1172:, 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 carâa 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
2721:
1946:
1261:, 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 â 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.
2716:{\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}}}
3693:
753:
1154:) 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).
766:
3056:
1134:" 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 frameâthe calculations are simpler, and descriptions more intuitive. When this choice is made, fictitious forces, including the centrifugal force, arise.
3383:
1204:, 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.
5486:
1233:" 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
3620:)} 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.
1011:, 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 .
2852:. 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:
2855:
3371:
1137:
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
1129:
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
1094:
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
1006:
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
1253:
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.
41:
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
3429:, 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.
1207:
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
3416:
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
1167:
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
1224:
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
3060:
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
3417:
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.
1607:
1188:
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.
3524:
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.
3500:
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
1208:
accelerate in the direction of the net applied forceâtowards the axis of rotationâwhich 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.
3420:
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
3361:
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.
3051:{\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\ .}
1819:
3236:
3396:
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.
3456:
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.
3116:
2795:. 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
1142:
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.
1086:
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.
2850:
5105:, 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.
1510:
1871:
1095:
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.
1667:
107:
131:
1941:
1732:
3186:
1951:
4319:
1273:, 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.
4981:
3537:
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.
3359:
1753:
4855:
4597:
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.
3325:
3276:
4922:
3327:, 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
5011:
4877:
888:
5103:
3238:, 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
3593:
3303:
3191:
1627:
3505:
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
2793:
3412:
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.
1044:
3067:
5261:
946:
797:
3670:, 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.
1249:
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
386:
4383:
1269:
In fact, the observed weight difference is more â about 0.53%. Earth's gravity is a bit stronger at the poles than at the equator, because the Earth is
505:
5170:"The intrinsic derivative and centrifugal forces in general relativity: II. Applications to circular orbits in some stationary axisymmetric spacetimes"
2798:
478:
3386:
When analysed in a rotating reference frame of the planet, centrifugal force causes rotating planets to assume the shape of an oblate spheroid.
38:
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752:
5443:
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4701:
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4253:
4113:
3984:
3875:
3711:
1698:
4576:
3897:
3437:
The operations of numerous common rotating mechanical systems are most easily conceptualized in terms of centrifugal force. For example:
1833:
1294:
1007:
one. I originally intended to publish here a lengthy description of these clocks, along with matters pertaining to circular motion and
460:
4828:, there are three types of terms. The first involves the second derivative of the generalized co-ordinates. The second is quadratic in
4365:
1642:
1323:
of timeâsuch as the velocity and acceleration vectors of an objectâwill differ from its time derivatives in the stationary frame. If
5302:
5236:
3950:
3923:
3832:
790:
4173:
3673:
The concept of the reactive centrifugal force is sometimes used in mechanics and engineering. It is sometimes referred to as just
3491:
3796:
5062:
Geometrical
Structures Of Phase Space In Multi-dimensional Chaos: Applications to chemical reaction dynamics in complex systems
3663:
the other body that provides the centripetal force and its direction is from that other body toward the body in curved motion.
3520:'s spin forces riders against a wall and allows riders to be elevated above the machine's floor in defiance of Earth's gravity.
1602:{\displaystyle {\frac {\mathrm {d} {\boldsymbol {P}}}{\mathrm {d} t}}=\left+{\boldsymbol {\omega }}\times {\boldsymbol {P}}\ ,}
126:
63:
3494:
are production methods that use centrifugal force to disperse liquid metal or plastic throughout the negative space of a mold.
121:
3891:
3863:
Christiaan
Huygens' the pendulum clock, or, Geometrical demonstrations concerning the motion of pendula as applied to clocks
3838:
3124:
1876:
381:
5377:
3449:, as the engine changes speed. In the reference frame of the spinning masses, centrifugal force causes the radial movement.
4825:
3647:
is provided by a centripetal force, which is exerted on the body in curved motion by some other body. In accordance with
3606:
376:
4482:
3918:(Andrew Motte translation of 1729, revised by Florian Cajori ed.). University of California Press. pp. 10â12.
3706:
1304:
826:
783:
770:
531:
454:
5490:
219:
1300:
1193:
1123:
822:
450:
251:
3405:. The shape of the surface becomes concave to balance the centrifugal force against the other forces upon the liquid.
854:
5511:
4488:
4008:
3648:
3636:
1197:
1169:
929:
670:
559:
485:
345:
278:
4931:
3370:
3477:
3330:
1053:
424:
4807:
4582:
3644:
1639:
in the stationary frame is the sum of its apparent rate of change in the rotating frame and a rate of rotation
1284:
1119:
994:
921:
700:
544:
4831:
4394:
3506:
1196:, were it not for this net force acting on the stone, the stone would travel in a straight line, according to
3308:
3550:
3241:
690:
650:
414:
17:
4882:
4419:
1237:
orbiting around the Earth. This is due to the large mass and velocity of the Sun (relative to the Earth).
695:
512:
5506:
3716:
3595:
or a much more extensive list of variables. Within this formulation the motion is described in terms of
1103:
705:
680:
366:
184:
4994:
4860:
3824:
A Catalogue of the
Manuscripts of Christiaan Huygens including a concordance with his Oeuvres Complètes
3426:
5389:
5342:
5191:
5141:
4138:
4060:
3546:
3442:
1830:
By applying the transformation above from the stationary to the rotating frame three times (twice to
1630:
1074:
about detection of absolute motion. Newton suggested two arguments to answer the question of whether
999:
901:
725:
720:
685:
593:
589:
581:
571:
361:
354:
110:
5079:
5120:"The intrinsic derivative and centrifugal forces in general relativity: I. Theoretical foundations"
4235:
3563:
3458:
1814:{\displaystyle {\boldsymbol {a}}={\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}\ ,}
1226:
1221:
1091:
1071:
1023:
and replied "I pray you return my humble thanks I am glad we can expect another discourse of the
986:
909:
818:
500:
441:
419:
164:
159:
154:
54:
821:(also called an "inertial" or "pseudo" force) that appears to act on all objects when viewed in a
5521:
5358:
5207:
5181:
5157:
5131:
4337:
4154:
4084:
4050:
4002:
3652:
3629:
3597:
3473:
3453:
3231:{\displaystyle -m{\boldsymbol {\omega }}\times ({\boldsymbol {\omega }}\times {\boldsymbol {r}})}
1107:
1099:
1028:
960:
905:
630:
371:
246:
214:
174:
5060:. In Mikito Toda; Tamiki Komatsuzaki; Stuart A. Rice; Tetsuro Konishi; R. Stephen Berry (eds.).
3867:
3281:
4670:
4203:
5526:
5468:
5439:
5433:
5416:
5327:
5308:
5298:
5292:
5242:
5232:
5065:
5036:
5030:
4813:
4786:
4759:
4725:
4697:
4693:
4643:
4616:
4610:
4586:
4555:
4549:
4519:
4513:
4492:
4461:
4425:
4276:
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4239:
4109:
4076:
3990:
3980:
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3946:
3919:
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3828:
3391:
1201:
1075:
934:
640:
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266:
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149:
31:
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5057:
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4455:
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3913:
1612:
5397:
5350:
5199:
5149:
4719:
4146:
4103:
4068:
3726:
3602:
3445:
regulates the speed of an engine by using spinning masses that move radially, adjusting the
3409:
1477:
1290:
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1139:
1083:
1064:
897:
845:
814:
735:
715:
660:
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601:
576:
431:
289:
234:
209:
4362:
4220:
3111:{\displaystyle -m\mathrm {d} {\boldsymbol {\omega }}/\mathrm {d} t\times {\boldsymbol {r}}}
2733:
4369:
4349:
4272:
Introduction to
Mechanics and Symmetry: A Basic Exposition of Classical Mechanical Systems
4037:
Restuccia, S.; ToroĹĄ, M.; Gibson, G. M.; Ulbricht, H.; Faccio, D.; Padgett, M. J. (2019).
3640:
3422:
3402:
1680:
1679:
equal to the rate of rotation and is directed along the axis of rotation according to the
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1079:
1020:
913:
730:
675:
625:
620:
539:
5393:
5346:
5195:
5145:
4142:
4064:
1827:
is the position vector of the particle (not to be confused with radius, as used above.)
