).
5032:. In Edward N. Zalta (ed.).
4919:Absolute or Relative Motion?
4802:The Principle of Relativity.
2879:locates the body and vector
2637:), rotating at angular rate
2529:Inertial frames and rotation
2034:{\displaystyle 200+22t=30t,}
1599:theory of special relativity
1525:was summarized by Einstein:
1515:Galilean group of symmetries
1503:Newton's first law of motion
1454:Newton's first law of motion
1181:{\displaystyle \mathbf {s} }
925:geodesic motion in spacetime
892:non-inertial reference frame
841:Newton's first law of motion
441:Non-inertial reference frame
7:
6217:. Birkhäuser. p. 445.
6198:The Principle of Relativity
5938:"Is the Universe rotating?"
5856:"The Paradigm of Inflation"
5256:. Basic Books. p. 50.
4974:Milutin Blagojević (2002).
4945:, p. 34, and translated by
4820:. Basic Books. p. 73.
4763:Milutin Blagojević (2002).
4512:
4425:Inertial navigation systems
3011:about the galactic center.
2631:rotating frame of reference
2606:the mass of a particle and
2424:Rotating frame of reference
1970:{\displaystyle x_{1}=x_{2}}
1930:{\displaystyle x_{1}=x_{2}}
1639:
1501:is applied, and (following
1074:inertial frame of reference
806:inertial frame of reference
368:Appell's equation of motion
238:Inertial frame of reference
10:
6440:
5936:Birch, P. (29 July 1982).
5542:Green, Herbert S. (2000).
4911:Julian B. Barbour (2001).
4847:. Birkhäuser. p. 98.
4602:reference laws of physics.
4578:Milton A. Rothman (1989).
4249:
4243:
3038:is invoked to explain the
2446:
2436:
2413:
1664:attached to the first car.
1634:relativity of simultaneity
1588:
1058:
946:will reduce the effective
6378:"Is Gravity An Illusion?"
6331:Is the Universe rotating?
6038:. Springer. p. 129.
5854:J Garcio-Bellido (2005).
5707:The Astrophysical Journal
5674:The Music of the Big Bang
5548:. Springer. p. 154.
5209:The Meaning of Relativity
4914:The Discovery of Dynamics
4366:rotating reference frames
4344:are subject to so-called
4239:
2992:expansion of the universe
1540:The Meaning of Relativity
921:general relativity theory
6205:Rotation of the Universe
5776:Einstein from "B" to "Z"
5773:John J. Stachel (2002).
5677:. Springer. p. 59.
5470:24 December 2020 at the
5285:Andrew Motte Translation
5229:. CRC Press. p. 3.
5061:The Theory of Relativity
4980:. CRC Press. p. 5.
4871:The Science of Mechanics
4790:Albert Einstein (1920).
4769:. CRC Press. p. 4.
4739:The Structure of Science
4690:Ferraro, Rafael (2007),
3064:quantum reference frames
3032:Big Bang nucleosynthesis
1752:{\displaystyle x_{2}(t)}
1712:{\displaystyle x_{1}(t)}
814:Galilean reference frame
531:Rotating reference frame
363:Hamilton–Jacobi equation
6358:4 December 2010 at the
6316:10.1023/A:1018867011142
5915:10.1023/A:1027301723533
5515:Allan Franklin (2007).
4943:Die Relativitätstheorie
4625:. McGraw-Hill. p.
4555:Quantum reference frame
3040:galactic rotation curve
3024:measurement uncertainty
2951:Newton's laws of motion
2866:, symbol × denotes the
2067:{\displaystyle 8t=200,}
1619:Galilean transformation
1456:is valid. However, the
1164:Galilean transformation
1061:Absolute space and time
1040:Lorentz transformations
868:Galilean transformation
472:Newton's laws of motion
332:Newton's laws of motion
6179:Archives Neerlandaises
6154:John Archibald Wheeler
5297:Lorentz transformation
5179:NMJ Woodhouse (2003).
5001:NMJ Woodhouse (2003).
4894:Philosophische Studien
4409:
4338:
4335:Second Edition, p. 129
4308:
4283:
4272:
4220:
4045:
3954:
3868:
3649:
3503:
3338:
3246:
3199:
3147:
2849:
2682:
2585:
2533:In an inertial frame,
2475:
2227:
2124:
2068:
2035:
1991:
1971:
1931:
1884:
1753:
1713:
1665:
1615:Lorentz transformation
1574:
1546:
1491:
1445:
1426:
1326:
1277:
1211:
1182:
1155:
1132:
1100:
1090:operational definition
1081:
1024:
997:
876:Lorentz transformation
499:Simple harmonic motion
412:Euler's laws of motion
206:D'Alembert's principle
89:
6253:B Ciobanu, I Radinchi
6200:, page 38. Dover 1923
5860:Advances in Astronomy
5827:Henning Genz (2001).
5671:Amedeo Balbi (2008).
5313:Skinner, Ray (2014).
5093:Henning Genz (2001).
4736:Ernest Nagel (1979).
4540:Local reference frame
4392:
4316:
4292:
4278:
4267:
4221:
4046:
3955:
3869:
3650:
3504:
3339:
3247:
3200:
3148:
2941:In Newton's time the
2850:
2683:
2586:
2468:Douglas C. Giancoli,
2459:
2449:Equivalence principle
2222:
2125:
2069:
2036:
1992:
1972:
1932:
1885:
1754:
1714:
1652:
1558:
1527:
1497:only when a physical
1485:
1427:
1391:
1385:|) is also the same.
1327:
1278:
1212:
1183:
1137:
1104:
1094:
1005:
980:
353:Hamiltonian mechanics
171:Statistical mechanics
90:
6419:Theory of relativity
6326:5 March 2016 at the
6258:19 July 2013 at the
5401:David Morin (2008).
