49:
856:
1109:
4949:
3496:. Where Newtonian mechanics and special relativity differ is in how different observers would describe the same situation. In particular, in Newtonian mechanics, all observers agree on the value of t and the transformation rules for position create a situation in which all non-accelerating observers would describe the acceleration of an object with the same values. Neither is true for special relativity. In other words, only relative velocity can be calculated.
869:
3972:. The escape velocity from Earth's surface is about 11 200 m/s, and is irrespective of the direction of the object. This makes "escape velocity" somewhat of a misnomer, as the more correct term would be "escape speed": any object attaining a velocity of that magnitude, irrespective of atmosphere, will leave the vicinity of the base body as long as it does not intersect with something in its path.
1374:
2490:
3401:
3222:
5397:
2726:
2168:
4952:
Representation of radial and tangential components of velocity at different moments of linear motion with constant velocity of the object around an observer O (it corresponds, for example, to the passage of a car on a straight street around a pedestrian standing on the sidewalk). The radial component
3226:
5196:
3070:
1624:
1253:
1463:
to emphasize the distinction from the average velocity. In some applications the average velocity of an object might be needed, that is to say, the constant velocity that would provide the same resultant displacement as a variable velocity in the same time interval,
1921:
5282:
2526:
3061:
5483:
in scalar form is the mass times the distance to the origin times the transverse velocity, or equivalently, the mass times the distance squared times the angular speed. The sign convention for angular momentum is the same as that for angular velocity.
4073:
is a measurement of velocity between two objects as determined in a single coordinate system. Relative velocity is fundamental in both classical and modern physics, since many systems in physics deal with the relative motion of two or more particles.
2097:
5476:
1630:
The average velocity is always less than or equal to the average speed of an object. This can be seen by realizing that while distance is always strictly increasing, displacement can increase or decrease in magnitude as well as change direction.
5649:, angular momentum is constant, and transverse speed is inversely proportional to the distance, angular speed is inversely proportional to the distance squared, and the rate at which area is swept out is constant. These relations are known as
4220:
4155:
5116:
1419:
For example, a car moving at a constant 20 kilometres per hour in a circular path has a constant speed, but does not have a constant velocity because its direction changes. Hence, the car is considered to be undergoing an acceleration.
4356:, velocity is broken up into components that correspond with each dimensional axis of the coordinate system. In a two-dimensional system, where there is an x-axis and a y-axis, corresponding velocity components are defined as
2485:{\displaystyle {\bar {v}}={s_{1}+s_{2}+s_{3}+\dots +s_{n} \over t_{1}+t_{2}+t_{3}+\dots +t_{n}}={{s_{1}+s_{2}+s_{3}+\dots +s_{n}} \over {{s_{1} \over v_{1}}+{s_{2} \over v_{2}}+{s_{3} \over v_{3}}+\dots +{s_{n} \over v_{n}}}}}
3468:
1489:
1162:
5036:
2932:
1416:, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed.
1358:
Although the concept of an instantaneous velocity might at first seem counter-intuitive, it may be thought of as the velocity that the object would continue to travel at if it stopped accelerating at that moment.
4049:
3396:{\displaystyle (2{\boldsymbol {a}})\cdot {\boldsymbol {x}}=(2{\boldsymbol {a}})\cdot ({\boldsymbol {u}}t+{\tfrac {1}{2}}{\boldsymbol {a}}t^{2})=2t({\boldsymbol {a}}\cdot {\boldsymbol {u}})+a^{2}t^{2}=v^{2}-u^{2}}
3954:
4979:, which is the rate of rotation about the origin (with positive quantities representing counter-clockwise rotation and negative quantities representing clockwise rotation, in a right-handed coordinate system).
2813:
3748:
3217:{\displaystyle v^{2}={\boldsymbol {v}}\cdot {\boldsymbol {v}}=({\boldsymbol {u}}+{\boldsymbol {a}}t)\cdot ({\boldsymbol {u}}+{\boldsymbol {a}}t)=u^{2}+2t({\boldsymbol {a}}\cdot {\boldsymbol {u}})+a^{2}t^{2}}
2876:
1353:
973:(m/s or m⋅s). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object is said to be undergoing an
4806:
1736:
210:
1099:
4713:
2989:
3549:
4591:
3622:
4512:
1960:
5402:
5247:
5540:
4172:
4107:
5606:
4982:
The radial and traverse velocities can be derived from the
Cartesian velocity and displacement vectors by decomposing the velocity vector into radial and transverse components. The
4337:
4286:
5099:
5068:
48:
5218:
234:
5392:{\displaystyle v_{T}={\frac {|{\boldsymbol {r}}\times {\boldsymbol {v}}|}{|{\boldsymbol {r}}|}}={\boldsymbol {v}}\cdot {\hat {\boldsymbol {t}}}=\omega |{\boldsymbol {r}}|}
4645:
4457:
4406:
2721:{\displaystyle {\bar {v}}=n\left({1 \over v_{1}}+{1 \over v_{2}}+{1 \over v_{3}}+\dots +{1 \over v_{n}}\right)^{-1}=n\left(\sum _{i=1}^{n}{\frac {1}{v_{i}}}\right)^{-1}.}
6992:
3405:
1044:
1021:
5277:
5639:
3853:
3772:
3673:
4989:
5563:
4928:
4908:
4888:
4868:
4848:
4828:
3820:
3798:
6384:
7082:
3875:
is the minimum speed a ballistic object needs to escape from a massive body such as Earth. It represents the kinetic energy that, when added to the object's
2896:
5256:
of the unit vector in the radial direction and the velocity vector. It is also the dot product of velocity and transverse direction, or the product of the
3992:
3890:
2768:
5191:{\displaystyle v_{R}={\frac {{\boldsymbol {v}}\cdot {\boldsymbol {r}}}{\left|{\boldsymbol {r}}\right|}}={\boldsymbol {v}}\cdot {\hat {\boldsymbol {r}}}}
3679:
6351:
2836:
1313:
4720:
1049:
900:
3521:
1619:{\displaystyle \mathbf {\bar {v}} ={\frac {\Delta \mathbf {x} }{\Delta t}}={\frac {\int _{t_{0}}^{t_{1}}\mathbf {v} (t)dt}{t_{1}-t_{0}}}.}
1409:
magnitude of a velocity vector, denotes only how fast an object is moving, while velocity indicates both an object's speed and direction.
489:
4523:
3572:
1405:
are often colloquially used interchangeably to connote how fast an object is moving, in scientific terms they are different. Speed, the
6377:
4225:
In
Newtonian mechanics, the relative velocity is independent of the chosen inertial reference frame. This is not the case anymore with
1248:{\displaystyle {\boldsymbol {v}}=\lim _{{\Delta t}\to 0}{\frac {\Delta {\boldsymbol {s}}}{\Delta t}}={\frac {d{\boldsymbol {s}}}{dt}}.}
608:
53:
As a change of direction occurs while the racing cars turn on the curved track, their velocity is not constant even if their speed is.
581:
2764:
graph at that point. In other words, instantaneous acceleration is defined as the derivative of velocity with respect to time:
2735:
Although velocity is defined as the rate of change of position, it is often common to start with an expression for an object's
166:
6370:
6219:
6189:
6111:
6081:
6030:
6000:
5970:
5937:
5907:
5877:
5847:
5817:
5787:
5487:
4652:
4291:
4240:
3648:
is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. The drag force,
6277:
5650:
563:
4464:
5732:
4595:
In three-dimensional systems where there is an additional z-axis, the corresponding velocity component is defined as
3879:(which is always negative), is equal to zero. The general formula for the escape velocity of an object at a distance
893:
1916:{\displaystyle {\bar {v}}={v_{1}t_{1}+v_{2}t_{2}+v_{3}t_{3}+\dots +v_{n}t_{n} \over t_{1}+t_{2}+t_{3}+\dots +t_{n}}}
7118:
7093:
7054:
1257:
From this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time (
5645:. If forces are in the radial direction only with an inverse square dependence, as in the case of a gravitational
4600:
4412:
4361:
855:
1459:
Velocity is defined as the rate of change of position with respect to time, which may also be referred to as the
229:
3056:{\displaystyle {\boldsymbol {x}}={\frac {({\boldsymbol {u}}+{\boldsymbol {v}})}{2}}t={\boldsymbol {\bar {v}}}t.}
484:
224:
5223:
6396:
962:
5570:
5075:
5044:
4983:
886:
873:
634:
557:
479:
322:
4353:
553:
354:
4222:
Usually, the inertial frame chosen is that in which the latter of the two mentioned objects is in rest.
3632:
is the kinetic energy. Kinetic energy is a scalar quantity as it depends on the square of the velocity.