1052:("centrifugal force"). Around this time, the concept is also further evolved by Newton,
5516:
4664:
4296:
3861:
3698:
3651:, the body in curved motion exerts an equal and opposite force on the other body. This
3513:
3119:
1307:
that is rotating relative to an inertial reference frame denoted the stationary frame.
1246:
1173:
1147:
1063:
In the late 18th century, the modern conception of the centrifugal force evolved as a "
757:
665:
566:
283:
229:
37:
4686:
4181:
3609:. Among the generalized forces, those involving the square of the time derivatives {(d
971:
5500:
5461:
5362:
5354:
4879:. These are further classified into two types. Terms involving a product of the type
4158:
4150:
4088:
3781:
3731:
3502:
3462:
645:
472:
5281:. Michigan State University, "Acceleration and force in circular motion", §5b, p. 7.
5211:
5161:
4072:
3777:
3721:
3487:
1747:
1057:
1016:
917:
710:
635:
324:
204:
3382:
5275:
4747:
4554:(Reprint of Fourth Edition of 1970 ed.). Dover Publications. Chapter 4, §5.
4038:
3822:
3378:
liquids rotating around a vertical axis is an upward-opening circular paraboloid.
5076:
As is evident from the first terms ..., which are proportional to the square of
3375:
3062:
1151:
1131:
965:
5203:
5153:
3688:
3497:
2845:{\displaystyle {\frac {\mathrm {d} ^{2}{\boldsymbol {r}}}{\mathrm {d} t^{2}}}}
1315:
In a rotating frame of reference, the time derivatives of any vector function
1150:. If the rate of rotation of the frame changes, a third fictitious force (the
893:
495:
169:
4129:
Kobayashi, Yukio (2008). "Remarks on viewing situation in a rotating frame".
3994:
3681:
centrifugal force although this usage is deprecated in elementary mechanics.
1146:
Motion relative to a rotating frame results in another fictitious force: the
1098:
Around 1914, the analogy between centrifugal force (sometimes used to create
5312:
5246:
3960:
3517:
3466:
1036:
1032:
977:
952:
517:
4080:
3509:
as generated by centrifugal force as opposed to being generated by gravity.
5485:
933:, a real frame-independent Newtonian force that exists as a reaction to a
4180:. Goddard Space Flight Center Space Physics Data Facility. Archived from
3446:
436:
319:
294:
5186:
5136:
3643:, is accelerating toward a center at any particular point in time. This
1750:(that is, acceleration in an inertial frame) of the particle, given by:
4424:(Reprint of Second Edition of 1942 ed.). Read Books. p. 347.
4221:
The
Feynman Lectures on Physics Vol. I Ch. 12: Characteristics of Force
1258:
1177:
1130:
that moves with no rotation and at constant velocity) relative to the "
409:
262:
179:
5401:
1740:
is the vector sum of the physical forces applied to the particle and
1507:
with respect to the stationary frame is related to by the equation:
468:
314:
224:
5418:
An elementary treatise on analytic mechanics: with numerous examples
5169:
5119:
4724:(Reprint of 1970 University of Toronto ed.). Dover. p. 1.
892:
This fictitious force is often applied to rotating devices, such as
4055:
1866:{\textstyle {\frac {\mathrm {d} {\boldsymbol {r}}}{\mathrm {d} t}}}
4782:
Cartesian
Impedance Control of Redundant and Flexible-Joint Robots
3632:
3381:
3369:
1217:
304:
299:
241:
36:
4108:. Sausalito CA: University Science Books. Chapter 9, pp. 344 ff.
3469:
used in many automobile seat belts operate on the same principle.
5297:(2nd ed.). New Delhi: Prentice-Hall of India. p. 121.
3481:
1943:), the absolute acceleration of the particle can be written as:
1176:
where the magnitude of the apparent force is often reported in "
844:
from the axis of rotation of a frame of reference rotating with
834:
309:
272:
3979:. Ingrid V. Eriksson. New York: Nova Science Publishers. 2008.
3942:
Mach's principle : from Newton's bucket to quantum gravity
3896:(in French). Vol. 7. The Hague: M. Nijhoff. 1897. p.
1662:{\displaystyle {\boldsymbol {\omega }}\times {\boldsymbol {P}}}
4460:(Third ed.). Oxford: Butterworth-Heinemann. p. 128.
3533:
While the majority of the scientific literature uses the term
1234:
1122:. It does not exist when a system is described relative to an
4806:
Shuzhi S. Ge; Tong Heng Lee; Christopher John Harris (1998).
1669:
attributable to the motion of the rotating frame. The vector
5058:"Effects of an intrinsic metric of molecular internal space"
5231:. Princeton, N.J.: Princeton University Press. p. 47.
4024:
Mechanics, mechanical waves, kinetic theory, thermodynamics
927:
Confusingly, the term has sometimes also been used for the
3484:-level gravity on mice with gravity simulated in this way.
3476:, as in proposed designs for rotating space stations. The
1220:
constitutes a rotating reference frame because it rotates
1200:. In order to keep the stone moving in a circular path, a
5264:. Vol. 25. American Journal of Physics. p. 325.
3560:}, which can be as simple as the usual polar coordinates
3305:
is the component of the position vector perpendicular to
102:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
3549:. Lagrangian mechanics formulates mechanics in terms of
4809:
Adaptive Neural
Network Control of Robotic Manipulators
1936:{\textstyle {\frac {\mathrm {d} }{\mathrm {d} t}}\left}
1727:{\displaystyle {\boldsymbol {F}}=m{\boldsymbol {a}}\ ,}
1070:
Centrifugal force has also played a role in debates in
5421:(25th ed.). D. Van Nostrand Company. p. 357.
3181:{\displaystyle -2m{\boldsymbol {\omega }}\times \left}
1879:
1836:
1425:
with respect to the rotating frame is, by definition,
5082:
4997:
4934:
4885:
4863:
4834:
4754:(2 ed.). Cambridge University Press. p. 90
3566:
3333:
3311:
3284:
3244:
3194:
3127:
3070:
2858:
2801:
2736:
1949:
1756:
1701:
1645:
1615:
1513:
857:
66:
5168:
Donato Bini; Paolo Carini; Robert T Jantzen (1997).
5118:
Donato Bini; Paolo Carini; Robert T Jantzen (1997).
1373:
directed along the axes of the rotating frame (i.e.
1118:
Centrifugal force is an outward force apparent in a
4748:"Generalized coordinates and kinematic constraints"
2730:The apparent acceleration in the rotating frame is
1241:
Weight of an object at the poles and on the equator
5460:
5097:
5005:
4975:
4916:
4871:
4849:
4744:For a description of generalized coordinates, see
4685:
3587:
3353:
3319:
3297:
3270:
3230:
3180:
3110:
3050:
2844:
2787:
2715:
1935:
1865:
1813:
1726:
1661:
1621:
1601:
882:
101:
5435:Robotics: a reference guide to the new technology
4393:. Arlington, Texas: S.A.W.E., Inc. Archived from
3939:Julian B. Barbour; Herbert Pfister, eds. (1995).
5262:"Centrifugal Forces and Newton's Laws of Motion"
4578:Contemporary Physics and the Limits of Knowledge
3666:This reaction force is sometimes described as a
3516:make use of centrifugal forces. For instance, a
4245:Theoretical Mechanics of Particles and Continua
4039:"Photon Bunching in a Rotating Reference Frame"
4022:Richard T. Weidner and Robert L. Sells (1973).
4248:. Courier Dover Publications. pp. 38â39.
1691:Newton's law of motion for a particle of mass
4636:I. Bernard Cohen; George Edwin Smith (2002).
4318:Knight, Judson (2016). Schlager, Neil (ed.).
3866:. Ames: Iowa State University Press. p.