4474:improve this section
4061:
3970:
3884:
3669:
3519:
3373:
3285:
3210:
3163:
3111:
2998:. For instance, the
2994:, and partly due to
2968:two spheres rotating
2907:, and the third the
2868:vector cross product
2706:
2648:
2556:
2079:
2046:
2004:
1981:
1941:
1937:. Therefore, we set
1901:
1770:
1727:
1687:
1522:straight-line motion
1399:
1290:
1224:
1192:
1170:
1125:Milutin Blagojević:
1017:Milutin Blagojević:
839:, or, equivalently,
576:Angular acceleration
568:Rotational frequency
348:Lagrangian mechanics
341:Analytical mechanics
97:Second law of motion
50:
6414:Frames of reference
6409:Classical mechanics
6299:9 July 2017 at the
6274:9 July 2017 at the
6017:2004physics...9010G
5999:Mach's Principle II
5956:1982Natur.298..451B
5907:2003GReGr..35.2171G
5729:2005ApJ...633..894L
5637:20 May 2017 at the
5621:Extract of page 329
5591:Extract of page 116
5561:Extract of page 154
5206:A Einstein (1950).
5152:RG Takwale (1980).
4947:Harald Iro (2002).
4868:Ernst Mach (1915).
4702:2007esti.book.....F
4530:Galilean invariance
4388:linear acceleration
4110:
4010:
3915:
3842:
3792:
3751:
3366:for a derivation):
3276:Newton's second law
2996:peculiar velocities
2976:Newton's second law
2958:, for example, the
2543:Newton's second law
2410:Non-inertial frames
2314:and finds it to be
1481:classical mechanics
1158:Newtonian mechanics
1001:non-inertial frames
968:frames of reference
901:classical mechanics
428:Harmonic oscillator
406:Equations of motion
41:Classical mechanics
35:Part of a series on
6068:a different frame.
5476:Annalen der Physik
5332:Extract of page 27
5182:Special relativity
5004:Special relativity
4550:Newton's first law
4545:Lorentz covariance
4535:General covariance
4427:used a cluster of
4284:
4273:
4252:Non-inertial frame
4216:
4064:
4041:
3973:
3950:
3887:
3864:
3796:
3755:
3723:
3645:
3499:
3334:
3278:can be written as
3242:
3195:
3143:
2845:
2678:
2581:
2535:Newton's first law
2513:Karl Schwarzschild
2498:geodesic deviation
2439:General relativity
2433:General relativity
2420:Non-inertial frame
2228:
2215:Additional example
2120:
2064:
2031:
1987:
1967:
1927:
1880:
1749:
1709:
1666:
1630:length contraction
1591:Special relativity
1585:Special relativity
1446:
1422:
1322:
1273:
1207:
1178:
972:special relativity
905:special relativity
880:special relativity
829:rectilinear motion
818:frame of reference
802:special relativity
744:Physics portal
358:Routhian mechanics
233:Frame of reference
85:
6232:PJ Nahin (1999).
6170:, 15th ed. (1954)
6158:Spacetime Physics
6045:978-0-387-96890-2
5950:(5873): 451–454.
5891:(12): 2171–2187.
5684:978-3-540-78726-6
5528:978-0-8229-5968-7
5450:978-0-13-149508-1
5420:978-0-521-87622-3
5379:978-0-465-09334-2
5354:978-0-7506-2768-9
5326:978-0-486-79367-2
5059:C Møller (1976).
4917:(Reprint of 1989
4520:Absolute rotation
4510:
4509:
4502:
4358:centrifugal force
4288:fictitious forces
4228:centrifugal force
3934:
3552:
3406:
2964:centrifugal force
2956:fictitious forces
2929:electrical forces
2905:centrifugal force
2903:, the second the
2841:
2822:
2674:
2598:the net force (a
2577:
2511:: The astronomer
2479:Eötvös experiment
2453:Eötvös experiment
2093:
1990:{\displaystyle t}
1578:special principle
1537:Albert Einstein:
1419:
1416:
990:Albert Einstein:
944:centrifugal force
913:fictitious forces
872:Newtonian physics
854:According to the
798:classical physics
794:
793:
541:Centrifugal force
536:Centripetal force
492:Euler's equations
477:Relative velocity
253:Moment of inertia
83:
57:
16:(Redirected from
6431:
6395:
6367:
6249:
6228:
6186:
6137:
6136:
6125:
6119:
6118:
6100:
6094:
6093:
6075:
6069:
6065:
6059:
6056:
6050:
6049:
6026:
6020:
6019:
6010:
5994:
5988:
5987:
5985:
5983:
5964:10.1038/298451a0
5933:
5927:
5926:
5900:
5898:astro-ph/0303248
5880:
5874:
5873:
5851:
5845:
5844:
5824:
5818:
5817:
5797:
5791:
5790:
5770:
5764:
5763:
5761:
5759:
5753:
5722:
5720:astro-ph/0506609
5704:
5695:
5689:
5688:
5668:
5662:
5661:
5659:
5648:
5642:
5629:
5623:
5619:
5599:
5593:
5589:
5569:
5563:
5559:
5539:
5533:
5532:
5512:
5506:
5505:
5485:
5479:
5461:
5455:
5454:
5434:
5428:
5427:
5408:
5398:
5392:
5391:
5365:
5359:
5358:
5340:
5334:
5330:
5310:
5304:
5293:
5287:
5277:
5268:
5267:
5247:
5241:
5240:
5220:
5214:
5213:
5203:
5197:
5196:
5176:
5170:
5169:
5149:
5143:
5142:
5140:physics resnick.