2092:{\displaystyle {\bar {v}}={v_{1}+v_{2}+v_{3}+\dots +v_{n} \over n}={\frac {1}{n}}\sum _{i=1}^{n}{v_{i}}}
1149:
of an object is the limit average velocity as the time interval approaches zero. At any particular time
332:
6249:
5471:{\displaystyle \omega ={\frac {|{\boldsymbol {r}}\times {\boldsymbol {v}}|}{|{\boldsymbol {r}}|^{2}}}.}
5201:
4943:
3969:
3510:
773:
662:
588:
448:
381:
133:
17:
4939:
2739:. As seen by the three green tangent lines in the figure, an object's instantaneous acceleration at a
7389:
7025:
6830:
6684:
527:
31:
6797:
6270:
6240:
4810:
While some textbooks use subscript notation to define
Cartesian components of velocity, others use
4097:
3823:
803:
647:
1128:
lines represent the values for acceleration at different points along the curve) and displacement
7399:
6808:
6321:
5710:
4962:
997:
954:
753:
517:
6968:
6868:
4215:{\displaystyle {\boldsymbol {v}}_{B{\text{ relative to }}A}={\boldsymbol {w}}-{\boldsymbol {v}}}
4150:{\displaystyle {\boldsymbol {v}}_{A{\text{ relative to }}B}={\boldsymbol {v}}-{\boldsymbol {w}}}
793:
6037:
3961:
3677:
3063:
It is also possible to derive an expression for the velocity independent of time, known as the
798:
615:
6088:
5944:
3990:
3517:, p, as a vector that is the product of an object's mass and velocity, given mathematically as
1311:
1026:
1003:
6943:
6813:
6551:
6196:
6118:
6007:
5914:
5884:
5824:
5794:
5262:
3570:
3519:
2766:
1487:
808:
783:
469:
287:
6226:
5977:
5854:
5614:
7265:
7190:
6818:
6590:
6245:
3876:
3860:
3831:
3757:
3651:
1428:
Since the derivative of the position with respect to time gives the change in position (in
1406:
828:
788:
696:
692:
684:
674:
464:
457:
213:
823:
8:
7394:
6996:
6725:
6673:
6393:
6263:
6049:
5667:
3489:
3064:
2886:
933:
603:
544:
522:
267:
262:
257:
157:
2162:
respectively, then the average speed of the particle over the total distance is given as
6129:
6053:
5548:
5252:
The transverse speed (or magnitude of the transverse velocity) is the magnitude of the
4913:
4893:
4873:
4853:
4833:
4813:
4515:
4226:
3981:
3805:
3783:
3493:
2831:
acceleration vs. time graph. As above, this is done using the concept of the integral:
1449:
733:
474:
349:
317:
277:
7384:
7015:
6933:
6769:
6528:
6215:
6185:
6107:
6077:
6057:
6026:
5996:
5966:
5933:
5903:
5873:
5843:
5813:
5783:
5728:
5700:
5642:
4078:
4065:
970:
943:
940:
743:
700:
657:
652:
593:
369:
359:
252:
6141:
5752:
4237:
In the one-dimensional case, the velocities are scalars and the equation is either:
1646:) graph, the instantaneous velocity (or, simply, velocity) can be thought of as the
7102:
7072:
7038:
6757:
6713:
6668:
5480:
4976:
3856:
1437:
947:
838:
818:
763:
758:
704:
679:
534:
392:
337:
312:
5805:
3463:{\displaystyle \therefore v^{2}=u^{2}+2({\boldsymbol {a}}\cdot {\boldsymbol {x}})}
7347:
7307:
6209:
6179:
6101:
6071:
6020:
5990:
5960:
5927:
5897:
5867:
5837:
5807:
5777:
5688:
4967:
3872:
1954:
1660:
coordinates equal to the boundaries of the time period for the average velocity.
925:
833:
778:
728:
723:
642:
107:
7110:
7046:
4957:, the tangential component causes visible changes of the position of the object.
2885:
In the special case of constant acceleration, velocity can be studied using the
7291:
7255:
7180:
6961:
6848:
6738:
6639:
6362:
6346:
5705:
5683:
5673:
4954:
3985:
3645:
3641:
3565:
950:
860:
768:
669:
386:
103:
7378:
7165:
7033:
6747:
5678:
5663:
5257:
5253:
5031:{\displaystyle {\boldsymbol {v}}={\boldsymbol {v}}_{T}+{\boldsymbol {v}}_{R}}
4986:
velocity is the component of velocity along a circle centered at the origin.
4971:, defined as the component of velocity away from or toward the origin, and a
2740:
2520:
1730:
966:
748:
575:
3568:
of a moving object is dependent on its velocity and is given by the equation
1112:
Example of a velocity vs. time graph, and the relationship between velocity
7240:
7226:
7126:
7062:
6787:
6570:
6481:
6341:
5812:(illustrated, reprinted ed.). Cambridge University Press. p. 84.
2736:
975:
813:
738:
427:
307:
115:
6608:
6142:"The Feynman Lectures on Physics Vol. I Ch. 9: Newton's Laws of Dynamics"
5110:
1651:
1108:
6018:
5895:
5775:
4948:
2986:, it is possible to relate the displacement and the average velocity by
6302:
6286:
1647:
1156:
929:
598:
272:
2927:{\displaystyle {\boldsymbol {v}}={\boldsymbol {u}}+{\boldsymbol {a}}t}
1309:. In the figure, this corresponds to the yellow area under the curve.
6701:
6628:
6616:
5865:
4044:{\displaystyle \gamma ={\frac {1}{\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}}
620:
5113:
of the velocity vector and the unit vector in the radial direction.
4514:. The magnitude of this vector represents speed and is found by the
3949:{\displaystyle v_{\text{e}}={\sqrt {\frac {2GM}{r}}}={\sqrt {2gr}},}
7005:
6904:
6517:
6471:
6325:
6316:
6298:
6177:
5929:
The
Calculus Lifesaver: All the Tools You Need to Excel at Calculus
5694:
4715:
with its magnitude also representing speed and being determined by
4104:
object B is defined as the difference of the two velocity vectors:
3514:
2808:{\displaystyle {\boldsymbol {a}}={\frac {d{\boldsymbol {v}}}{dt}}.}
1280:
539:
397:
4157:
Similarly, the relative velocity of object B moving with velocity
961:, being a coherent derived unit whose quantity is measured in the
7331:
5932:(illustrated ed.). Princeton University Press. p. 350.
3775:
3743:{\displaystyle F_{D}\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{D}\,A}
2748:
1125:
512:
365:
282:
7245:
7214:
7170:
7148:
6602:
6501:
6466:
5806:
Richard P. Olenick; Tom M. Apostol; David L. Goodstein (2008).
1433:
921:
571:
417:
327:
126:
30:
This article is about velocity in physics. For other uses, see
7279:
7204:
7138:
6742:
6648:
6643:
6580:
6555:
6335:
6255:
5691:(in relativity, using traveler time instead of observer time)
5646:
4229:
in which velocities depend on the choice of reference frame.
2893:
as being equal to some arbitrary constant vector, this shows
2871:{\displaystyle {\boldsymbol {v}}=\int {\boldsymbol {a}}\ dt.}
2744:
1429:
1373:
1368:
1348:{\displaystyle {\boldsymbol {s}}=\int {\boldsymbol {v}}\ dt.}
917:
407:
402:
344:
122:
4801:{\displaystyle |v|={\sqrt {v_{x}^{2}+v_{y}^{2}+v_{z}^{2}}}.}
3499:
946:: both magnitude and direction are needed to define it. The
7361:
7321:
6894:
6560:
6491:
6456:
5869:
College
Physics Essentials, Eighth Edition (Two-Volume Set)
5809:
The
Mechanical Universe: Introduction to Mechanics and Heat
3975:
1135:
412:
375:
4288:
if the two objects are moving in opposite directions, or:
205:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
3675:, is dependent on the square of velocity and is given as
1362:
1094:{\displaystyle {\bar {v}}={\frac {\Delta s}{\Delta t}}.}
5697:(a version of velocity additive at relativistic speeds)
4708:{\displaystyle {\textbf {v}}=<v_{x},v_{y},v_{z}>}
4461:
The two-dimensional velocity vector is then defined as
2818:
From there, velocity is expressed as the area under an
5753:"The Feynman Lectures on Physics Vol. I Ch. 8: Motion"
3699:
3590:
3287:
6971:
6207:
6076:(illustrated ed.). Nelson Thornes. p. 231.
6019:
David
Halliday; Robert Resnick; Jearl Walker (2010).
5896:
David
Halliday; Robert Resnick; Jearl Walker (2021).
5776:
David
Halliday; Robert Resnick; Jearl Walker (2021).
5617:
5573:
5551:
5490:
5405:
5285:
5265:
5226:
5204:
5119:
5078:
5047:
4992:
4916:
4896:
4876:
4856:
4836:
4816:
4723:
4655:
4603:
4526:
4467:
4415:
4364:
4339:
if the two objects are moving in the same direction.
4294:
4243:
4175:
4110:
3995:
3893:
3834:
3808:
3786:
3760:
3682:
3654:
3575:
3524:
3408:
3229:
3073:
2992:
2963:. By combining this equation with the suvat equation
2899:
2839:
2771:
2529:
2171:
1963:
1739:
1492:
1316:
1165:
1052:
1029:
1006:
169:
5958:
5902:(12th ed.). John Wiley & Sons. p. 70.
5835:
5782:(12th ed.). John Wiley & Sons. p. 71.