1027:, which speculation may prove of good use in
947:History of centrifugal and centripetal forces
791:
8:
4976:{\displaystyle {\dot {q}}_{i}{\dot {q}}_{j}}
4928:while those involving a product of the type
4515:A universe of atoms, an atom in the universe
3915:Philosophiae naturalis principia mathematica
18:Centrifugal force (rotating reference frame)
5276:"Acceleration and force in circular motion"
4615:. Cambridge University Press. p. 324.
4269:Jerrold E. Marsden; Tudor S. Ratiu (1999).
4026:(2 ed.). Allyn and Bacon. p. 123.
3639:. A body undergoing curved motion, such as
3628:In another instance the term refers to the
3472:Centrifugal forces can be used to generate
3354:{\displaystyle ({\boldsymbol {\omega }}=0)}
1229:: the strength and direction of the local "
4642:. Cambridge University Press. p. 43.
798:
784:
45:
5185:
5174:International Journal of Modern Physics D
5135:
5124:International Journal of Modern Physics D
5084:
5083:
5081:
4998:
4996:
4967:
4956:
4955:
4948:
4937:
4936:
4933:
4908:
4901:
4890:
4889:
4887:
4884:
4864:
4862:
4836:
4835:
4833:
4418:John L. Synge; Byron A. Griffith (2007).
4372:, Cornell University, retrieved June 2007
4299:. EncyclopĂŚdia Britannica. 17 August 2016
4230:
4228:
4054:
3565:
3337:
3332:
3312:
3310:
3289:
3283:
3262:
3252:
3243:
3220:
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3201:
3193:
3165:
3160:
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3137:
3126:
3103:
3092:
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3020:
3013:
3007:
3002:
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2800:
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2017:
2011:
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1529:
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1517:
1514:
1512:
963:' notes and letters. Note, that in Latin
871:
856:
83:
77:
68:
67:
65:
42:centrifugal forces present in this frame.
4850:{\displaystyle {\boldsymbol {\dot {q}}}}
3772:
3770:
1633:. In other words, the rate of change of
825:. It is directed radially away from the
4999:
4865:
4838:
4721:The variational principles of mechanics
4551:The Variational Principles of Mechanics
3766:
3743:
3338:
3320:{\displaystyle {\boldsymbol {\omega }}}
3313:
3221:
3213:
3202:
3156:
3138:
3104:
3083:
3014:
2981:
2973:
2962:
2934:
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2283:
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2201:
2169:
2127:
2119:
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2037:
1982:
1955:
1912:
1846:
1781:
1758:
1714:
1703:
1655:
1647:
1589:
1581:
1556:
1523:
1257:When the same object is weighed on the
117:
53:
5467:. Princeton University Press. p.
5225:Mook, Delo E.; Thomas Vargish (1987).
4692:. Greenwood Publishing Group. p.
4609:Louis N. Hand; Janet D. Finch (1998).
4481:Louis N. Hand; Janet D. Finch (1998).
4345:
4335:
4000:
3893:Ĺuvres complètes de Christiaan Huygens
3271:{\displaystyle m\omega ^{2}r_{\perp }}
1417:), then the first time derivative of
1245:If an object is weighed with a simple
1102:) and gravitational forces led to the
924:such as a rotating coordinate system.
4857:where the coefficients may depend on
4716:For an introduction, see for example
4518:(2 ed.). Springer. p. 249.
3976:Science education in the 21st century
3712:Centrifugal mechanism of acceleration
985:means "fleeing from the center" in a
959:("centrifugal force") is attested in
829:. The magnitude of centrifugal force
480:Newton's law of universal gravitation
7:
5029:R. K. Mittal; I. J. Nagrath (2003).
4917:{\displaystyle {{\dot {q}}_{i}}^{2}}
4812:. World Scientific. pp. 47â48.
3782:"Christiaan Huygens' Great Treasure"
3408:The tension in a string joining two
1311:Time derivatives in a rotating frame
3910:An English translation is found at
1303:is regarded as a special case of a
1295:Mechanics of planar particle motion
1067:" arising in a rotating reference.
998:, Huygens writes (as translated by
981:) means "fleeing, avoiding". Thus,
461:Mechanics of planar particle motion
69:
4669:. Harper & Brothers. pp.
3945:. Boston: Birkhäuser. p. 69.
3841:from the original on 16 March 2020
3802:from the original on 13 April 2018
3480:would have studied the effects of
3401:The shape of the surface of water
3166:
3151:
3093:
3078:
3021:
3003:
2941:
2929:
2886:
2874:
2825:
2807:
2764:
2746:
2659:
2647:
2607:
2595:
2567:
2549:
2492:
2480:
2438:
2426:
2405:
2393:
2353:
2335:
2306:
2294:
2261:
2249:
2228:
2216:
2176:
2158:
2101:
2089:
2066:
2060:
2044:
2032:
2018:
2012:
1989:
1971:
1919:
1907:
1889:
1883:
1853:
1841:
1788:
1770:
1563:
1551:
1530:
1518:
1222:once every 23 hours and 56 minutes
25:
5035:. Tata McGraw-Hill. p. 202.
5006:{\displaystyle {\boldsymbol {q}}}
4991:. The third type is functions of
4872:{\displaystyle {\boldsymbol {q}}}
4639:The Cambridge companion to Newton
4174:"Frames of Reference: The Basics"
3545:One of these instances occurs in
1299:For the following formalism, the
5484:
5438:. Greenwood Press. p. 267.
5328:"Introducing motion in a circle"
4841:
3691:
765:
764:
751:
84:
4454:LD Landau; LM Lifshitz (1976).
883:{\displaystyle F=m\omega ^{2}r}
5463:Physics for the Inquiring Mind
5378:"Physics, the pioneer science"
5326:Roche, John (September 2001).
5098:{\displaystyle {\dot {\phi }}}
4826:Euler–Lagrange equations
4324:. Thomson Learning. p. 47
4073:10.1103/physrevlett.123.110401
3860:Blackwell, Richard J. (1986).
3607:Euler–Lagrange equations
3582:
3567:
3348:
3334:
3225:
3209:
2985:
2969:
2700:
2684:
1078:can be detected: the rotating
920:, when they are analyzed in a
1:
5415:Edward Albert Bowser (1920).
5376:Lloyd William Taylor (1959).
5056:T Yanao; K Takatsuka (2005).
4752:Dynamics of Multibody Systems
4384:"Precise Measurement of Mass"
3821:Yoder, Joella (17 May 2013).
3668:centrifugal inertial reaction
3588:{\displaystyle (r,\ \theta )}
3459:Inertial drum brake ascenders
1353:with respect to unit vectors
1170:Newton's second law of motion
1163:Vehicle driving round a curve
387:Koopmanâvon Neumann mechanics
4178:From Stargazers to Starships
3707:Balancing of rotating masses
3649:Newton's third law of motion
3188:, and the centrifugal force
1305:non-inertial reference frame
1198:Newton's first law of motion
922:nonâinertial reference frame
455:Non-inertial reference frame
5382:American Journal of Physics
4131:European Journal of Physics
4102:John Robert Taylor (2004).
3635:to a centripetal force, or
1695:written in vector form is:
1301:rotating frame of reference
1194:inertial frame of reference
1124:inertial frame of reference
823:rotating frame of reference
382:Appell's equation of motion
252:Inertial frame of reference
5543:
5355:10.1088/0031-9120/36/5/305
4718:Cornelius Lanczos (1986).
4548:Cornelius Lanczos (1986).
4489:Cambridge University Press
4363:"Curious About Astronomy?"
4151:10.1088/0143-0807/29/3/019
3659:the body in curved motion
3637:reactive centrifugal force
3425:shape reflects, following
3389:
3298:{\displaystyle r_{\perp }}
1288:
1282:
1048:, Newton further develops
1019:received Huygens work via
944:
930:reactive centrifugal force
29:
5432:Joseph A. Angelo (2007).
5204:10.1142/S021827189700011X
5166:. The companion paper is
5154:10.1142/S021827189700011X
4746:Ahmed A. Shabana (2003).
4512:Mark P Silverman (2002).
4382:Boynton, Richard (2001).
4368:January 17, 2015, at the
4275:. Springer. p. 251.