5127:
5117:
5111:
5110:
5089:
5083:
5082:
5056:
5050:
5049:
5047:
5045:
5025:
5019:
5018:
4998:
4992:
4991:
4971:
4965:
4964:
4939:
4933:
4932:
4908:
4902:
4901:
4889:
4883:
4882:
4865:
4859:
4858:
4838:
4832:
4831:
4811:
4805:
4804:
4787:
4781:
4780:
4760:
4754:
4753:
4733:
4727:
4726:
4725:
4723:
4687:
4681:
4680:
4645:
4639:
4638:
4624:
4614:
4605:
4604:
4585:
4575:
4505:
4498:
4494:
4491:
4485:
4454:
4446:
4407:
4336:
4306:
4256:Rotating spheres
4246:Fictitious force
4225:
4223:
4222:
4217:
4212:
4204:
4200:
4191:
4180:
4176:
4170:
4169:
4148:
4144:
4135:
4124:
4106:
4105:
4069:
4050:
4048:
4047:
4042:
4040:
4036:
4027:
4006:
4005:
3978:
3959:
3957:
3956:
3951:
3949:
3945:
3936:
3935:
3927:
3911:
3910:
3892:
3873:
3871:
3870:
3865:
3860:
3859:
3854:
3838:
3837:
3801:
3788:
3787:
3760:
3747:
3746:
3728:
3719:
3718:
3717:
3690:
3681:
3677:
3654:
3652:
3651:
3646:
3641:
3640:
3635:
3623:
3619:
3610:
3599:
3591:
3587:
3578:
3567:
3563:
3554:
3553:
3545:
3539:
3531:
3527:
3508:
3506:
3505:
3500:
3495:
3494:
3489:
3477:
3473:
3464:
3453:
3445:
3441:
3432:
3421:
3417:
3408:
3407:
3399:
3393:
3389:
3380:
3364:Fictitious force
3343:
3341:
3340:
3335:
3330:
3326:
3314:
3303:
3292:
3251:
3249:
3248:
3243:
3238:
3234:
3225:
3217:
3204:
3202:
3201:
3196:
3191:
3187:
3178:
3170:
3152:
3150:
3149:
3144:
3139:
3135:
3126:
3118:
3049:
3047:
3000:Andromeda Galaxy
2854:
2852:
2851:
2846:
2839:
2838:
2837:
2832:
2823:
2821:
2813:
2812:
2803:
2792:
2791:
2786:
2777:
2766:
2755:
2754:
2749:
2740:
2726:
2718:
2714:
2687:
2685:
2684:
2679:
2672:
2671:
2660:
2656:
2590:
2588:
2587:
2582:
2575:
2574:
2563:
2549:takes the form:
2522:angular momentum
2509:Milky Way galaxy
2473:
2416:Fictitious force
2405:
2400:in the negative
2399:
2385:
2380:in the positive
2375:
2370:in the negative
2369:
2355:
2350:in the negative
2349:
2343:
2338:in the negative
2337:
2331:
2325:
2320:in the negative
2319:
2306:
2300:
2294:
2289:in the negative
2288:
2282:
2276:
2267:
2262:in the positive
2261:
2252:
2246:
2240:
2206:
2202:
2200:
2198:
2197:
2194:
2191:
2184:
2182:
2181:
2166:
2163:
2153:
2129:
2127:
2126:
2121:
2116:
2091:
2073:
2071:
2070:
2065:
2040:
2038:
2037:
2032:
1996:
1994:
1993:
1988:
1976:
1974:
1973:
1968:
1966:
1965:
1953:
1952:
1936:
1934:
1933:
1928:
1926:
1925:
1913:
1912:
1889:
1887:
1886:
1881:
1864:
1863:
1842:
1841:
1810:
1809:
1782:
1781:
1758:
1756:
1755:
1750:
1739:
1738:
1718:
1716:
1715:
1710:
1699:
1698:
1682:
1572:
1551:Mach's principle
1544:
1477:privileged frame
1440:. They are both
1431:
1429:
1428:
1423:
1421:
1420:
1418:
1417:
1409:
1406:
1404:
1331:
1329:
1328:
1323:
1321:
1320:
1302:
1301:
1282:
1280:
1279:
1274:
1269:
1261:
1260:
1255:
1246:
1238:
1237:
1232:
1216:
1214:
1213:
1208:
1206:
1205:
1200:
1187:
1185:
1184:
1179:
1177:
1153:
1130:
1084:) was coined by
1022:
995:
932:Earth's rotation
897:physical objects
786:
779:
772:
759:
754:
753:
746:
742:
741:
647:Johann Bernoulli
642:Daniel Bernoulli
563:Tangential speed
467:
443:
418:Fictitious force
413:
265:Mechanical power
255:
196:Angular momentum
94:
92:
91:
86:
84:
82:
74:
73:
64:
59:
58:
32:
31:
21:
6439:
6438:
6434:
6433:
6432:
6430:
6429:
6428:
6399:
6398:
6386:. 3 June 2015.