4649:
The three-dimensional velocity vector is defined as
3544:{\displaystyle {\boldsymbol {p}}=m{\boldsymbol {v}}}
1669:
When a particle moves with different uniform speeds
4975:, perpendicular to the radial one. Both arise from
1648:
slope of the tangent line to the curve at any point
1377:Kinematic quantities of a classical particle: mass
6986:
5866:Jerry D. Wilson; Anthony J. Buffa; Bo Lou (2022).
5633:
5600:
5557:
5534:
5470:
5391:
5271:
5241:
5212:
5190:
5093:
5062:
5030:
4922:
4902:
4882:
4862:
4842:
4822:
4800:
4707:
4639:
4586:{\displaystyle |v|={\sqrt {v_{x}^{2}+v_{y}^{2}}}.}
4585:
4506:
4451:
4400:
4331:
4280:
4214:
4149:
4043:
3948:
3847:
3814:
3792:
3766:
3742:
3667:
3617:{\displaystyle E_{\text{k}}={\tfrac {1}{2}}mv^{2}}
3616:
3543:
3462:
3395:
3216:
3055:
2926:
2870:
2807:
2720:
2484:
2091:
1915:
1618:
1347:
1247:
1093:
1038:
1015:
204:
6099:
4507:{\displaystyle {\textbf {v}}=<v_{x},v_{y}>}
3800:is the speed of the object relative to the fluid,
3041:
1499:
7376:
6392:
6178:E. Graham; Aidan Burrows; Brian Gaulter (2002).
5279:and the radius (the magnitude of the position).
1175:
6184:(illustrated ed.). Heinemann. p. 77.
5872:(illustrated ed.). CRC Press. p. 40.
4965:, a two-dimensional velocity is described by a
2730:
1650:, and the average velocity as the slope of the
6069:
5988:
6378:
6271:
5925:
5109:(or magnitude of the radial velocity) is the
894:
6073:New Understanding Physics for Advanced Level
5992:Classical Physics: A Two-Semester Coursebook
4163:, relative to object A moving with velocity
4940:Circular_motion § In_polar_coordinates
1733:over the total time of journey is given as
6385:
6371:
6278:
6264:
4077:Consider an object A moving with velocity
3635:
2102:When a particle moves different distances
996:of an object over a period of time is its
901:
887:
6052:, the air density can be found using the
3736:
3725:
3714:
3710:
3697:
3693:
3500:Quantities that are dependent on velocity
1482:. Average velocity can be calculated as:
1103:
1023:, divided by the duration of the period,
5727:, Wiley; 7 Sub edition (June 16, 2004).
5242:{\displaystyle {\hat {\boldsymbol {r}}}}
4947:
4347:
3976:The Lorentz factor of special relativity
2880:
1372:
1107:
6025:. John Wiley & Sons. p. 1080.
6022:Fundamentals of Physics, Chapters 33-37
5586:
5535:{\displaystyle L=mrv_{T}=mr^{2}\omega }
5446:
5429:
5421:
5380:
5359:
5349:
5333:
5316:
5308:
5230:
5206:
5179:
5169:
5155:
5145:
5137:
5081:
5050:
5018:
5003:
4994:
4208:
4200:
4178:
4143:
4135:
4113:
3537:
3526:
3488:The above equations are valid for both
3453:
3445:
3337:
3329:
3299:
3276:
3262:
3248:
3237:
3184:
3176:
3140:
3132:
3115:
3107:
3096:
3088:
3038:
3016:
3008:
2994:
2917:
2909:
2901:
2852:
2841:
2787:
2773:
1329:
1318:
1227:
1202:
1167:
928:. Velocity is a fundamental concept in
14:
7377:
5954:
5952:
5666:(relativistic version of velocity for
5601:{\displaystyle r=|{\boldsymbol {r}}|.}
4332:{\displaystyle v_{\text{rel}}=v-(+w),}
4281:{\displaystyle v_{\text{rel}}=v-(-w),}
3883:from the center of a planet with mass
1159:of the position with respect to time:
6366:
6259:
6214:. Technical Publications. p. 8.
5094:{\displaystyle {\boldsymbol {v}}_{R}}
5063:{\displaystyle {\boldsymbol {v}}_{T}}
4342:
4086:and an object B with velocity vector
2519:, then average speed is given by the
1953:, then average speed is given by the
1454:
1443:
1363:Difference between speed and velocity
936:that describes the motion of bodies.
920:in combination with the direction of
583:Newton's law of universal gravitation
4933:
4232:
4096:are typically expressed in the same
4059:
1432:) divided by the change in time (in
5949:
5842:. Universal-Publishers. p. 5.
4658:
4470:
3988:appears frequently, and is given by
3676:
987:
564:Mechanics of planar particle motion
172:
24:
5965:. Academic Publishers. p. 4.
4052:where γ is the Lorentz factor and
3989:
3867:
1521:
1511:
1310:
1208:
1198:
1180:
1079:
1071:
1030:
1007:
25:
7411:
6234:
6056:. It is 1.293 kg/m at 0 °C and 1
5899:Fundamentals of Physics, Extended
5779:Fundamentals of Physics, Extended
5723:Robert Resnick and Jearl Walker,
5651:Kepler's laws of planetary motion
5213:{\displaystyle {\boldsymbol {r}}}
4100:. Then, the velocity of object A
3569:
3559:
3518:
2765:
1634:In terms of a displacement-time (
1486:
6208:Anup Goel; H. J. Sawant (2021).
6106:. World Scientific. p. 98.
1663:
1566:
1515:
1496:
868:
867:
854:
187:
47:
6409:Linear/translational quantities
6201:
6171:
6158:
6146:www.feynmanlectures.caltech.edu
6134:
6123:
6093:
6063:
6042:
6012:
5995:. Springer Nature. p. 41.
5962:Statistical Tools and Technique
5839:Fundamental Concepts of Physics
5757:www.feynmanlectures.caltech.edu
27:Speed and direction of a motion
6285:
5982:
5919:
5889:
5859:
5829:
5799:
5769:
5745:
5591:
5581:
5452:
5441:
5434:
5416:
5385:
5375:
5362:
5338:
5328:
5321:
5303:
5233:
5182:
4733:
4725:
4536:
4528:
4323:
4314:
4272:
4263:
3877:gravitational potential energy
3457:
3441:
3341:
3325:
3313:
3272:
3266:
3255:
3241:
3230:
3188:
3172:
3147:
3128:
3122:
3103:
3020:
3004:
2536:
2178:
1970:
1746:
1576:
1570:
1187:
1155:, it can be calculated as the
1059:
13:
1:
6414:Angular/rotational quantities
6168:. The McGraw Hill Companies,.
5959:Giri & Bannerjee (2002).
5836:Michael J. Cardamone (2007).
5739:
1296:is the displacement function
982:
490:Koopman–von Neumann mechanics
6103:Modern Aspects Of Relativity
4640:{\displaystyle v_{z}=dz/dt.}
4452:{\displaystyle v_{y}=dy/dt.}
4401:{\displaystyle v_{x}=dx/dt,}
4354:Cartesian coordinate systems
2731:Relationship to acceleration
1699:in different time intervals
1271:graph) is the displacement,
1118:on the y-axis, acceleration
558:Non-inertial reference frame
7:
5656:
4953:can be observed due to the
3556:is the mass of the object.
3504:
1436:), velocity is measured in
485:Appell's equation of motion
355:Inertial frame of reference
10:
7416:
6987:{\displaystyle {\dot {m}}}
6411:
6250:Carnegie Mellon University
6246:Introduction to Mechanisms
6100:Eckehard W Mielke (2022).
5070:is the transverse velocity
4944:Radial, transverse, normal
4937:
4063:
3970:gravitational acceleration
1447:
1366:
29:
6685:specific angular momentum
6413:
6408:
6403:
6312:
6293:
6241:Velocity and Acceleration
5249:is the radial direction.
1283:of the velocity function
1279:. In calculus terms, the
1046:, given mathematically as
132:
113:
97:
58:
46:
41:
32:Velocity (disambiguation)
5717:
4098:inertial reference frame
3509:In classical mechanics,
2956:as the velocity at time
2942:as the velocity at time
1654:between two points with
1475:, over some time period
1423:
1039:{\displaystyle \Delta t}
1016:{\displaystyle \Delta s}
957:) of velocity is called
648:Rotating reference frame
480:Hamilton–Jacobi equation
6809:rotational acceleration
6070:Jim Breithaupt (2000).
5989:Bekir Karaoglu (2020).
5725:Fundamentals of Physics
5711:Velocity vs. time graph
5272:{\displaystyle \omega }
5101:is the radial velocity.
4188: relative to
4123: relative to
4056:is the speed of light.
3636:Drag (fluid resistance)
939:Velocity is a physical
589:Newton's laws of motion
449:Newton's laws of motion
6988:
5926:Adrian Banner (2007).