3478:Mars Gravity Biosatellite
1480:of the rotating frame is
1054:Gottfried Wilhelm Leibniz
5176:(Submitted manuscript).
5126:(Submitted manuscript).
4785:. Springer. p. 23.
4684:Myers, Rusty L. (2006).
4583:Rutgers University Press
3645:centripetal acceleration
1285:Rotating reference frame
1120:rotating reference frame
995:Horologium Oscillatorium
545:Rotating reference frame
377:HamiltonâJacobi equation
30:Not to be confused with
5291:Mohanty, A. K. (1994).
5274:Signell, Peter (2002).
5260:G. David Scott (1957).
4421:Principles of Mechanics
4208:EncyclopĂŚdia Britannica
4172:David P. Stern (2006).
4043:Physical Review Letters
3551:generalized coordinates
3541:In Lagrangian mechanics
1622:{\displaystyle \times }
486:Newton's laws of motion
346:Newton's laws of motion
5459:Eric M Rogers (1960).
5099:
5007:
4977:
4918:
4873:
4851:
4779:Christian Ott (2008).
4663:Simon Newcomb (1878).
4538:Taylor (2005). p. 329.
4444:Taylor (2005). p. 342.
4007:: CS1 maint: others (
3589:
3529:Other uses of the term
3387:
3379:
3355:
3321:
3299:
3272:
3232:
3182:
3112:
3052:
2846:
2789:
2717:
1937:
1867:
1815:
1728:
1663:
1623:
1603:
1345:are the components of
1013:
976:
970:
964:
884:
513:Simple harmonic motion
426:Euler's laws of motion
220:D'Alembert's principle
103:
43:
27:Type of inertial force
5100:
5064:. Wiley. p. 98.
5008:
4978:
4919:
4874:
4852:
4688:The basics of physics
4575:Morton Tavel (2002).
3912:Isaac Newton (1934).
3717:Equivalence principle
3590:
3507:Archimedes' principle
3385:
3374:The interface of two
3373:
3356:
3322:
3300:
3273:
3233:
3183:
3113:
3053:
2847:
2790:
2788:{\displaystyle \left}
2718:
1938:
1868:
1816:
1729:
1664:
1624:
1604:
1104:equivalence principle
1004:
902:centrifugal governors
885:
367:Hamiltonian mechanics
185:Statistical mechanics
104:
40:
5493:at Wikimedia Commons
5080:
5032:Robotics and Control
5015:gravitational forces
5013:only and are called
4995:
4932:
4883:
4861:
4832:
4612:Analytical Mechanics
4484:Analytical Mechanics
3601:, using in place of
3564:
3547:Lagrangian mechanics
3443:centrifugal governor
3403:rotating in a bucket
3331:
3309:
3282:
3242:
3192:
3125:
3068:
2856:
2799:
2734:
1947:
1877:
1834:
1754:
1699:
1643:
1631:vector cross product
1613:
1511:
1486:then the derivative
1271:not a perfect sphere
1000:Richard J. Blackwell
910:centrifugal railways
906:centrifugal clutches
855:
590:Angular acceleration
582:Rotational frequency
362:Lagrangian mechanics
355:Analytical mechanics
111:Second law of motion
64:
5394:1961AmJPh..29..563T
5347:2001PhyEd..36..399R
5196:1997IJMPD...6..143B
5146:1997IJMPD...6..143B
4391:Sawe Paper No. 3147
4297:"Centrifugal force"
4236:Alexander L. Fetter
4143:2008EJPh...29..599K
4105:Classical Mechanics
4065:2019PhRvL.123k0401R
3624:As a reactive force
3492:centrifugal casting
1476:. If the absolute
1227:gravitational force
1072:classical mechanics
987:literal translation
969:means "center" and
819:Newtonian mechanics
442:Harmonic oscillator
420:Equations of motion
55:Classical mechanics
49:Part of a series on
5095:
5003:
4973:
4926:centrifugal forces
4914:
4869:
4847:
3598:generalized forces
3585:
3474:artificial gravity
3454:centrifugal clutch
3427:Clairaut's theorem
3388:
3380:
3351:
3317:
3295:
3268:
3228:
3178:
3108:
3048:
2842:
2785:
2713:
2711:
1933:
1863:
1811:
1724:
1659:
1619:
1599:
1138:the square of the
1108:general relativity
1100:artificial gravity
1029:natural philosophy
961:Christiaan Huygens
880:
758:Physics portal
372:Routhian mechanics
247:Frame of reference
99:
44:
5512:Fictitious forces
5491:Centrifugal force
5489:Media related to
5445:978-1-57356-337-6
5402:10.1119/1.1937847
5335:Physics Education
5228:Inside relativity
5092:
5071:978-0-471-71157-5
5042:978-0-07-048293-7
4964:
4945:
4898:
4844:
4819:978-981-02-3452-2
4792:978-3-540-69253-9
4765:978-0-521-54411-5
4731:978-0-486-65067-8
4703:978-0-313-32857-2
4666:Popular astronomy
4649:978-0-521-65696-2
4622:978-0-521-57572-0
4592:978-0-8135-3077-2
4561:978-0-486-65067-8
4525:978-0-387-95437-0
4498:978-0-521-57572-0
4467:978-0-7506-2896-9
4431:978-1-4067-4670-9
4321:Centripetal Force
4282:978-0-387-98643-2
4255:978-0-486-43261-8
4240:John Dirk Walecka
4210:. April 30, 2015.
4115:978-1-891389-22-1
3986:978-1-60021-951-1
3877:978-0-8138-0933-5
3675:centrifugal force
3655:force is exerted
3578:
3535:centrifugal force
3392:Absolute rotation
3366:Absolute rotation
3044:
3036:
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2894:
2840:
2779:
2705:
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2004:
1927:
1897:
1861:
1807:
1803:
1720:
1595:
1571:
1538:
1275:
1202:centripetal force
1184:Stone on a string
1076:absolute rotation
1009:centrifugal force
935:centripetal force
898:centrifugal pumps
811:Centrifugal force
808:
807:
555:Centrifugal force
550:Centripetal force
506:Euler's equations
491:Relative velocity
267:Moment of inertia
97:
71:
32:Centripetal force
16:(Redirected from
5534:
5488:
5473:
5472:
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5456:
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5449:
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3727:Lagrangian point
3701:
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3594:
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3586:
3576:
3410:spheres rotating
3360:
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3173:
3169:
3164:
3159:
3154:
3141:
3117:
3115:
3114:
3109:
3107:
3096:
3091:
3086:
3081:
3057:
3055:
3054:
3049:
3042:
3041:
3037:
3035:
3034:
3033:
3024:
3018:
3017:
3012:
3011:
3006:
2999:
2984:
2976:
2965:
2954:
2950:
2948:
2944:
2938:
2937:
2932:
2926:
2917:
2903:
2895:
2893:
2889:
2883:
2882:
2877:
2871:
2863:
2851:
2849:
2848:
2843:
2841:
2839:
2838:
2837:
2828:
2822:
2821:
2816:
2815:
2810:
2803:
2794:
2792:
2791:
2786:
2784:
2780:
2778:
2777:
2776:
2767:
2761:
2760:
2755:
2754:
2749:
2742:
2722:
2720:
2719:
2714:
2712:
2703:
2699:
2691:
2680:
2672:
2668:
2666:
2662:
2656:
2655:
2650:
2644:
2635:
2624:
2616:
2614:
2610:
2604:
2603:
2598:
2592:
2587:
2583:
2581:
2580:
2579:
2570:
2564:
2563:
2558:
2557:
2552:
2545:
2533:
2529:
2525:
2522:
2521:
2513:
2505:
2501:
2499:
2495:
2489:
2488:
2483:
2477:
2463:
2455:
2447:
2445:
2441:
2435:
2434:
2429:
2423:
2418:
2414:
2412:
2408:
2402:
2401:
2396:
2390:
2381:
2373:
2369:
2367:
2366:
2365:
2356:
2350:
2349:
2344:
2343:
2338:
2331:
2319:
2315:
2313:
2309:
2303:
2302:
2297:
2291:
2286:
2278:
2270:
2268:
2264:
2258:
2257:
2252:
2246:
2241:
2237:
2235:
2231:
2225:
2224:
2219:
2213:
2204:
2196:
2192:
2190:
2189:
2188:
2179:
2173:
2172:
2167:
2166:
2161:
2154:
2142:
2138:
2134:
2131:
2130:
2122:
2114:
2110:
2108:
2104:
2098:
2097:
2092:
2086:
2075:
2073:
2069:
2063:
2058:
2053:
2051:
2047:
2041:
2040:
2035:
2029:
2027:
2025:
2021:
2015:
2010:
2005:
2003:
2002:
2001:
1992:
1986:
1985:
1980:
1979:
1974:
1967:
1958:
1942:
1940:
1939:
1934:
1932:
1928:
1926:
1922:
1916:
1915:
1910:
1904:
1898:
1896:
1892:
1886:
1881:
1872:
1870:
1869:
1864:
1862:
1860:
1856:
1850:
1849:
1844:
1838:
1826:
1820:
1818:
1817:
1812:
1805:
1804:
1802:
1801:
1800:
1791:
1785:
1784:
1779:
1778:
1773:
1766:
1761:
1746:is the absolute
1745:
1739:
1733:
1731:
1730:
1725:
1718:
1717:
1706:
1694:
1678:
1674:
1668:
1666:
1665:
1660:
1658:
1650:
1638:
1628:
1626:
1625:
1620:
1608:
1606:
1605:
1600:
1593:
1592:
1584:
1576:
1572:
1570:
1566:
1560:
1559:
1554:
1548:
1539:
1537:
1533:
1527:
1526:
1521:
1515:
1506:
1498:
1485:
1478:angular velocity
1475:
1424:
1416:
1372:
1352:
1344:
1322:
1291:Fictitious force
1264:
1140:angular velocity
1092:Mach's principle
1084:rotating spheres
1065:fictitious force
914:planetary orbits
889:
887:
886:
881:
876:
875:
850:
846:angular velocity
840:at the distance
833:on an object of
827:axis of rotation
815:fictitious force
800:
793:
786:
773:
768:
767:
760:
756:
755:
661:Johann Bernoulli
656:Daniel Bernoulli
577:Tangential speed
481:
457:
432:Fictitious force
427:
279:Mechanical power
269:
210:Angular momentum
108:
106:
105:
100:
98:
96:
88:
87:
78:
73:
72:
46:
21:
5542:
5541:
5537:
5536:
5535:
5533:
5532:
5531:
5497:
5496:
5481:
5476:
5458:
5457:
5453:
5446:
5431:
5430:
5426:
5414:
5413:
5409:
5375:
5374:
5370:
5330:
5325:
5324:
5320:
5305:
5294:Fluid mechanics
5290:
5289:
5285:
5273:
5269:
5259:
5258:
5254:
5239:
5224:
5223:
5219:
5187:gr-qc/0106014v1
5167:
5137:gr-qc/0106014v1
5117:
5115:
5111:
5078:
5077:
5072:
5055:
5054:
5050:
5043:
5028:
5027:
5023:
4993:
4992:
4989:Coriolis forces
4954:
4935:
4930:
4929:
4888:
4886:
4881:
4880:
4859:
4858:
4830:
4829:
4820:
4805:
4804:
4800:
4793:
4778:
4777:
4773:
4766:
4745:
4743:
4739:
4732:
4717:
4715:
4711:
4704:
4683:
4682:
4678:
4662:
4661:
4657:
4650:
4635:
4634:
4630:
4623:
4608:
4607:
4603:
4593:
4574:
4573:
4569:
4562:
4547:
4546:
4542:
4537:
4533:
4526:
4511:
4510:
4506:
4499:
4491:. p. 267.
4480:
4479:
4475:
4468:
4453:
4452:
4448:
4443:
4439:
4432:
4417:
4416:
4412:
4403:
4401:
4397:
4386:
4381:
4380:
4376:
4370:Wayback Machine
4361:
4357:
4344:
4334:
4327:
4325:
4317:
4316:
4312:
4302:
4300:
4295:
4294:
4290:
4283:
4268:
4267:
4263:
4256:
4234:
4233:
4226:
4219:
4215:
4202:
4201:
4197:
4187:
4185:
4184:on 6 April 2020
4171:
4170:
4166:
4128:
4127:
4123:
4116:
4101:
4100:
4096:
4036:
4035:
4031:
4021:
4020:
4016:
3999:
3987:
3973:
3972:
3968:
3953:
3938:
3937:
3933:
3926:
3911:
3909:
3905:
3890:
3889:
3885:
3878:
3859:
3858:
3854:
3844:
3842:
3835:
3820:
3819:
3815:
3805:
3803:
3799:
3784:
3776:
3775:
3768:
3764:
3759:
3758:
3752:vim centrifugam
3749:
3745:
3740:
3697:
3690:
3687:
3677:rather than as
3641:circular motion
3626:
3614:
3562:
3561:
3558:
3543:
3531:
3514:amusement rides
3435:
3423:oblate spheroid
3394:
3368:
3329:
3328:
3307:
3306:
3285:
3280:
3279:
3258:
3248:
3240:
3239:
3190:
3189:
3149:
3145:
3123:
3122:
3066:
3065:
3025:
3019:
3001:
3000:
2994:
2939:
2927:
2921:
2884:
2872:
2854:
2853:
2829:
2823:
2805:
2804:
2797:
2796:
2768:
2762:
2744:
2743:
2737:
2732:
2731:
2728:
2710:
2709:
2657:
2645:
2639:
2605:
2593:
2571:
2565:
2547:
2546:
2540:
2531:
2530:
2490:
2478:
2472:
2471:
2467:
2436:
2424:
2403:
2391:
2385:
2357:
2351:
2333:
2332:
2326:
2317:
2316:
2304:
2292:
2259:
2247:
2226:
2214:
2208:
2180:
2174:
2156:
2155:
2149:
2140:
2139:
2099:
2087:
2081:
2080:
2076:
2064:
2042:
2030:
2016:
1993:
1987:
1969:
1968:
1959:
1945:
1944:
1917:
1905:
1899:
1887:
1875:
1874:
1851:
1839:
1832:
1831:
1822:
1792:
1786:
1768:
1767:
1752:
1751:
1741:
1735:
1697:
1696:
1692:
1689:
1681:right-hand rule
1676:
1670:
1641:
1640:
1634:
1611:
1610:
1561:
1549:
1543:
1528:
1516:
1509:
1508:
1500:
1487:
1481:
1465:
1449:
1433:
1426:
1418:
1410:
1398:
1386:
1374:
1354:
1346:
1343:
1336:
1330:
1324:
1316:
1313:
1297:
1287:
1281:
1251:restoring force
1243:
1214:
1186:
1174:roller coasters
1165:
1160:
1116:
1080:bucket argument
1021:Henry Oldenburg
1015:The same year,
951:From 1659, the
949:
943:
867:
853:
852:
848:
804:
763:
750:
749:
742:
741:
740:
615:
607:
606:
586:
540:Circular motion
534:
524:
523:
522:
479:
449:
446:
425:
404:
396:
395:
392:
391:
349:
339:
331:
330:
329:
288:
284:Mechanical work
277:
261:
199:
191:
190:
189:
144:
136:
113:
89:
79:
62:
61:
35:
28:
23:
22:
15:
12:
11:
5:
5540:
5538:
5530:
5529:
5524:
5519:
5514:
5509:
5499:
5498:
5495:
5494:
5480:
5479:External links
5477:
5475:
5474:
5451:
5444:
5424:
5407:
5368:
5341:(5): 399â405.
5318:
5303:
5283:
5267:
5252:
5237:
5217:
5180:(1): 143â198.
5130:(1): 143â198.
5109:
5091:
5088:
5070:
5048:
5041:
5021:
5001:
4970:
4963:
4960:
4951:
4944:
4941:
4911:
4904:
4897:
4894:
4867:
4843:
4840:
4818:
4798:
4791:
4771:
4764:
4737:
4730:
4709:
4702:
4676:
4655:
4648:
4628:
4621:
4601:
4591:
4585:. p. 93.