6376:
6365:
6360:Wayback Machine
6349:
6328:Wayback Machine
6301:Wayback Machine
6285:Yuri N. Obukhov
6276:Wayback Machine
6260:Wayback Machine
6246:
6225:
6190:Albert Einstein
6175:Poincaré, Henri
6164:Albert Einstein
6150:Edwin F. Taylor
6146:
6144:Further reading
6141:
6140:
6127:
6126:
6122:
6115:
6101:
6097:
6090:
6076:
6072:
6066:
6062:
6057:
6053:
6046:
6027:
6023:
6008:physics/0409010
5995:
5991:
5981:
5979:
5934:
5930:
5881:
5877:
5870:
5852:
5848:
5841:
5825:
5821:
5814:
5798:
5794:
5787:
5771:
5767:
5757:
5755:
5751:
5702:
5696:
5692:
5685:
5669:
5665:
5657:
5649:
5645:
5639:Wayback Machine
5630:
5626:
5616:
5600:
5596:
5586:
5570:
5566:
5556:
5540:
5536:
5529:
5513:
5509:
5502:
5486:
5482:
5472:Wayback Machine
5462:
5458:
5451:
5435:
5431:
5421:
5399:
5395:
5380:
5366:
5362:
5355:
5341:
5337:
5327:
5311:
5307:
5294:
5290:
5278:
5271:
5264:
5248:
5244:
5237:
5221:
5217:
5204:
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5193:
5177:
5173:
5166:
5150:
5146:
5136:
5118:
5114:
5107:
5090:
5086:
5071:
5057:
5053:
5043:
5041:
5026:
5022:
5015:
4999:
4995:
4988:
4972:
4968:
4961:
4940:
4936:
4929:
4909:
4905:
4890:
4886:
4866:
4862:
4855:
4839:
4835:
4828:
4812:
4808:
4788:
4784:
4777:
4761:
4757:
4750:
4734:
4730:
4721:
4719:
4712:
4688:
4684:
4677:
4646:
4642:
4615:
4608:
4598:
4576:
4569:
4564:
4559:
4515:
4506:
4495:
4489:
4486:
4471:
4455:
4422:
4408:
4401:
4354:reference frame
4337:
4325:
4307:
4300:
4262:
4260:Bucket argument
4248:
4242:
4237:
4208:
4196:
4195:
4187:
4172:
4171:
4165:
4161:
4140:
4139:
4131:
4120:
4071:
4070:
4065:
4062:
4059:
4058:
4032:
4031:
4023:
3980:
3979:
3974:
3971:
3968:
3967:
3941:
3940:
3926:
3925:
3894:
3893:
3888:
3885:
3882:
3881:
3855:
3850:
3849:
3803:
3802:
3797:
3762:
3761:
3756:
3730:
3729:
3724:
3692:
3691:
3686:
3685:
3673:
3672:
3670:
3667:
3666:
3636:
3631:
3630:
3615:
3614:
3606:
3595:
3583:
3582:
3574:
3559:
3558:
3544:
3543:
3535:
3523:
3522:
3520:
3517:
3516:
3490:
3485:
3484:
3469:
3468:
3460:
3449:
3437:
3436:
3428:
3413:
3412:
3398:
3397:
3385:
3384:
3376:
3374:
3371:
3370:
3354:Coriolis effect
3322:
3321:
3310:
3299:
3288:
3286:
3283:
3282:
3230:
3229:
3221:
3213:
3211:
3208:
3207:
3183:
3182:
3174:
3166:
3164:
3161:
3160:
3131:
3130:
3122:
3114:
3112:
3109:
3108:
3072:
3045:
3043:
2972:rotating bucket
2887:
2878:
2833:
2828:
2827:
2814:
2808:
2804:
2802:
2787:
2782:
2781:
2773:
2762:
2750:
2745:
2744:
2736:
2722:
2710:
2709:
2707:
2704:
2703:
2667:
2652:
2651:
2649:
2646:
2645:
2570:
2559:
2557:
2554:
2553:
2531:
2494:geodesic motion
2490:Minkowski Space
2474:
2467:
2455:
2445:
2437:Main articles:
2435:
2426:
2414:Main articles:
2412:
2401:
2387:
2381:
2371:
2357:
2351:
2345:
2339:
2333:
2327:
2321:
2315:
2302:
2296:
2290:
2284:
2278:
2272:
2263:
2257:
2253:axis with some
2248:
2242:
2236:
2217:
2204:
2195:
2192:
2189:
2188:
2186:
2180:
2173:
2167:
2164:
2159:
2158:
2156:
2155:
2151:
2144:
2138:
2094:
2080:
2077:
2076:
2047:
2044:
2043:
2005:
2002:
2001:
1982:
1979:
1978:
1961:
1957:
1948:
1944:
1942:
1939:
1938:
1921:
1917:
1908:
1904:
1902:
1899:
1898:
1859:
1855:
1837:
1833:
1805:
1801:
1777:
1773:
1771:
1768:
1767:
1734:
1730:
1728:
1725:
1724:
1723:in seconds and
1694:
1690:
1688:
1685:
1684:
1677:
1647:
1642:
1593:
1587:
1581:further below.
1573:
1566:
1545:
1536:
1483:is defined as:
1442:inertial frames
1408:
1407:
1405:
1403:
1402:
1400:
1397:
1396:
1384:
1377:
1366:
1359:
1348:
1341:
1316:
1312:
1297:
1293:
1291:
1288:
1287:
1265:
1256:
1251:
1250:
1242:
1233:
1228:
1227:
1225:
1222:
1221:
1201:
1196:
1195:
1193:
1190:
1189:
1173:
1171:
1168:
1167:
1160:
1154:
1148:Robert DiSalle
1146:
1131:
1124:
1072:The expression
1063:
1057:
1052:
1046:of symmetries.
1023:
1016:
1010:
996:
994:, Section A, §1
989:
964:
936:Coriolis effect
909:physical forces
889:By contrast, a
790:
749:
736:
735:
728:
727:
726:
601:
593:
592:
572:
526:Circular motion
520:
510:
509:
508:
465:
435:
432:
411:
390:
382:
381:
378:
377:
335:
325:
317:
316:
315:
274:
270:Mechanical work
263:
247:
185:
177:
176:
175:
130:
122:
99:
75:
69:
65:
63:
54:
53:
51:
48:
47:
28:
23:
22:
15:
12:
11:
5:
6437:
6427:
6426:
6421:
6416:
6411:
6397:
6396:
6383:PBS Space Time
6374:
6366:Animation clip
6362:
6348:
6347:External links
6345:
6344:
6343:
6334:
6318:
6291:
6282:
6266:
6250:
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6229:
6223:
6207:
6206:
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6201:
6196:, included in
6187:
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6070:
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5839:
5819:
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5792:
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5765:
5737:10.1086/491644
5713:(2): 894–898.