4567:
4560:
4540:
4531:
4524:
4504:
4497:
4473:
4466:
4446:
4437:
4430:
4410:
4374:
4355:
4310:
4288:
4281:
4261:
4254:
4224:
4213:
4195:
4164:
4137:(3): 599â606.
4121:
4114:
4094:
4049:(11): 110401.
4029:
4014:
3985:
3966:
3951:
3931:
3924:
3903:
3883:
3876:
3852:
3833:
3813:
3765:
3763:
3760:
3757:
3756:
3742:
3741:
3739:
3736:
3735:
3734:
3729:
3724:
3719:
3714:
3709:
3703:
3702:
3699:Physics portal
3686:
3683:
3625:
3622:
3612:
3584:
3581:
3575:
3572:
3569:
3556:
3542:
3539:
3530:
3527:
3522:
3521:
3510:
3503:buoyant forces
3495:
3485:
3470:
3450:
3434:
3431:
3414:
3413:
3406:
3390:Main article:
3367:
3364:
3350:
3347:
3344:
3340:
3336:
3315:
3292:
3288:
3265:
3261:
3255:
3251:
3247:
3227:
3223:
3219:
3215:
3211:
3208:
3204:
3200:
3197:
3176:
3172:
3168:
3163:
3158:
3153:
3148:
3144:
3140:
3136:
3133:
3130:
3120:Coriolis force
3106:
3102:
3099:
3095:
3090:
3085:
3080:
3076:
3073:
3047:
3040:
3032:
3028:
3023:
3016:
3010:
3005:
2997:
2993:
2990:
2987:
2983:
2979:
2975:
2971:
2968:
2964:
2960:
2957:
2953:
2947:
2943:
2936:
2931:
2924:
2920:
2916:
2912:
2909:
2906:
2902:
2898:
2892:
2888:
2881:
2876:
2869:
2866:
2862:
2836:
2832:
2827:
2820:
2814:
2809:
2783:
2775:
2771:
2766:
2759:
2753:
2748:
2740:
2727:
2724:
2708:
2702:
2698:
2694:
2690:
2686:
2683:
2679:
2675:
2671:
2665:
2661:
2654:
2649:
2642:
2638:
2634:
2630:
2627:
2623:
2619:
2613:
2609:
2602:
2597:
2590:
2586:
2578:
2574:
2569:
2562:
2556:
2551:
2543:
2539:
2536:
2534:
2532:
2528:
2520:
2516:
2512:
2508:
2504:
2498:
2494:
2487:
2482:
2475:
2470:
2466:
2462:
2458:
2454:
2450:
2444:
2440:
2433:
2428:
2421:
2417:
2411:
2407:
2400:
2395:
2388:
2384:
2380:
2376:
2372:
2364:
2360:
2355:
2348:
2342:
2337:
2329:
2325:
2322:
2320:
2318:
2312:
2308:
2301:
2296:
2289:
2285:
2281:
2277:
2273:
2267:
2263:
2256:
2251:
2244:
2240:
2234:
2230:
2223:
2218:
2211:
2207:
2203:
2199:
2195:
2187:
2183:
2178:
2171:
2165:
2160:
2152:
2148:
2145:
2143:
2141:
2137:
2129:
2125:
2121:
2117:
2113:
2107:
2103:
2096:
2091:
2084:
2079:
2072:
2068:
2062:
2056:
2050:
2046:
2039:
2034:
2024:
2020:
2014:
2008:
2000:
1996:
1991:
1984:
1978:
1973:
1965:
1962:
1960:
1957:
1953:
1952:
1931:
1925:
1921:
1914:
1909:
1902:
1895:
1891:
1885:
1859:
1855:
1848:
1843:
1810:
1799:
1795:
1790:
1783:
1777:
1772:
1764:
1760:
1723:
1716:
1712:
1709:
1705:
1688:
1685:
1675:has magnitude
1657:
1653:
1649:
1618:
1598:
1591:
1587:
1583:
1579:
1575:
1569:
1565:
1558:
1553:
1546:
1542:
1536:
1532:
1525:
1520:
1463:
1447:
1431:
1408:
1396:
1384:
1341:
1334:
1328:
1312:
1309:
1283:Main article:
1280:
1277:
1247:spring balance
1242:
1239:
1213:
1210:
1185:
1182:
1164:
1161:
1159:
1156:
1148:Coriolis force
1115:
1112:
1050:vis centrifuga
1025:vis centrifuga
945:Main article:
942:
939:
879:
874:
870:
866:
863:
860:
806:
805:
803:
802:
795:
788:
780:
777:
776:
775:
774:
761:
744:
743:
739:
738:
733:
728:
723:
718:
713:
708:
703:
698:
693:
688:
683:
678:
673:
668:
663:
658:
653:
648:
643:
638:
633:
628:
623:
617:
616:
613:
612:
609:
608:
605:
604:
585:
584:
579:
574:
569:
567:Coriolis force
564:
563:
562:
552:
547:
542:
536:
535:
530:
529:
526:
525:
521:
520:
515:
510:
509:
508:
503:
493:
488:
483:
476:
465:
464:
463:
458:
445:
444:
439:
434:
429:
422:
417:
412:
406:
405:
402:
401:
398:
397:
394:
393:
390:
389:
384:
379:
374:
369:
364:
358:
352:
350:
343:
340:
337:
336:
333:
332:
328:
327:
322:
317:
312:
307:
302:
297:
292:
286:
281:
275:
270:
259:
254:
249:
244:
239:
238:
237:
232:
222:
217:
212:
207:
201:
200:
197:
196:
193:
192:
188:
187:
182:
177:
172:
167:
162:
157:
152:
146:
145:
142:
141:
138:
137:
135:
134:
129:
124:
118:
115:
114:
109:
95:
92:
86:
82:
76:
58:
57:
51:
50:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5539:
5528:
5525:
5523:
5520:
5518:
5515:
5513:
5510:
5508:
5505:
5504:
5502:
5492:
5487:
5483:
5482:
5478:
5470:
5465:
5464:
5455:
5452:
5447:
5441:
5437:
5436:
5428:
5425:
5420:
5419:
5411:
5408:
5403:
5399:
5395:
5391:
5387:
5383:
5379:
5372:
5369:
5364:
5360:
5356:
5352:
5348:
5344:
5340:
5336:
5329:
5322:
5319:
5314:
5310:
5306:
5304:81-203-0894-8
5300:
5296:
5295:
5287:
5284:
5280:
5277:
5271:
5268:
5263:
5256:
5253:
5248:
5244:
5240:
5238:0-691-08472-6
5234:
5230:
5229:
5221:
5218:
5213:
5209:
5205:
5201:
5197:
5193:
5188:
5183:
5179:
5175:
5171:
5163:
5159:
5155:
5151:
5147:
5143:
5138:
5133:
5129:
5125:
5121:
5113:
5110:
5106:
5089:
5086:
5073:
5067:
5063:
5059:
5052:
5049:
5044:
5038:
5034:
5033:
5025:
5022:
5018:
5016:
4990:
4986:
4968:
4961:
4958:
4949:
4942:
4939:
4927:
4909:
4902:
4895:
4892:
4827:
4824:In the above
4821:
4815:
4811:
4810:
4802:
4799:
4794:
4788:
4784:
4783:
4775:
4772:
4767:
4761:
4757:
4753:
4749:
4741:
4738:
4733:
4727:
4723:
4722:
4713:
4710:
4705:
4699:
4695:
4690:
4689:
4680:
4677:
4672:
4668:
4667:
4659:
4656:
4651:
4645:
4641:
4640:
4632:
4629:
4624:
4618:
4614:
4613:
4605:
4602:
4598:
4594:
4588:
4584:
4580:
4579:
4571:
4568:
4563:
4557:
4553:
4552:
4544:
4541:
4535:
4532:
4527:
4521:
4517:
4516:
4508:
4505:
4500:
4494:
4490:
4486:
4485:
4477:
4474:
4469:
4463:
4459:
4458:
4450:
4447:
4441:
4438:
4433:
4427:
4423:
4422:
4414:
4411:
4400:on 2007-02-27
4396:
4392:
4385:
4378:
4375:
4371:
4367:
4364:
4359:
4356:
4351:
4339:
4323:
4322:
4314:
4311:
4298:
4292:
4289:
4284:
4278:
4274:
4273:
4265:
4262:
4257:
4251:
4247:
4246:
4241:
4237:
4231:
4229:
4225:
4222:
4217:
4214:
4209:
4205:
4199:
4196:
4183:
4179:
4175:
4168:
4165:
4160:
4156:
4152:
4148:
4144:
4140:
4136:
4132:
4125:
4122:
4117:
4111:
4107:
4106:
4098:
4095:
4090:
4086:
4082:
4078:
4074:
4070:
4066:
4062:
4057:
4052:
4048:
4044:
4040:
4033:
4030:
4025:
4018:
4015:
4010:
4004:
3996:
3992:
3988:
3982:
3978:
3977:
3970:
3967:
3962:
3958:
3954:
3952:0-8176-3823-7
3948:
3944:
3943:
3935:
3932:
3927:
3925:9780520009271
3921:
3917:
3916:
3907:
3904:
3899:
3895:
3894:
3887:
3884:
3879:
3873:
3869:
3865:
3864:
3856:
3853:
3840:
3836:
3834:9789004235656
3830:
3826:
3825:
3817:
3814:
3798:
3794:
3790:
3783:
3779:
3778:Yoder, Joella
3773:
3771:
3767:
3761:
3753:
3747:
3744:
3737:
3733:
3732:Lamm equation
3730:
3728:
3725:
3723:
3720:
3718:
3715:
3713:
3710:
3708:
3705:
3704:
3700:
3694:
3689:
3684:
3682:
3680:
3676:
3671:
3669:
3664:
3662:
3658:
3654:
3650:
3646:
3642:
3638:
3634:
3631:
3623:
3621:
3619:
3615:
3608:
3604:
3603:Newton's laws
3600:
3599:
3579:
3573:
3570:
3559:
3552:
3548:
3540:
3538:
3536:
3528:
3526:
3519:
3515:
3511:
3508:
3504:
3499:
3496:
3493:
3489:
3486:
3483:
3479:
3475:
3471:
3468:
3467:inertia reels
3464:
3463:rock climbing
3460:
3455:
3451:
3448:
3444:
3440:
3439:
3438:
3432:
3430:
3428:
3424:
3418:
3411:
3407:
3404:
3400:
3399:
3398:
3393:
3384:
3377:
3372:
3365:
3363:
3345:
3342:
3290:
3286:
3263:
3259:
3253:
3249:
3245:
3217:
3206:
3198:
3195:
3174:
3170:
3161:
3146:
3142:
3134:
3131:
3128:
3121:
3100:
3097:
3088:
3074:
3071:
3064:
3058:
3045:
3038:
3030:
3026:
3008:
2995:
2991:
2988:
2977:
2966:
2958:
2955:
2951:
2945:
2922:
2918:
2910:
2907:
2904:
2896:
2890:
2867:
2864:
2834:
2830:
2812:
2781:
2773:
2769:
2751:
2738:
2725:
2723:
2706:
2692:
2681:
2673:
2669:
2663:
2640:
2636:
2628:
2625:
2617:
2611:
2588:
2584:
2576:
2572:
2554:
2541:
2537:
2535:
2526:
2514:
2506:
2502:
2496:
2473:
2468:
2464:
2456:
2448:
2442:
2419:
2415:
2409:
2386:
2382:
2374:
2370:
2362:
2358:
2340:
2327:
2323:
2321:
2310:
2287:
2279:
2271:
2265:
2242:
2238:
2232:
2209:
2205:
2197:
2193:
2185:
2181:
2163:
2150:
2146:
2144:
2135:
2123:
2115:
2111:
2105:
2082:
2077:
2070:
2054:
2048:
2022:
2006:
1998:
1994:
1976:
1963:
1961:
1929:
1923:
1900:
1893:
1857:
1828:
1825:
1808:
1797:
1793:
1775:
1762:
1749:
1744:
1738:
1721:
1710:
1707:
1686:
1684:
1682:
1673:
1651:
1637:
1632:
1616:
1596:
1585:
1577:
1573:
1567:
1544:
1540:
1534:
1505:
1504:
1497:
1493:
1492:
1484:
1479:
1474:
1473:
1469:
1462:
1458:
1457:
1453:
1446:
1442:
1441:
1437:
1430:
1423:
1422:
1415:
1414:
1407:
1403:
1402:
1395:
1391:
1390:
1383:
1379:
1378:
1371:
1370:
1365:
1364:
1359:
1358:
1351:
1350:
1340:
1333:
1327:
1321:
1320:
1310:
1308:
1306:
1302:
1296:
1292:
1286:
1278:
1276:
1274:
1272:
1267:
1262:
1260:
1255:
1252:
1248:
1240:
1238:
1236:
1232:
1228:
1223:
1219:
1211:
1209:
1205:
1203:
1199:
1195:
1190:
1183:
1181:
1179:
1175:
1171:
1162:
1157:
1155:
1153:
1149:
1144:
1141:
1135:
1133:
1127:
1125:
1121:
1113:
1111:
1109:
1105:
1101:
1096:
1093:
1090:Around 1883,
1088:
1085:
1081:
1077:
1073:
1068:
1066:
1061:
1059:
1055:
1051:
1047:
1046:
1040:
1038:
1035:, as well as
1034:
1030:
1026:
1022:
1018:
1012:
1010:
1003:
1001:
997:
996:
990:
988:
984:
980:
979:
974:
973:
968:
967:
962:
958:
957:vi centrifuga
954:
948:
940:
938:
936:
932:
931:
925:
923:
919:
918:banked curves
915:
911:
907:
903:
899:
895:
890:
877:
872:
868:
864:
861:
858:
847:
843:
839:
836:
832:
828:
824:
820:
816:
812:
801:
796:
794:
789:
787:
782:
781:
779:
778:
772:
762:
759:
754:
748:
747:
746:
745:
737:
734:
732:
729:
727:
724:
722:
719:
717:
714:
712:
709:
707:
704:
702:
699:
697:
694:
692:
689:
687:
684:
682:
679:
677:
674:
672:
669:
667:
664:
662:
659:
657:
654:
652:
649:
647:
644:
642:
639:
637:
634:
632:
629:
627:
624:
622:
619:
618:
611:
610:
603:
599:
595:
591:
588:
587:
583:
580:
578:
575:
573:
570:
568:
565:
561:
558:
557:
556:
553:
551:
548:
546:
543:
541:
538:
537:
533:
528:
527:
519:
516:
514:
511:
507:
504:
502:
499:
498:
497:
494:
492:
489:
487:
484:
482:
477:
474:
470:
467:
466:
462:
459:
456:
452:
448:
447:
443:
440:
438:
435:
433:
430:
428:
423:
421:
418:
416:
413:
411:
408:
407:
400:
399:
388:
385:
383:
380:
378:
375:
373:
370:
368:
365:
363:
360:
359:
357:
356:
351:
348:
347:
342:
341:
335:
334:
326:
323:
321:
318:
316:
313:
311:
308:
306:
303:
301:
298:
296:
293:
291:
287:
285:
282:
280:
276:
274:
271:
268:
264:
260:
258:
255:
253:
250:
248:
245:
243:
240:
236:
233:
231:
228:
227:
226:
223:
221:
218:
216:
213:
211:
208:
206:
203:
202:
195:
194:
186:
183:
181:
178:
176:
173:
171:
168:
166:
163:
161:
158:
156:
153:
151:
148:
147:
140:
139:
133:
130:
128:
125:
123:
120:
119:
116:
112:
93:
90:
80:
74:
60:
59:
56:
52:
48:
47:
39:
33:
19:
5507:Acceleration
5462:
5454:
5434:
5427:
5417:
5410:
5385:
5381:
5371:
5338:
5334:
5321:
5293:
5286:
5278:
5270:
5255:
5227:
5220:
5177:
5173:
5127:
5123:
5116:See p. 5 in
5112:
5075:
5061:
5051:
5031:
5024:
5014:
4988:
4984:
4925:
4823:
4808:
4801:
4781:
4774:
4755:
4751:
4740:
4720:
4712:
4687:
4679:
4665:
4658:
4638:
4631:
4611:
4604:
4596:
4577:
4570:
4550:
4543:
4534:
4514:
4507:
4483:
4476:
4456:
4449:
4440:
4420:
4413:
4402:. Retrieved
4395:the original
4390:
4377:
4358:
4326:. Retrieved
4320:
4313:
4301:. Retrieved
4291:
4271:
4264:
4244:
4216:
4207:
4204:"Centrifuge"
4198:
4186:. Retrieved
4182:the original
4177:
4167:
4134:
4130:
4124:
4104:
4097:
4046:
4042:
4032:
4023:
4017:
3975:
3969:
3941:
3934:
3914:
3906:
3892:
3886:
3862:
3855:
3843:. Retrieved
3823:
3816:
3804:. Retrieved
3792:
3788:
3751:
3746:
3722:Folk physics
3678:
3674:
3672:
3667:
3665:
3660:
3656:
3627:
3617:
3610:
3596:
3554:
3544:
3534:
3532:
3523:
3488:Spin casting
3436:
3433:Applications
3419:
3415:
3395:
3059:
2729:
1873:and once to
1829:
1823:
1748:acceleration
1742:
1736:
1690:
1687:Acceleration
1671:
1635:
1629:denotes the
1502:
1501:
1495:
1490:
1489:
1482:
1471:
1470:
1467:
1460:
1455:
1454:
1451:
1444:
1439:
1438:
1435:
1428:
1420:
1419:
1412:
1411:
1405:
1400:
1399:
1393:
1388:
1387:
1381:
1376:
1375:
1368:
1367:
1362:
1361:
1356:
1355:
1348:
1347:
1338:
1331:
1325:
1318:
1317:
1314:
1298:
1268:
1265:
1263:
1256:
1244:
1215:
1206:
1191:
1187:
1166:
1145:
1136:
1128:
1117:
1114:Introduction
1097:
1089:
1069:
1062:
1058:Robert Hooke
1049:
1043:
1042:In 1687, in
1041:
1024:
1017:Isaac Newton
1014:
1008:
1005:
993:
992:In 1673, in
991:
982:
956:
950:
928:
926:
891:
841:
837:
830:
810:
809:
600: /
596: /
594:displacement
592: /
554:
453: /
415:Displacement
353:
344:
338:Formulations
325:Virtual work
265: /
205:Acceleration
198:Fundamentals
4987:are called
4924:are called
4346:|work=
3498:Centrifuges
3063:Euler force
1152:Euler force
1132:fixed stars
983:centrifugus
894:centrifuges
736:von Neumann
403:Core topics
5501:Categories
5388:(8): 173.
4404:2007-01-21
4056:1906.03400
3762:References
3750:In Latin:
3376:immiscible
1289:See also:
1279:Derivation
1082:, and the
671:d'Alembert
651:Maupertuis
614:Scientists
496:Rigid body
170:Kinematics
5522:Mechanics
5363:250827660
5090:˙
5087:ϕ
4962:˙
4943:˙
4896:˙
4842:˙
4457:Mechanics
4348:ignored (
4338:cite book
4159:120947179
4089:182952610
4003:cite book
3995:165958146
3827:. BRILL.
3580:θ
3518:Gravitron
3339:ω
3314:ω
3291:⊥
3264:⊥
3250:ω
3218:×
3214:ω
3207:×
3203:ω
3196:−
3143:×
3139:ω
3129:−
3101:×
3084:ω
3072:−
2978:×
2974:ω
2967:×
2963:ω
2956:−
2919:×
2915:ω
2905:−
2897:×
2880:ω
2865:−
2693:×
2689:ω
2682:×
2678:ω
2637:×
2633:ω
2618:×
2601:ω
2515:×
2511:ω
2465:×
2461:ω
2449:×
2432:ω
2383:×
2379:ω
2288:×
2284:ω
2272:×
2255:ω
2206:×
2202:ω
2124:×
2120:ω
1652:×
1648:ω
1617:×
1586:×
1582:ω
1045:Principia
1037:mechanics
1033:astronomy
953:Neo-Latin
908:, and in
869:ω
716:Liouville
598:frequency
518:Vibration
235:potential
160:Continuum
155:Celestial
132:Textbooks
5527:Rotation
5313:44020947
5247:16089285
5212:10652293
5162:10652293
4366:Archived
4328:19 April
4303:20 April
4242:(2003).
4188:20 April
4081:31573252
3961:32664808
3845:12 April
3839:Archived
3806:12 April
3797:Archived
3795:: 1â13.
3789:Tractrix
3780:(1991).
3685:See also
3679:reactive
3653:reactive
3630:reaction
3465:and the
3461:used in
3447:throttle
3278:, where
1158:Examples
771:Category
696:Hamilton
681:Lagrange
676:Clairaut
641:Horrocks
602:velocity
572:Pendulum
560:reactive
532:Rotation
501:dynamics
451:Inertial
437:Friction
320:Velocity
295:Momentum
175:Kinetics
165:Dynamics
143:Branches
127:Timeline
5390:Bibcode
5343:Bibcode
5279:Physnet
5192:Bibcode
5142:Bibcode
4139:Bibcode
4061:Bibcode
1259:equator
1231:gravity
966:centrum
941:History
731:Koopman
691:Poisson
686:Laplace
631:Huygens
626:Galileo
471: (
410:Damping
263:Inertia
257:Impulse
230:kinetic
180:Statics
150:Applied
122:History
5442:
5361:
5311:
5301:
5245:
5235:
5210:
5160:
5068:
5039:
4816:
4789:
4762:
4728:
4700:
4646:
4619:
4589:
4558:
4522:
4495:
4464:
4428:
4279:
4252:
4157:
4112:
4087:
4079:
3993:
3983:
3959:
3949:
3922:
3874:
3831:
3577:
3118:, the
3043:
2704:
2523:
2132:
1821:where
1806:
1734:where
1719:
1609:where
1594:
1192:In an
1056:, and
975:(from
972:âfugus
904:, and
769:
721:Appell
706:Cauchy
701:Jacobi
646:Halley
636:Newton
621:Kepler
473:linear
469:Motion
315:Torque
290:Moment
225:Energy
215:Couple
5517:Force
5359:S2CID
5331:(PDF)
5208:S2CID
5182:arXiv
5158:S2CID
5132:arXiv
4985:i â j
4398:(PDF)
4387:(PDF)
4155:S2CID
4085:S2CID
4051:arXiv
3800:(PDF)
3785:(PDF)
3738:Notes
3633:force
3512:Some
2726:Force
1266:Note:
1218:Earth
1212:Earth
978:fugiĹ
955:term
813:is a
726:Gibbs
711:Routh
666:Euler
305:Speed
300:Space
242:Force
5440:ISBN
5309:OCLC
5299:ISBN
5243:OCLC
5233:ISBN
5066:ISBN
5037:ISBN
4983:for
4814:ISBN
4787:ISBN
4760:ISBN
4726:ISBN
4698:ISBN
4673:â88.
4644:ISBN
4617:ISBN
4587:ISBN
4556:ISBN
4520:ISBN
4493:ISBN
4462:ISBN
4426:ISBN
4350:help
4330:2017
4305:2017
4277:ISBN
4250:ISBN
4190:2017
4110:ISBN
4077:PMID
4009:link
3991:OCLC
3981:ISBN
3957:OCLC
3947:ISBN
3920:ISBN
3872:ISBN
3847:2018
3829:ISBN
3808:2018
3605:the
3490:and
3482:Mars
1293:and
1216:The
1031:and
916:and
851:is:
835:mass
310:Time
273:Mass
5469:302
5398:doi
5351:doi
5200:doi
5150:doi
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