5690:
5683:
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5643:
5624:
5614:
5594:
5584:
5564:
5554:
5534:
5527:
5507:
5500:
5480:
5463:A. Einstein, "
5456:
5449:
5429:
5419:
5393:
5378:
5360:
5353:
5335:
5325:
5305:
5301:speed of light
5288:
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4682:
4675:
4653:Lorentz, H. A.
4640:
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4566:
4565:
4563:
4560:
4558:
4557:
4552:
4547:
4542:
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4525:Diffeomorphism
4522:
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4514:
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4508:
4507:
4458:
4456:
4449:
4434:dead reckoning
4421:
4418:
4402:Isaac Newton:
4399:
4377:force carriers
4362:Coriolis force
4323:
4298:
4244:Main article:
4241:
4238:
4236:
4233:
4232:
4231:
4215:
4211:
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4203:
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4080:
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4074:
4068:
4056:
4053:Coriolis force
4039:
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4022:
4019:
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3169:
3154:
3153:
3142:
3138:
3134:
3129:
3125:
3121:
3117:
3071:
3068:
2988:proper motions
2960:Coriolis force
2947:absolute space
2925:nuclear forces
2901:Coriolis force
2883:
2874:
2856:
2855:
2844:
2836:
2831:
2826:
2820:
2817:
2811:
2807:
2801:
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2725:
2721:
2717:
2713:
2689:
2688:
2677:
2670:
2666:
2663:
2659:
2655:
2624:contact forces
2592:
2591:
2580:
2573:
2569:
2566:
2562:
2539:law of inertia
2530:
2527:
2486:general theory
2465:
2434:
2431:
2411:
2408:
2216:
2213:
2178:
2171:
2149:
2142:
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2130:
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2063:
2060:
2057:
2054:
2051:
2041:
2030:
2027:
2024:
2021:
2018:
2015:
2012:
2009:
1986:
1977:and solve for
1964:
1960:
1956:
1951:
1947:
1924:
1920:
1916:
1911:
1907:
1891:
1890:
1879:
1876:
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1737:
1733:
1708:
1705:
1702:
1697:
1693:
1646:
1645:Simple example
1643:
1641:
1638:
1603:speed of light
1589:Main article:
1586:
1583:
1567:Isaac Newton:
1564:
1534:
1473:absolute space
1465:absolute space
1415:
1412:
1382:
1375:
1364:
1357:
1346:
1339:
1333:
1332:
1319:
1315:
1311:
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1305:
1300:
1296:
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1272:
1268:
1264:
1259:
1254:
1249:
1245:
1241:
1236:
1231:
1204:
1199:
1188:, to another,
1176:
1159:
1156:
1144:
1122:
1116:
1115:
1112:
1109:
1082:Inertialsystem
1059:Main article:
1056:
1055:Absolute space
1053:
1051:
1048:
1044:Galilean group
1036:Poincaré group
1014:
987:
963:
960:
884:speed of light
810:inertial space
792:
791:
789:
788:
781:
774:
766:
763:
762:
761:
760:
747:
730:
729:
725:
724:
719:
714:
709:
704:
699:
694:
689:
684:
679:
674:
669:
664:
659:
654:
649:
644:
639:
634:
629:
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619:
614:
609:
603:
602:
599:
598:
595:
594:
591:
590:
571:
570:
565:
560:
555:
553:Coriolis force
550:
549:
548:
538:
533:
528:
522:
521:
516:
515:
512:
511:
507:
506:
501:
496:
495:
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489:
479:
474:
469:
462:
451:
450:
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431:
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408:
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104:
101:
100:
95:
81:
78:
72:
68:
62:
44:
43:
37:
36:
26:
18:Inertial frame
9:
6:
4:
3:
2:
6436:
6425:
6422:
6420:
6417:
6415:
6412:
6410:
6407:
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6393:
6389:
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6280:
6277:
6273:
6270:
6267:
6264:
6261:
6257:
6254:
6251:
6247:
6245:0-387-98571-9
6241:
6237:
6236:
6235:Time Machines
6230:
6226:
6224:0-8176-3823-7
6220:
6216:
6215:
6209:
6208:
6204:
6203:
6199:
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6116:
6114:9780203860748
6110:
6106:
6099:
6091:
6089:9781600864278
6085:
6081:
6074:
6064:
6055:
6047:
6041:
6037:
6036:
6031:
6030:V. I. Arnol'd
6025:
6018:
6014:
6009:
6004:
6000:
5993:
5977:
5973:
5969:
5965:
5961:
5957:
5953:
5949:
5945:
5944:
5939:
5932:
5924:
5920:
5916:
5912:
5908:
5904:
5899:
5894:
5890:
5886:
5879:
5871:
5869:1-86094-577-5
5865:
5861:
5857:
5850:
5842:
5840:0-7382-0610-5
5836:
5832:
5831:
5823:
5815:
5813:981-256-754-2
5809:
5805:
5804:
5796:
5788:
5786:0-8176-4143-2
5782:
5778:
5777:
5769:
5750:
5746:
5742:
5738:
5734:
5730:
5726:
5721:
5716:
5712:
5708:
5701:
5694:
5686:
5680:
5676:
5675:
5667:
5656:
5655:
5647:
5640:
5636:
5633:
5628:
5622:
5617:
5615:0-521-57598-2
5611:
5607:
5606:
5598:
5592:
5587:
5581:
5577:
5576:
5568:
5562:
5557:
5551:
5547:
5546:
5538:
5530:
5524:
5520:
5519:
5511:
5503:
5501:0-309-03579-1
5497:
5493:
5492:
5484:
5477:
5473:
5469:
5466:
5460:
5452:
5446:
5442:
5441:
5433:
5426:
5422:
5416:
5412:
5407:
5406:
5397:
5389:
5385:
5381:
5375:
5371:
5364:
5356:
5350:
5346:
5339:
5333:
5328:
5322:
5318:
5317:
5309:
5302:
5298:
5292:
5286:
5282:
5276:
5274:
5265:
5263:0-201-32842-9
5259:
5255:
5254:
5246:
5238:
5236:0-85066-838-7
5232:
5228:
5227:
5219:
5211:
5210:
5202:
5194:
5192:1-85233-426-6
5188:
5184:
5183:
5175:
5167:
5165:0-07-096617-6
5161:
5157:
5156:
5148:
5141:
5137:
5135:0-471-32057-9
5131:
5126:
5125:
5116:
5108:
5106:0-7382-0610-5
5102:
5098:
5097:
5088:
5080:
5076:
5072:
5070:0-19-560539-X
5066:
5062:
5055:
5039:
5035:
5031:
5024:
5016:
5014:1-85233-426-6
5010:
5006:
5005:
4997:
4989:
4987:0-7503-0767-6
4983:
4979:
4978:
4970:
4962:
4960:981-238-213-5
4956:
4952:
4951:
4944:
4938:
4930:
4928:0-19-513202-5
4924:
4920:
4916:
4915:
4907:
4899:
4895:
4888:
4881:
4877:
4873:
4872:
4864:
4856:
4854:0-387-25799-3
4850:
4846:
4845:
4837:
4829:
4827:0-201-32842-9
4823:
4819:
4818:
4810:
4803:
4799:
4795:
4794:
4786:
4778:
4776:0-7503-0767-6
4772:
4768:
4767:
4759:
4751:
4749:0-915144-71-9
4745:
4741:
4740:
4732:
4717:
4713:
4711:9780387699462
4707:
4703:
4699:
4695:
4694:
4686:
4678:
4676:0-486-60081-5
4672:
4668:
4667:
4662:
4658:
4657:Minkowski, H.
4654:
4650:
4644:
4636:
4632:
4628:
4623:
4622:
4613:
4611:
4603:
4599:
4597:0-486-26178-6
4593:
4589:
4584:
4583:
4574:
4572:
4567:
4556:
4553:
4551:
4548:
4546:
4543:
4541:
4538:
4536:
4533:
4531:
4528:
4526:
4523:
4521:
4518:
4517:
4504:
4501:
4493:
4483:
4479:
4475:
4469:
4468:
4464:
4459:This section
4457:
4453:
4448:
4447:
4444:
4442:
4437:
4435:
4430:
4426:
4417:
4413:
4405:
4398:
4397:
4391:
4389:
4384:
4380:
4378:
4372:
4369:
4367:
4363:
4359:
4355:
4351:
4347:
4343:
4334:
4333:
4328:
4327:V. I. Arnol'd
4322:
4321:
4315:
4313:
4304:
4297:
4296:
4291:
4289:
4281:
4277:
4270:
4266:
4261:
4257:
4253:
4247:
4229:
4201:
4192:
4181:
4177:
4166:
4162:
4155:
4152:
4145:
4136:
4125:
4117:
4114:
4111:
4107:
4057:
4054:
4037:
4028:
4020:
4017:
4014:
4011:
4007:
3966:
3963:
3946:
3937:
3931:
3922:
3919:
3916:
3912:
3880:
3879:
3878:
3861:
3856:
3846:
3843:
3839:
3793:
3789:
3752:
3748:
3720:
3682:
3678:
3665:
3664:
3663:
3661:
3642:
3637:
3627:
3620:
3611:
3600:
3592:
3588:
3579:
3571:
3568:
3564:
3555:
3549:
3540:
3532:
3528:
3515:
3514:
3513:
3496:
3491:
3481:
3474:
3465:
3454:
3446:
3442:
3433:
3425:
3422:
3418:
3409:
3403:
3394:
3390:
3381:
3369:
3368:
3367:
3365:
3360:
3357:
3355:
3351:
3331:
3327:
3318:
3315:
3307:
3304:
3296:
3293:
3281:
3280:
3279:
3277:
3272:
3270:
3266:
3262:
3258:
3239:
3235:
3226:
3218:
3206:
3192:
3188:
3179:
3171:
3159:
3158:
3157:
3140:
3136:
3127:
3119:
3107:
3106:
3105:
3102:
3100:
3096:
3092:
3087:
3085:
3081:
3077:
3070:Primed frames
3067:
3065:
3061:
3056:
3053:
3041:
3037:
3033:
3029:
3025:
3021:
3020:discrepancies
3017:
3012:
3008:
3005:
3001:
2997:
2993:
2989:
2985:
2980:
2977:
2973:
2969:
2965:
2961:
2957:
2952:
2948:
2944:
2939:
2937:
2932:
2930:
2926:
2922:
2918:
2914:
2910:
2906:
2902:
2898:
2893:
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2886:
2882:
2877:
2873:
2869:
2865:
2861:
2842:
2834:
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2818:
2815:
2805:
2799:
2796:
2788:
2778:
2767:
2759:
2756:
2751:
2741:
2733:
2730:
2727:
2719:
2715:
2702:
2701:
2700:
2698:
2694:
2675:
2664:
2661:
2657:
2644:
2643:
2642:
2640:
2636:
2632:
2627:
2625:
2621:
2617:
2613:
2609:
2605:
2601:
2597:
2578:
2567:
2564:
2552:
2551:
2550:
2548:
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1531:acceleration.
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956:approximation
953:
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910:
906:
902:
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873:
869:
865:
861:
860:physical laws
857:
852:
850:
846:
842:
838:
834:
830:
825:
823:
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811:
808:(also called
807:
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5992:
5980:. Retrieved
5947:
5941:
5931:
5888:
5884:
5878:
5859:
5849:
5829:
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5756:. Retrieved
5710:
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5042:. Retrieved
5033:
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4720:, retrieved
4692:
4685:
4665:
4649:Einstein, A.
4643:
4620:
4601:
4581:
4496:
4487:
4472:Please help
4460:
4438:
4423:
4420:Applications
4414:
4410:
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4394:
4393:
4385:
4381:
4373:
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2612:acceleration
2607:
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2518:Solar System
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2469:
2461:
2460:
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2312:acceleration
2309:
2307:-direction.
2303:
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1379:
1372:
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1336:
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1149:
1139:
1138:
1133:
1126:
1119:
1118:
1105:
1101:
1096:
1095:
1086:Ludwig Lange
1073:
1071:
1064:
1032:
1025:
1018:
1007:
1006:
1000:
998:
991:
982:
981:
965:
962:Introduction
929:
907:, the usual
890:
888:
864:Measurements
853:
845:Isaac Newton
826:
813:
809:
805:
795:
586: /
582: /
580:displacement
578: /
439: /
436:
401:Displacement
339:
330:
324:Formulations
311:Virtual work
251: /
237:
191:Acceleration
184:Fundamentals
29:
5982:14 December
5830:Nothingness
5758:15 December
5283:on line at
5044:9 September
4441:gyrocompass
3962:Euler force
3350:centrifugal
3036:dark matter
2943:fixed stars
2909:Euler force
2484:Einstein's
1997:, that is:
1495:accelerates
1469:fixed stars
1067:fixed stars
976:translation
849:fixed stars
722:von Neumann
389:Core topics
6403:Categories
6337:Kurt Gödel
5585:8186358528
5555:354066517X
4722:2 November
4635:B000GQB02A
4562:References
4429:gyroscopes
4346:fictitious
4340:Bodies in
4250:See also:
2620:vector sum
2447:See also:
1632:, and the
1617:, not the
1607:free space
1596:Einstein's
942:, and the
915:caused by
657:d'Alembert
637:Maupertuis
600:Scientists
482:Rigid body
156:Kinematics
6294:Li-Xin Li
6185:: 253–78.
5923:118988129
5654:Mechanics
5388:968771417
5281:Principia
5079:220221617
4490:July 2013
4461:does not
4404:Principia
4210:ω
4193:⋅
4189:ω
4182:−
4163:ω
4137:×
4133:ω
4126:×
4122:ω
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4029:×
4025:ω
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3932:˙
3929:ω
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3608:ω
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3597:ω
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3430:ω
3410:×
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3401:ω
3016:Milky Way
2984:Milky Way
2870:, vector
2825:×
2810:Ω
2797:−
2779:×
2775:Ω
2768:×
2764:Ω
2757:−
2742:×
2738:Ω
2728:−
2505:spacetime
2472:, p. 155.
1611:invariant
1569:Principia
1414:→
1310:−
1299:′
1263:−
1248:−
1235:′
1203:′
1028:Newtonian
833:net force
702:Liouville
584:frequency
504:Vibration
221:potential
146:Continuum
141:Celestial
118:Textbooks
6388:Archived
6356:Archived
6324:Archived
6297:Archived
6272:Archived
6256:Archived
6082:. AIAA.
6032:(1989).
5976:Archived
5749:Archived
5745:17099715
5635:Archived
5468:Archived
5279:See the
5038:Archived
4716:archived
4663:(1952).
4661:Weyl, H.
4513:See also
4400:—
4360:and the
4324:—
4305:, p. 138
4299:—
4280:Figure 3
4269:Figure 2
4202:′
4178:′
4146:′
4108:′
4038:′
4008:′
3947:′
3913:′
3840:′
3790:′
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3565:′
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3475:′
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3391:′
3328:′
3236:′
3189:′
3137:′
3022:or less
2962:and the
2890:velocity
2716:′
2658:′
2547:particle
2466:—
2255:velocity
2224:Figure 2
1654:Figure 1
1640:Examples
1565:—
1535:—
1450:inertial
1432:. Frame
1393:Figure 1
1369:distance
1145:—
1123:—
1015:—
988:—
837:velocity
757:Category
682:Hamilton
667:Lagrange
662:Clairaut
627:Horrocks
588:velocity
558:Pendulum
546:reactive
518:Rotation
487:dynamics
437:Inertial
423:Friction
306:Velocity
281:Momentum
161:Kinetics
151:Dynamics
129:Branches
113:Timeline
6392:YouTube
6371:YouTube
6321:P Birch
6310:(1998)
6013:Bibcode
5972:4343095
5952:Bibcode
5903:Bibcode
5725:Bibcode
5124:Physics
4698:Bibcode
4482:removed
4467:sources
4396:forces.
4320:system.
3060:quantum
2888:is the
2618:is the
2199:
2187:
2183:
2157:
2152:= 8 m/s
1681:= 200 m
1543:, p. 58
952:equator
950:at the
948:gravity
930:Due to
917:inertia
874:or the
822:inertia
717:Koopman
677:Poisson
672:Laplace
617:Huygens
612:Galileo
457: (
396:Damping
249:Inertia
243:Impulse
216:kinetic
166:Statics
136:Applied
108:History
6424:Orbits
6290:(2000)
6242:
6221:
6111:
6086:
6042:
5970:
5943:Nature
5921:
5866:
5837:
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4350:forces
4258:, and
4240:Theory
3877:where
3662:gives
3255:where
3002:is on
2921:matter
2840:
2673:
2600:vector
2576:
2545:for a
2537:, the
2422:, and
2092:
1335:where
1129:, p. 5
1078:German
1021:, p. 4
858:, all
755:
707:Appell
692:Cauchy
687:Jacobi
632:Halley
622:Newton
607:Kepler
459:linear
455:Motion
301:Torque
276:Moment
211:Energy
201:Couple
6003:arXiv
5968:S2CID
5919:S2CID
5893:arXiv
5752:(PDF)
5741:S2CID
5715:arXiv
5703:(PDF)
5658:(PDF)
4588:23-24
3058:When
2594:with
2205:8 m/s
1511:speed
1499:force
1475:or a
1141:them.
940:Earth
812:, or
804:, an
712:Gibbs
697:Routh
652:Euler
291:Speed
286:Space
228:Force
6240:ISBN
6219:ISBN
6152:and
6133:Life
6109:ISBN
6084:ISBN
6040:ISBN
5984:2008
5864:ISBN
5835:ISBN
5808:ISBN
5781:ISBN
5760:2008
5679:ISBN
5610:ISBN
5580:ISBN
5550:ISBN
5523:ISBN
5496:ISBN
5445:ISBN
5415:ISBN
5384:OCLC
5374:ISBN
5349:ISBN
5321:ISBN
5258:ISBN
5231:ISBN
5187:ISBN
5160:ISBN
5130:ISBN
5101:ISBN
5075:OCLC
5065:ISBN
5046:2008
5009:ISBN
4982:ISBN
4955:ISBN
4923:ISBN
4849:ISBN
4822:ISBN
4771:ISBN
4744:ISBN
4724:2022
4706:ISBN
4671:ISBN
4631:ASIN
4592:ISBN
4465:any
4463:cite
4386:For
3267:and
3259:and
2610:the
2451:and
2441:and
1507:rest
1342:and
903:and
800:and
296:Time
259:Mass
6369:on
6312:doi
5960:doi
5948:298
5911:doi
5733:doi
5711:633
5474:",
5411:649
4627:138
4476:by
4364:in
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3052:any
3030:or
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2190:200
2059:200
2008:200
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4214:)
4206:)
4198:r
4185:(
4174:r
4167:2
4159:(
4156:m
4153:=
4150:)
4142:r
4129:(
4118:m
4112:=
4103:l
4100:a
4097:g
4094:u
4091:f
4088:i
4085:r
4082:t
4079:n
4076:e
4073:c
4067:F
4051:(
4034:v
4021:m
4018:2
4012:=
4003:s
4000:i
3997:l
3994:o
3991:i
3988:r
3985:o
3982:C
3976:F
3960:(
3943:r
3923:m
3917:=
3908:r
3905:e
3902:l
3899:u
3896:E
3890:F
3862:,
3857:0
3852:A
3847:m
3835:l
3832:a
3829:t
3826:e
3823:p
3820:i
3817:r
3814:t
3811:n
3808:e
3805:c
3799:F
3794:+
3785:s
3782:i
3779:l
3776:o
3773:i
3770:r
3767:o
3764:C
3758:F
3753:+
3744:r
3741:e
3738:l
3735:u
3732:E
3726:F
3721:+
3715:l
3712:a
3709:c
3706:i
3703:s
3700:y
3697:h
3694:p
3688:F
3683:=
3675:F
3660:m
3643:.
3638:0
3633:A
3625:)
3617:r
3604:(
3585:v
3572:2
3561:r
3537:a
3533:=
3525:a
3497:,
3492:0
3487:A
3482:+
3479:)
3471:r
3458:(
3447:+
3439:v
3426:2
3423:+
3415:r
3395:+
3387:a
3382:=
3378:a
3332:.
3324:a
3319:m
3316:+
3312:A
3308:m
3305:=
3301:a
3297:m
3294:=
3290:F
3269:a
3265:v
3261:A
3257:V
3240:.
3232:a
3227:+
3223:A
3219:=
3215:a
3193:,
3185:v
3180:+
3176:V
3172:=
3168:v
3141:.
3133:r
3128:+
3124:R
3120:=
3116:r
3095:r
3091:R
3046:×
3044:6
2936:F
2917:Ω
2913:Ω
2897:F
2885:B
2881:v
2876:B
2872:x
2864:Ω
2860:Ω
2843:,
2835:B
2830:x
2819:t
2816:d
2806:d
2800:m
2794:)
2789:B
2784:x
2771:(
2760:m
2752:B
2747:v
2734:m
2731:2
2724:F
2720:=
2712:F
2697:F
2693:F
2676:,
2669:a
2665:m
2662:=
2654:F
2639:Ω
2616:F
2608:a
2604:m
2596:F
2579:,
2572:a
2568:m
2565:=
2561:F
2403:y
2397:A
2393:a
2383:y
2378:A
2373:y
2367:A
2363:a
2353:y
2347:A
2341:y
2335:a
2329:v
2323:x
2317:a
2304:y
2298:y
2292:y
2286:v
2280:y
2274:x
2265:x
2259:v
2250:x
2244:y
2238:x
2201:s
2196:8
2193:/
2179:1
2176:v
2172:2
2169:v
2165:/
2161:d
2150:1
2147:v
2143:2
2140:v
2118:.
2114:s
2111:d
2108:n
2105:o
2102:c
2099:e
2096:s
2086:=
2083:t
2062:,
2056:=
2053:t
2050:8
2029:,
2026:t
2020:=
2017:t
2011:+
1985:t
1963:2
1959:x
1955:=
1950:1
1946:x
1923:2
1919:x
1915:=
1910:1
1906:x
1895:t
1878:.
1875:t
1869:=
1866:t
1861:2
1857:v
1853:=
1850:)
1847:t
1844:(
1839:2
1835:x
1830:,
1827:t
1821:+
1815:=
1812:t
1807:1
1803:v
1799:+
1796:d
1793:=
1790:)
1787:t
1784:(
1779:1
1775:x
1761:t
1747:)
1744:t
1741:(
1736:2
1732:x
1721:t
1707:)
1704:t
1701:(
1696:1
1692:x
1679:d
1674:S
1658:S
1438:S
1411:v
1383:1
1380:r
1376:2
1373:r
1365:1
1362:t
1358:2
1355:t
1351:v
1347:0
1344:t
1340:0
1337:r
1318:0
1314:t
1307:t
1304:=
1295:t
1271:t
1267:v
1258:0
1253:r
1244:r
1240:=
1230:r
1198:s
1175:s
1076:(
978::
785:e
778:t
771:v
461:)
80:t
77:d
71:p
67:d
61:=
56:F
20:)
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