5635:
5634:{\displaystyle mr^{2}}
5602:
5559:
5536:
5472:
5393:
5273:
5243:
5214:
5192:
5095:
5064:
5032:
4958:
4924:
4904:
4884:
4864:
4844:
4824:
4802:
4709:
4641:
4587:
4508:
4453:
4402:
4333:
4282:
4216:
4151:
4045:
3962:gravitational constant
3950:
3849:
3816:
3794:
3768:
3744:
3669:
3618:
3545:
3464:
3397:
3218:
3057:
2928:
2872:
2809:
2722:
2683:
2486:
2093:
2076:
1917:
1620:
1461:instantaneous velocity
1394:
1349:
1249:
1139:
1104:Instantaneous velocity
1095:
1040:
1017:
616:Simple harmonic motion
529:Euler's laws of motion
323:D'Alembert's principle
206:
6989:
6211:Engineering Mechanics
6164:White, F. M. (2008).
5636:
5603:
5560:
5537:
5473:
5394:
5274:
5244:
5215:
5193:
5096:
5065:
5033:
4951:
4925:
4905:
4885:
4865:
4845:
4825:
4803:
4710:
4642:
4588:
4509:
4454:
4403:
4352:In multi-dimensional
4348:Cartesian coordinates
4334:
4283:
4217:
4152:
4046:
3951:
3850:
3848:{\displaystyle C_{D}}
3817:
3795:
3769:
3767:{\displaystyle \rho }
3745:
3670:
3668:{\displaystyle F_{D}}
3619:
3546:
3465:
3398:
3219:
3058:
2929:
2881:Constant acceleration
2873:
2810:
2723:
2663:
2487:
2094:
2056:
1918:
1621:
1376:
1350:
1250:
1111:
1096:
1041:
1018:
470:Hamiltonian mechanics
288:Statistical mechanics
207:
6969:
6819:angular acceleration
6591:angular displacement
6038:Extract of page 1080
5615:
5571:
5549:
5488:
5403:
5283:
5263:
5224:
5202:
5117:
5076:
5045:
4990:
4930:-axes respectively.
4914:
4894:
4874:
4854:
4834:
4814:
4721:
4653:
4601:
4524:
4465:
4413:
4362:
4292:
4241:
4173:
4108:
3993:
3984:, the dimensionless
3891:
3861:dimensionless number
3832:
3824:cross sectional area
3806:
3784:
3758:
3680:
3652:
3573:
3522:
3406:
3227:
3071:
2990:
2897:
2837:
2769:
2527:
2169:
1961:
1737:
1490:
1314:
1163:
1050:
1027:
1004:
693:Angular acceleration
685:Rotational frequency
465:Lagrangian mechanics
458:Analytical mechanics
214:Second law of motion
167:
6909:weighted position:
6726:rotational velocity
6674:kinematic viscosity
6394:Classical mechanics
6181:Mechanics, Volume 6
6089:Extract of page 231
5945:Extract of page 350
5668:Minkowski spacetime
4973:transverse velocity
4792:
4774:
4756:
4577:
4559:
4094:absolute velocities
3511:Newton's second law
3490:Newtonian mechanics
3065:Torricelli equation
1729:respectively, then
1564:
934:classical mechanics
545:Harmonic oscillator
523:Equations of motion
158:Classical mechanics
152:Part of a series on
6984:
6352:Higher derivatives
6197:Extract of page 77
6119:Extract of page 98
6054:barometric formula
6050:Earth's atmosphere
6008:Extract of page 41
5915:Extract of page 70
5885:Extract of page 40
5825:Extract of page 84
5795:Extract of page 71
5631:
5598:
5555:
5532:
5468:
5389:
5269:
5239:
5210:
5188:
5091:
5060:
5028:
4959:
4920:
4900:
4880:
4860:
4840:
4820:
4798:
4778:
4760:
4742:
4705:
4637:
4583:
4563:
4545:
4504:
4449:
4398:
4343:Coordinate systems
4329:
4278:
4227:special relativity
4212:
4147:
4041:
3982:special relativity
3946:
3845:
3812:
3790:
3764:
3740:
3708:
3665:
3614:
3599:
3541:
3494:special relativity
3460:
3393:
3296:
3214:
3053:
2924:
2868:
2805:
2751:to the curve of a
2718:
2482:
2089:
1913:
1616:
1536:
1450:Equation of motion
1444:Equation of motion
1395:
1345:
1245:
1194:
1140:
1091:
1036:
1013:
998:change in position
861:Physics portal
475:Routhian mechanics
350:Frame of reference
202:
117:SI base units
7372:
7371:
7367:
7366:
6981:
6934:moment of inertia
6360:
6359:
6227:Extract of page 8
6221:978-93-332-2190-0
6191:978-0-435-51311-5
6113:978-981-12-4406-3
6083:978-0-7487-4314-8
6032:978-0-470-54794-6
6002:978-3-030-38456-2
5978:Extract of page 4
5972:978-81-87504-39-9
5939:978-0-691-13088-0
5909:978-1-119-77351-1
5879:978-1-351-12991-6
5855:Extract of page 5
5849:978-1-59942-433-0
5819:978-0-521-71592-8
5789:978-1-119-77351-1
5701:Terminal velocity
5643:moment of inertia
5558:{\displaystyle m}
5463:
5365:
5343:
5236:
5185:
5163:
4963:polar coordinates
4934:Polar coordinates
4923:{\displaystyle z}
4903:{\displaystyle y}
4883:{\displaystyle x}
4863:{\displaystyle w}
4843:{\displaystyle v}
4823:{\displaystyle u}
4793:
4660:
4578:
4472:
4302:
4251:
4233:Scalar velocities
4189:
4124:
4071:Relative velocity
4066:Relative velocity
4060:Relative velocity
4039:
4038:
4036:
3941:
3925:
3924:
3901:
3815:{\displaystyle A}
3793:{\displaystyle v}
3707:
3598:
3583:
3295:
3044:
3027:
2889:. By considering
2858:
2800:
2699:
2635:
2609:
2589:
2569:
2539:
2480:
2477:
2444:
2417:
2390:
2303:
2181:
2054:
2041:
1973:
1911:
1749:
1611:
1528:
1502:
1438:metres per second
1414:constant velocity
1335:
1240:
1215:
1174:
1138:under the curve.)
1124:(the three green
1086:
1062:
971:metres per second
911:
910:
658:Centrifugal force
653:Centripetal force
609:Euler's equations
594:Relative velocity
370:Moment of inertia
200:
174:
147:
146:
84:
16:(Redirected from
7407:
7390:Motion (physics)
7359:
7355:
7343:
7339:
7319:
7315:
7303:
7299:
7277:
7273:
7263:
7253:
7238:
7234:
7224:
7202:
7198:
7188:
7178:
7163:
7159:
7146:
7122:
7116:
7108:
7097:
7091:
7080:
7073:angular momentum
7058:
7052:
7044:
7029:
7023:
7013:
7000:
6994:
6993:
6991:
6990:
6985:
6983:
6982:
6974:
6947:
6941:
6925:
6902:
6883:
6878:
6856:
6834:
6828:
6811:
6795:
6773:
6767:
6758:angular velocity
6755:
6736:
6735:
6722:
6721:
6714:rotational speed
6710:
6709:
6692:
6681:
6666:
6656:
6637:
6636:
6619:
6614:
6600:
6588:
6568:
6549:
6548:
6542:
6536:
6525:
6499:
6479:
6464:
6448:
6441:
6406:
6405:
6387:
6380:
6373:
6364:
6363:
6280:
6273:
6266:
6257:
6256:
6229:
6225:
6205:
6199:
6195:
6175:
6169:
6162:
6156:
6155:
6153:
6152:
6138:
6132:
6127:
6121:
6117:
6097:
6091:
6087:
6067:
6061:
6046:
6040:
6036:
6016:
6010:
6006:
5986:
5980:
5976:
5956:
5947:
5943:
5923:
5917:
5913:
5893:
5887:
5883:
5863:
5857:
5853:
5833:
5827:
5823:
5803:
5797:
5793:
5773:
5767:
5766:
5764:
5763:
5749:
5640:
5638:
5637:
5632:
5630:
5629:
5607:
5605:
5604:
5599:
5594:
5589:
5584:
5564:
5562:
5561:
5556:
5541:
5539:
5538:
5533:
5528:
5527:
5512:
5511:
5481:Angular momentum
5477:
5475:
5474:
5469:
5464:
5462:
5461:
5460:
5455:
5449:
5444:
5438:
5437:
5432:
5424:
5419:
5413:
5398:
5396:
5395:
5390:
5388:
5383:
5378:
5367:
5366:
5358:
5352:
5344:
5342:
5341:
5336:
5331:
5325:
5324:
5319:
5311:
5306:
5300:
5295:
5294:
5278:
5276:
5275:
5270:
5248:
5246:
5245:
5240:
5238:
5237:
5229:
5220:is position and
5219:
5217:
5216:
5211:
5209:
5197:
5195:
5194:
5189:
5187:
5186:
5178:
5172:
5164:
5162:
5158:
5149:
5148:
5140:
5134:
5129:
5128:
5100:
5098:
5097:
5092:
5090:
5089:
5084:
5069:
5067:
5066:
5061:
5059:
5058:
5053:
5037:
5035:
5034:
5029:
5027:
5026:
5021:
5012:
5011:
5006:
4997:
4977:angular velocity
4929:
4927:
4926:
4921:
4909:
4907:
4906:
4901:
4889:
4887:
4886:
4881:
4869:
4867:
4866:
4861:
4849:
4847:
4846:
4841:
4829:
4827:
4826:
4821:
4807:
4805:
4804:
4799:
4794:
4791:
4786:
4773:
4768:
4755:
4750:
4741:
4736:
4728:
4714:
4712:
4711:
4706:
4701:
4700:
4688:
4687:
4675:
4674:
4662:
4661:
4646:
4644:
4643:
4638:
4627:
4613:
4612:
4592:
4590:
4589:
4584:
4579:
4576:
4571:
4558:
4553:
4544:
4539:
4531:
4516:distance formula
4513:
4511:
4510:
4505:
4500:
4499:
4487:
4486:
4474:
4473:
4458:
4456:
4455:
4450:
4439:
4425:
4424:
4407:
4405:
4404:
4399:
4388:
4374:
4373:
4338:
4336:
4335:
4330:
4304:
4303:
4300:
4287:
4285:
4284:
4279:
4253:
4252:
4249:
4221:
4219:
4218:
4213:
4211:
4203:
4195:
4194:
4190:
4187:
4181:
4156:
4154:
4153:
4148:
4146:
4138:
4130:
4129:
4125:
4122:
4116:
4051:
4048:
4047:
4042:
4040:
4037:
4035:
4034:
4025:
4024:
4015:
4007:
4003:
3955:
3953:
3952:
3947:
3942:
3931:
3926:
3920:
3909:
3908:
3903:
3902:
3899:
3857:drag coefficient
3854:
3852:
3851:
3846:
3844:
3843:
3821:
3819:
3818:
3813:
3799:
3797:
3796:
3791:
3773:
3771:
3770:
3765:
3750:
3747:
3746:
3741:
3735:
3734:
3724:
3723:
3709:
3700:
3692:
3691:
3674:
3672:
3671:
3666:
3664:
3663:
3624:
3621:
3620:
3615:
3613:
3612:
3600:
3591:
3585:
3584:
3581:
3551:
3548:
3547:
3542:
3540:
3529:
3484:
3482:
3469:
3467:
3466:
3461:
3456:
3448:
3434:
3433:
3421:
3420:
3402:
3400:
3399:
3394:
3392:
3391:
3379:
3378:
3366:
3365:
3356:
3355:
3340:
3332:
3312:
3311:
3302:
3297:
3288:
3279:
3265:
3251:
3240:
3223:
3221:
3220:
3215:
3213:
3212:
3203:
3202:
3187:
3179:
3162:
3161:
3143:
3135:
3118:
3110:
3099:
3091:
3083:
3082:
3062:
3060:
3059:
3054:
3046:
3045:
3037:
3028:
3023:
3019:
3011:
3002:
2997:
2985:
2962:
2955:
2947:
2941:
2933:
2931:
2930:
2925:
2920:
2912:
2904:
2877:
2875:
2874:
2869:
2856:
2855:
2844:
2830:
2815:
2812:
2811:
2806:
2801:
2799:
2791:
2790:
2781:
2776:
2763:
2727:
2725:
2724:
2719:
2714:
2713:
2705:
2701:
2700:
2698:
2697:
2685:
2682:
2677:
2650:
2649:
2641:
2637:
2636:
2634:
2633:
2621:
2610:
2608:
2607:
2595:
2590:
2588:
2587:
2575:
2570:
2568:
2567:
2555:
2541:
2540:
2532:
2518:
2491:
2489:
2488:
2483:
2481:
2479:
2478:
2476:
2475:
2466:
2465:
2456:
2445:
2443:
2442:
2433:
2432:
2423:
2418:
2416:
2415:
2406:
2405:
2396:
2391:
2389:
2388:
2379:
2378:
2369:
2366:
2365:
2364:
2346:
2345:
2333:
2332:
2320:
2319:
2309:
2304:
2302:
2301:
2300:
2282:
2281:
2269:
2268:
2256:
2255:
2245:
2244:
2243:
2225:
2224:
2212:
2211:
2199:
2198:
2188:
2183:
2182:
2174:
2098:
2096:
2095:
2090:
2088:
2087:
2086:
2075:
2070:
2055:
2047:
2042:
2037:
2036:
2035:
2017:
2016:
2004:
2003:
1991:
1990:
1980:
1975:
1974:
1966:
1952:
1922:
1920:
1919:
1914:
1912:
1910:
1909:
1908:
1890:
1889:
1877:
1876:
1864:
1863:
1853:
1852:
1851:
1842:
1841:
1823:
1822:
1813:
1812:
1800:
1799:
1790:
1789:
1777:
1776:
1767:
1766:
1756:
1751:
1750:
1742:
1659:
1645:
1639:
1626:
1623:
1622:
1617:
1612:
1610:
1609:
1608:
1596:
1595:
1585:
1569:
1563:
1562:
1561:
1551:
1550:
1549:
1534:
1529:
1527:
1519:
1518:
1509:
1504:
1503:
1495:
1481:
1474:
1455:Average velocity
1397:While the terms
1355:
1352:
1351:
1346:
1333:
1332:
1321:
1308:
1295:
1278:
1270:
1264:
1254:
1252:
1251:
1246:
1241:
1239:
1231:
1230:
1221:
1216:
1214:
1206:
1205:
1196:
1193:
1186:
1170:
1154:
1100:
1098:
1097:
1092:
1087:
1085:
1077:
1069:
1064:
1063:
1055:
1045:
1043:
1042:
1037:
1022:
1020:
1019:
1014:
994:average velocity
988:Average velocity
932:, the branch of
903:
896:
889:
876:
871:
870:
863:
859:
858:
764:Johann Bernoulli
759:Daniel Bernoulli
680:Tangential speed
584:
560:
535:Fictitious force
530:
382:Mechanical power
372:
313:Angular momentum
211:
209:
208:
203:
201:
199:
191:
190:
181:
176:
175:
149:
148:
118:
93:
85:
82:
80:
74:
68:
51:
39:
38:
21:
7415:
7414:
7410:
7409:
7408:
7406:
7405:
7404:
7375:
7374:
7373:
7368:
7357:
7356:
7351:
7341:
7340:
7335:
7317:
7316:
7311:
7301:
7300:
7295:
7275:
7274:
7269:
7259:
7249:
7236:
7235:
7230:
7218:
7200:
7199:
7194:
7184:
7174:
7161:
7160:
7158:
7152:
7142:
7120:
7117:
7114:
7106:
7095:
7092:
7086:
7083:angular impulse
7076:
7056:
7053:
7050:
7042:
7027:
7024:
7019:
7009:
6998:
6995:
6973:
6972:
6970:
6967:
6966:
6965:
6945:
6942:
6937:
6910:
6903:
6898:
6881:
6879:
6872:
6857:
6852:
6832:
6829:
6822:
6812:
6807:
6796:
6791:
6771:
6768:
6761:
6751:
6737:
6729:
6724:
6717:
6712:
6705:
6700:
6693:
6688:
6683:
6677:
6667:
6662:
6652:
6638:
6632:
6627:
6615:
6612:
6607:
6601:
6594:
6584:
6569:
6564:
6554:
6544:
6538:
6532:
6527:
6521:
6500:
6495:
6480:
6475:
6465:
6460:
6444:
6437:
6399:
6391:
6361:
6356:
6308:
6289:
6284:
6237:
6232:
6222:
6206:
6202:
6192:
6176:
6172:
6166:Fluid mechanics
6163:
6159:
6150:
6148:
6140:
6139:
6135:
6130:Basic principle
6128:
6124:
6114:
6098:
6094:
6084:
6068:
6064:
6047:
6043:
6033:
6017:
6013:
6003:
5987:
5983:
5973:
5957:
5950:
5940:
5924:
5920:
5910:
5894:
5890:
5880:
5864:
5860:
5850:
5834:
5830:
5820:
5804:
5800:
5790:
5774:
5770:
5761:
5759:
5751:
5750:
5746:
5742:
5720:
5715:
5689:Proper velocity
5659:
5625:
5621:
5616:
5613:
5612:
5611:The expression
5590:
5585:
5580:
5572:
5569:
5568:
5550:
5547:
5546:
5523:
5519:
5507:
5503:
5489:
5486:
5485:
5456:
5451:
5450:
5445:
5440:
5439:
5433:
5428:
5420:
5415:
5414:
5412:
5404:
5401:
5400:
5384:
5379:
5374:
5357:
5356:
5348:
5337:
5332:
5327:
5326:
5320:
5315:
5307:
5302:
5301:
5299:
5290:
5286:
5284:
5281:
5280:
5264:
5261:
5260:
5228:
5227:
5225:
5222:
5221:
5205:
5203:
5200:
5199:
5177:
5176:
5168:
5154:
5150:
5144:
5136:
5135:
5133:
5124:
5120:
5118:
5115:
5114:
5085:
5080:
5079:
5077:
5074:
5073:
5054:
5049:
5048:
5046:
5043:
5042:
5022:
5017:
5016:
5007:
5002:
5001:
4993:
4991:
4988:
4987:
4968:radial velocity
4946:
4936:
4915:
4912:
4911:
4895:
4892:
4891:
4875:
4872:
4871:
4855:
4852:
4851:
4835:
4832:
4831:
4815:
4812:
4811:
4787:
4782:
4769:
4764:
4751:
4746:
4740:
4732:
4724:
4722:
4719:
4718:
4696:
4692:
4683:
4679:
4670:
4666:
4657:
4656:
4654:
4651:
4650:
4623:
4608:
4604:
4602:
4599:
4598:
4572:
4567:
4554:
4549:
4543:
4535:
4527:
4525:
4522:
4521:
4495:
4491:
4482:
4478:
4469:
4468:
4466:
4463:
4462:
4435:
4420:
4416:
4414:
4411:
4410:
4384:
4369:
4365:
4363:
4360:
4359:
4350:
4345:
4299:
4295:
4293:
4290:
4289:
4248:
4244:
4242:
4239:
4238:
4235:
4207:
4199:
4186:
4182:
4177:
4176:
4174:
4171:
4170:
4142:
4134:
4121:
4117:
4112:
4111:
4109:
4106:
4105:
4068:
4062:
4030:
4026:
4020:
4016:
4014:
4002:
3994:
3991:
3978:
3930:
3910:
3907:
3898:
3894:
3892:
3889:
3888:
3873:Escape velocity
3870:
3868:Escape velocity
3839:
3835:
3833:
3830:
3829:
3807:
3804:
3803:
3785:
3782:
3781:
3759:
3756:
3755:
3730:
3726:
3719:
3715:
3698:
3687:
3683:
3681:
3678:
3659:
3655:
3653:
3650:
3649:
3638:
3631:
3608:
3604:
3589:
3580:
3576:
3574:
3571:
3562:
3536:
3525:
3523:
3520:
3507:
3502:
3476:
3471:
3452:
3444:
3429:
3425:
3416:
3412:
3407:
3404:
3403:
3387:
3383:
3374:
3370:
3361:
3357:
3351:
3347:
3336:
3328:
3307:
3303:
3298:
3286:
3275:
3261:
3247:
3236:
3228:
3225:
3224:
3208:
3204:
3198:
3194:
3183:
3175:
3157:
3153:
3139:
3131:
3114:
3106:
3095:
3087:
3078:
3074:
3072:
3069:
3068:
3036:
3035:
3015:
3007:
3003:
3001:
2993:
2991:
2988:
2987:
2964:
2957:
2949:
2943:
2935:
2916:
2908:
2900:
2898:
2895:
2894:
2887:suvat equations
2883:
2851:
2840:
2838:
2835:
2834:
2819:
2792:
2786:
2782:
2780:
2772:
2770:
2767:
2752:
2733:
2706:
2693:
2689:
2684:
2678:
2667:
2662:
2658:
2657:
2642:
2629:
2625:
2620:
2603:
2599:
2594:
2583:
2579:
2574:
2563:
2559:
2554:
2553:
2549:
2548:
2531:
2530:
2528:
2525:
2524:
2513:
2506:
2499:
2493:
2471:
2467:
2461:
2457:
2455:
2438:
2434:
2428:
2424:
2422:
2411:
2407:
2401:
2397:
2395:
2384:
2380:
2374:
2370:
2368:
2367:
2360:
2356:
2341:
2337:
2328:
2324:
2315:
2311:
2310:
2308:
2296:
2292:
2277:
2273:
2264:
2260:
2251:
2247:
2246:
2239:
2235:
2220:
2216:
2207:
2203:
2194:
2190:
2189:
2187:
2173:
2172:
2170:
2167:
2166:
2161:
2152:
2145:
2138:
2131:
2122:
2115:
2108:
2082:
2078:
2077:
2071:
2060:
2046:
2031:
2027:
2012:
2008:
1999:
1995:
1986:
1982:
1981:
1979:
1965:
1964:
1962:
1959:
1958:
1955:arithmetic mean
1947:
1940:
1933:
1927:
1904:
1900:
1885:
1881:
1872:
1868:
1859:
1855:
1854:
1847:
1843:
1837:
1833:
1818:
1814:
1808:
1804:
1795:
1791:
1785:
1781:
1772:
1768:
1762:
1758:
1757:
1755:
1741:
1740:
1738:
1735:
1734:
1728:
1719:
1712:
1705:
1698:
1689:
1682:
1675:
1666:
1655:
1641:
1635:
1604:
1600:
1591:
1587:
1586:
1565:
1557:
1553:
1552:
1545:
1541:
1540:
1535:
1533:
1520:
1514:
1510:
1508:
1494:
1493:
1491:
1488:
1476:
1465:
1457:
1452:
1446:
1426:
1389:, acceleration
1371:
1365:
1328:
1317:
1315:
1312:
1297:
1284:
1272:
1266:
1258:
1232:
1226:
1222:
1220:
1207:
1201:
1197:
1195:
1179:
1178:
1166:
1164:
1161:
1160:
1150:
1106:
1078:
1070:
1068:
1054:
1053:
1051:
1048:
1047:
1028:
1025:
1024:
1005:
1002:
1001:
990:
985:
907:
866:
853:
852:
845:
844:
843:
718:
710:
709:
689:
643:Circular motion
637:
627:
626:
625:
582:
552:
549:
528:
507:
499:
498:
495:
494:
452:
442:
434:
433:
432:
391:
387:Mechanical work
380:
364:
302:
294:
293:
292:
247:
239:
216:
192:
186:
182:
180:
171:
170:
168:
165:
164:
116:
100:
87:
81:
76:
70:
64:
61:
54:
35:
28:
23:
22:
15:
12:
11:
5:
7413:
7403:
7402:
7400:Temporal rates
7397:
7392:
7387:
7370:
7369:
7365:
7364:
7345:
7329:
7327:
7324:
7305:
7289:
7287:
7283:
7282:
7243:
7212:
7210:
7207:
7168:
7156:
7136:
7134:
7130:
7129:
7100:
7070:
7068:
7065:
7036:
7003:
6980:
6977:
6962:Mass flow rate
6959:
6955:
6954:
6952:
6950:
6931:
6928:
6926:
6907:
6892:
6888:
6887:
6885:
6866:
6864:
6861:
6859:
6846:
6844:
6840:
6839:
6837:
6816:
6805:
6802:
6800:
6785:
6783:
6779:
6778:
6776:
6745:
6698:
6695:
6671:
6646:
6625:
6621:
6620:
6605:
6578:
6576:
6573:
6558:
6515:
6513:
6509:
6508:
6506:
6504:
6489:
6486:
6484:
6469:
6454:
6450:
6449:
6442:
6435:
6432:
6429:
6426:
6423:
6420:
6416:
6415:
6412:
6410:
6404:
6401:
6400:
6390:
6389:
6382:
6375:
6367:
6358:
6357:
6355:
6354:
6349:
6344:
6339:
6329:
6319:
6313:
6310:
6309:
6307:
6306:
6294:
6291:
6290:
6283:
6282:
6275:
6268:
6260:
6254:
6253:
6243:
6236:
6235:External links
6233:
6231:
6230:
6220:
6200:
6190:
6170:
6157:
6133:
6122:
6112:
6092:
6082:
6062:
6041:
6031:
6011:
6001:
5981:
5971:
5948:
5938:
5918:
5908:
5888:
5878:
5858:
5848:
5828:
5818:
5798:
5788:
5768:
5743:
5741:
5738:
5737:
5736:
5719:
5716:
5714:
5713:
5708:
5706:Velocity field
5703:
5698:
5692:
5686:
5684:Phase velocity
5681:
5676:
5674:Group velocity
5671:
5660:
5658:
5655:
5628:
5624:
5620:
5609:
5608:
5597:
5593:
5588:
5583:
5579:
5576:
5566:
5554:
5531:
5526:
5522:
5518:
5515:
5510:
5506:
5502:
5499:
5496:
5493:
5467:
5459:
5454:
5448:
5443:
5436:
5431:
5427:
5423:
5418:
5411:
5408:
5387:
5382:
5377:
5373:
5370:
5364:
5361:
5355:
5351:
5347:
5340:
5335:
5330:
5323:
5318:
5314:
5310:
5305:
5298:
5293:
5289:
5268:
5235:
5232:
5208:
5184:
5181:
5175:
5171:
5167:
5161:
5157:
5153:
5147:
5143:
5139:
5132:
5127:
5123:
5103:
5102:
5088:
5083:
5071:
5057:
5052:
5025:
5020:
5015:
5010:
5005:
5000:
4996:
4955:Doppler effect
4935:
4932:
4919:
4899:
4879:
4859:
4839:
4819:
4797:
4790:
4785:
4781:
4777:
4772:
4767:
4763:
4759:
4754:
4749:
4745:
4739:
4735:
4731:
4727:
4704:
4699:
4695:
4691:
4686:
4682:
4678:
4673:
4669:
4665:
4636:
4633:
4630:
4626:
4622:
4619:
4616:
4611:
4607:
4582:
4575:
4570:
4566:
4562:
4557:
4552:
4548:
4542:
4538:
4534:
4530:
4503:
4498:
4494:
4490:
4485:
4481:
4477:
4448:
4445:
4442:
4438:
4434:
4431:
4428:
4423:
4419:
4397:
4394:
4391:
4387:
4383:
4380:
4377:
4372:
4368:
4349:
4346:
4344:
4341:
4328:
4325:
4322:
4319:
4316:
4313:
4310:
4307:
4298:
4277:
4274:
4271:
4268:
4265:
4262:
4259:
4256:
4247:
4234:
4231:
4210:
4206:
4202:
4198:
4193:
4185:
4180:
4145:
4141:
4137:
4133:
4128:
4120:
4115:
4103:
4064:Main article:
4061:
4058:
4033:
4029:
4023:
4019:
4013:
4010:
4006:
4001:
3998:
3986:Lorentz factor
3977:
3974:
3945:
3940:
3937:
3934:
3929:
3923:
3919:
3916:
3913:
3906:
3897:
3869:
3866:
3865:
3864:
3842:
3838:
3827:
3811:
3801:
3789:
3779:
3763:
3739:
3733:
3729:
3722:
3718:
3713:
3706:
3703:
3696:
3690:
3686:
3662:
3658:
3642:fluid dynamics
3637:
3634:
3629:
3611:
3607:
3603:
3597:
3594:
3588:
3579:
3566:kinetic energy
3561:
3560:Kinetic energy
3558:
3539:
3535:
3532:
3528:
3506:
3503:
3501:
3498:
3459:
3455:
3451:
3447:
3443:
3440:
3437:
3432:
3428:
3424:
3419:
3415:
3411:
3390:
3386:
3382:
3377:
3373:
3369:
3364:
3360:
3354:
3350:
3346:
3343:
3339:
3335:
3331:
3327:
3324:
3321:
3318:
3315:
3310:
3306:
3301:
3294:
3291:
3285:
3282:
3278:
3274:
3271:
3268:
3264:
3260:
3257:
3254:
3250:
3246:
3243:
3239:
3235:
3232:
3211:
3207:
3201:
3197:
3193:
3190:
3186:
3182:
3178:
3174:
3171:
3168:
3165:
3160:
3156:
3152:
3149:
3146:
3142:
3138:
3134:
3130:
3127:
3124:
3121:
3117:
3113:
3109:
3105:
3102:
3098:
3094:
3090:
3086:
3081:
3077:
3067:, as follows:
3052:
3049:
3043:
3040:
3034:
3031:
3026:
3022:
3018:
3014:
3010:
3006:
3000:
2996:
2923:
2919:
2915:
2911:
2907:
2903:
2882:
2879:
2867:
2864:
2861:
2854:
2850:
2847:
2843:
2804:
2798:
2795:
2789:
2785:
2779:
2775:
2732:
2729:
2717:
2712:
2709:
2704:
2696:
2692:
2688:
2681:
2676:
2673:
2670:
2666:
2661:
2656:
2653:
2648:
2645:
2640:
2632:
2628:
2624:
2619:
2616:
2613:
2606:
2602:
2598:
2593:
2586:
2582:
2578:
2573:
2566:
2562:
2558:
2552:
2547:
2544:
2538:
2535:
2523:of the speeds
2511:
2504:
2497:
2474:
2470:
2464:
2460:
2454:
2451:
2448:
2441:
2437:
2431:
2427:
2421:
2414:
2410:
2404:
2400:
2394:
2387:
2383:
2377:
2373:
2363:
2359:
2355:
2352:
2349:
2344:
2340:
2336:
2331:
2327:
2323:
2318:
2314:
2307:
2299:
2295:
2291:
2288:
2285:
2280:
2276:
2272:
2267:
2263:
2259:
2254:
2250:
2242:
2238:
2234:
2231:
2228:
2223:
2219:
2215:
2210:
2206:
2202:
2197:
2193:
2186:
2180:
2177:
2164:
2163:
2157:
2150:
2143:
2136:
2127:
2120:
2113:
2106:
2085:
2081:
2074:
2069:
2066:
2063:
2059:
2053:
2050:
2045:
2040:
2034:
2030:
2026:
2023:
2020:
2015:
2011:
2007:
2002:
1998:
1994:
1989:
1985:
1978:
1972:
1969:
1957:of the speeds
1945:
1938:
1931:
1924:
1923:
1907:
1903:
1899:
1896:
1893:
1888:
1884:
1880:
1875:
1871:
1867:
1862:
1858:
1850:
1846:
1840:
1836:
1832:
1829:
1826:
1821:
1817:
1811:
1807:
1803:
1798:
1794:
1788:
1784:
1780:
1775:
1771:
1765:
1761:
1754:
1748:
1745:
1724:
1717:
1710:
1703:
1694:
1687:
1680:
1673:
1665:
1662:
1628:
1627:
1615:
1607:
1603:
1599:
1594:
1590:
1584:
1581:
1578:
1575:
1572:
1568:
1560:
1556:
1548:
1544:
1539:
1532:
1526:
1523:
1517:
1513:
1507:
1501:
1498:
1456:
1453:
1448:Main article:
1445:
1442:
1425:
1422:
1367:Main article:
1364:
1361:
1344:
1341:
1338:
1331:
1327:
1324:
1320:
1244:
1238:
1235:
1229:
1225:
1219:
1213:
1210:
1204:
1200:
1192:
1189:
1185:
1182:
1177:
1173:
1169:
1105:
1102:
1090:
1084:
1081:
1076:
1073:
1067:
1061:
1058:
1035:
1032:
1012:
1009:
989:
986:
984:
981:
960:
951:absolute value
909:
908:
906:
905:
898:
891:
883:
880:
879:
878:
877:
864:
847:
846:
842:
841:
836:
831:
826:
821:
816:
811:
806:
801:
796:
791:
786:
781:
776:
771:
766:
761:
756:
751:
746:
741:
736:
731:
726:
720:
719:
716:
715:
712:
711:
708:
707:
688:
687:
682:
677:
672:
670:Coriolis force
667:
666:
665:
655:
650:
645:
639:
638:
633:
632:
629:
628:
624:
623:
618:
613:
612:
611:
606:
596:
591:
586:
579:
568:
567:
566:
561:
548:
547:
542:
537:
532:
525:
520:
515:
509:
508:
505:
504:
501:
500:
497:
496:
493:
492:
487:
482:
477:
472:
467:
461:
455:
453:
446:
443:
440:
439:
436:
435:
431:
430:
425:
420:
415:
410:
405:
400:
395:
389:
384:
378:
373:
362:
357:
352:
347:
342:
341:
340:
335:
325:
320:
315:
310:
304:
303:
300:
299:
296:
295:
291:
290:
285:
280:
275:
270:
265:
260:
255:
249:
248:
245:
244:
241:
240:
238:
237:
232:
227:
221:
218:
217:
212:
198:
195:
189:
185:
179:
161:
160:
154:
153:
145:
144:
136:
130:
129:
120:
111:
110:
101:
98:
95:
94:
62:
60:Common symbols
59:
56:
55:
52:
44:
43:
26:
9:
6:
4:
3:
2:
7412:
7401:
7398:
7396:
7393:
7391:
7388:
7386:
7383:
7382:
7380:
7363:
7354:
7349:
7346:
7338:
7333:
7330:
7328:
7325:
7323:
7314:
7309:
7306:
7298:
7293:
7290:
7288:
7285:
7284:
7281:
7272:
7267:
7262:
7257:
7252:
7247:
7244:
7242:
7233:
7228:
7223:
7222:
7216:
7213:
7211:
7208:
7206:
7197:
7192:
7187:
7182:
7177:
7172:
7169:
7167:
7155:
7150:
7145:
7140:
7137:
7135:
7132:
7131:
7128:
7124:
7112:
7104:
7101:
7099:
7090:
7084:
7079:
7074:
7071:
7069:
7066:
7064:
7060:
7048:
7040:
7037:
7035:
7031:
7022:
7017:
7012:
7007:
7004:
7002:
6978:
6975:
6963:
6960:
6957:
6956:
6953:
6951:
6949:
6940:
6935:
6932:
6929:
6927:
6924:
6921:
6917:
6913:
6908:
6906:
6901:
6896:
6893:
6890:
6889:
6886:
6877:
6876:
6870:
6867:
6865:
6862:
6860:
6855:
6850:
6847:
6845:
6842:
6841:
6838:
6836:
6827:
6826:
6820:
6817:
6815:
6810:
6806:
6803:
6801:
6799:
6794:
6789:
6786:
6784:
6781:
6780:
6777:
6775:
6766:
6765:
6759:
6754:
6749:
6748:angular speed
6746:
6744:
6740:
6734:
6733:
6727:
6720:
6715:
6708:
6703:
6699:
6696:
6691:
6686:
6680:
6675:
6672:
6670:
6665:
6660:
6655:
6650:
6647:
6645:
6641:
6635:
6630:
6626:
6623:
6622:
6618:
6610:
6606:
6604:
6599:
6598:
6592:
6587:
6582:
6579:
6577:
6574:
6572:
6567:
6562:
6559:
6557:
6553:
6547:
6541:
6535:
6530:
6524:
6519:
6516:
6514:
6511:
6510:
6507:
6505:
6503:
6498:
6493:
6490:
6487:
6485:
6483:
6478:
6473:
6470:
6468:
6463:
6458:
6455:
6452:
6451:
6447:
6443:
6440:
6436:
6433:
6430:
6427:
6424:
6421:
6418:
6417:
6407:
6402:
6398:
6395:
6388:
6383:
6381:
6376:
6374:
6369:
6368:
6365:
6353:
6350:
6348:
6345:
6343:
6340:
6337:
6333:
6330:
6327:
6323:
6320:
6318:
6315:
6314:
6311:
6304:
6303:Differentiate
6300:
6296:
6295:
6292:
6288:
6281:
6276:
6274:
6269:
6267:
6262:
6261:
6258:
6251:
6247:
6244:
6242:
6239:
6238:
6228:
6223:
6217:
6213:
6212:
6204:
6198:
6193:
6187:
6183:
6182:
6174:
6167:
6161:
6147:
6143:
6137:
6131:
6126:
6120:
6115:
6109:
6105:
6104:
6096:
6090:
6085:
6079:
6075:
6074:
6066:
6059:
6055:
6051:
6045:
6039:
6034:
6028:
6024:
6023:
6015:
6009:
6004:
5998:
5994:
5993:
5985:
5979:
5974:
5968:
5964:
5963:
5955:
5953:
5946:
5941:
5935:
5931:
5930:
5922:
5916:
5911:
5905:
5901:
5900:
5892:
5886:
5881:
5875:
5871:
5870:
5862:
5856:
5851:
5845:
5841:
5840:
5832:
5826:
5821:
5815:
5811:
5810:
5802:
5796:
5791:
5785:
5781:
5780:
5772:
5758:
5754:
5748:
5744:
5734:
5733:0-471-23231-9
5730:
5726:
5722:
5721:
5712:
5709:
5707:
5704:
5702:
5699:
5696:
5693:
5690:
5687:
5685:
5682:
5680:
5679:Hypervelocity
5677:
5675:
5672:
5669:
5665:
5664:Four-velocity
5662:
5661:
5654:
5652:
5648:
5644:
5626:
5622:
5618:
5595:
5577:
5574:
5567:
5552:
5545:
5544:
5543:
5529:
5524:
5520:
5516:
5513:
5508:
5504:
5500:
5497:
5494:
5491:
5482:
5478:
5465:
5457:
5425:
5409:
5406:
5371:
5368:
5353:
5345:
5312:
5296:
5291:
5287:
5266:
5259:
5258:angular speed
5255:
5254:cross product
5250:
5173:
5165:
5159:
5151:
5141:
5130:
5125:
5121:
5112:
5108:
5086:
5072:
5055:
5041:
5040:
5039:
5023:
5013:
5008:
4998:
4985:
4980:
4978:
4974:
4970:
4969:
4964:
4956:
4950:
4945:
4941:
4931:
4917:
4897:
4877:
4857:
4837:
4817:
4808:
4795:
4788:
4783:
4779:
4775:
4770:
4765:
4761:
4757:
4752:
4747:
4743:
4737:
4729:
4716:
4702:
4697:
4693:
4689:
4684:
4680:
4676:
4671:
4667:
4663:
4647:
4634:
4631:
4628:
4624:
4620:
4617:
4614:
4609:
4605:
4596:
4593:
4580:
4573:
4568:
4564:
4560:
4555:
4550:
4546:
4540:
4532:
4519:
4517:
4501:
4496:
4492:
4488:
4483:
4479:
4475:
4459:
4446:
4443:
4440:
4436:
4432:
4429:
4426:
4421:
4417:
4408:
4395:
4392:
4389:
4385:
4381:
4378:
4375:
4370:
4366:
4357:
4355:
4340:
4326:
4320:
4317:
4311:
4308:
4305:
4296:
4275:
4269:
4266:
4260:
4257:
4254:
4245:
4230:
4228:
4223:
4204:
4196:
4191:
4183:
4168:
4167:
4162:
4161:
4139:
4131:
4126:
4118:
4101:
4099:
4095:
4091:
4090:
4085:
4084:
4080:
4075:
4072:
4067:
4057:
4055:
4050:
4031:
4027:
4021:
4017:
4011:
4008:
4004:
3999:
3996:
3987:
3983:
3973:
3971:
3967:
3963:
3959:
3943:
3938:
3935:
3932:
3927:
3921:
3917:
3914:
3911:
3904:
3895:
3886:
3882:
3878:
3874:
3862:
3858:
3840:
3836:
3828:
3825:
3809:
3802:
3787:
3780:
3778:of the fluid,
3777:
3761:
3754:
3753:
3752:
3749:
3737:
3731:
3727:
3720:
3716:
3711:
3704:
3701:
3694:
3688:
3684:
3660:
3656:
3647:
3643:
3633:
3628:
3623:
3609:
3605:
3601:
3595:
3592:
3586:
3577:
3567:
3557:
3555:
3550:
3533:
3530:
3516:
3512:
3497:
3495:
3491:
3486:
3481:
3480:
3474:
3449:
3438:
3435:
3430:
3426:
3422:
3417:
3413:
3409:
3388:
3384:
3380:
3375:
3371:
3367:
3362:
3358:
3352:
3348:
3344:
3333:
3322:
3319:
3316:
3308:
3304:
3292:
3289:
3283:
3280:
3269:
3258:
3252:
3244:
3233:
3209:
3205:
3199:
3195:
3191:
3180:
3169:
3166:
3163:
3158:
3154:
3150:
3144:
3136:
3125:
3119:
3111:
3100:
3092:
3084:
3079:
3075:
3066:
3050:
3047:
3032:
3029:
3024:
3012:
2998:
2983:
2981:
2976:
2974:
2969:
2968:
2960:
2954:
2953:
2946:
2940:
2939:
2921:
2913:
2905:
2892:
2888:
2878:
2865:
2862:
2859:
2848:
2845:
2832:
2828:
2824:
2823:
2816:
2814:
2802:
2796:
2793:
2783:
2777:
2761:
2757:
2756:
2750:
2746:
2742:
2741:point in time
2738:
2728:
2715:
2710:
2707:
2702:
2694:
2690:
2686:
2679:
2674:
2671:
2668:
2664:
2659:
2654:
2651:
2646:
2643:
2638:
2630:
2626:
2622:
2617:
2614:
2611:
2604:
2600:
2596:
2591:
2584:
2580:
2576:
2571:
2564:
2560:
2556:
2550:
2545:
2542:
2533:
2522:
2521:harmonic mean
2517:
2510:
2503:
2496:
2472:
2468:
2462:
2458:
2452:
2449:
2446:
2439:
2435:
2429:
2425:
2419:
2412:
2408:
2402:
2398:
2392:
2385:
2381:
2375:
2371:
2361:
2357:
2353:
2350:
2347:
2342:
2338:
2334:
2329:
2325:
2321:
2316:
2312:
2305:
2297:
2293:
2289:
2286:
2283:
2278:
2274:
2270:
2265:
2261:
2257:
2252:
2248:
2240:
2236:
2232:
2229:
2226:
2221:
2217:
2213:
2208:
2204:
2200:
2195:
2191:
2184:
2175:
2160:
2156:
2149:
2142:
2135:
2132:with speeds
2130:
2126:
2119:
2112:
2105:
2101:
2100:
2099:
2083:
2079:
2072:
2067:
2064:
2061:
2057:
2051:
2048:
2043:
2038:
2032:
2028:
2024:
2021:
2018:
2013:
2009:
2005:
2000:
1996:
1992:
1987:
1983:
1976:
1967:
1956:
1951:
1944:
1937:
1930:
1905:
1901:
1897:
1894:
1891:
1886:
1882:
1878:
1873:
1869:
1865:
1860:
1856:
1848:
1844:
1838:
1834:
1830:
1827:
1824:
1819:
1815:
1809:
1805:
1801:
1796:
1792:
1786:
1782:
1778:
1773:
1769:
1763:
1759:
1752:
1743:
1732:
1731:average speed
1727:
1723:
1716:
1709:
1702:
1697:
1693:
1686:
1679:
1672:
1668:
1667:
1664:Special cases
1661:
1658:
1653:
1649:
1644:
1638:
1632:
1625:
1613:
1605:
1601:
1597:
1592:
1588:
1582:
1579:
1573:
1558:
1554:
1546:
1542:
1537:
1530:
1524:
1505:
1485:
1484:
1483:
1480:
1472:
1468:
1462:
1451:
1441:
1439:
1435:
1431:
1421:
1417:
1415:
1410:
1408:
1404:
1400:
1392:
1388:
1384:
1380:
1375:
1370:
1360:
1356:
1354:
1342:
1339:
1336:
1325:
1322:
1306:
1302:
1301:
1293:
1289:
1288:
1282:
1277:
1276:
1269:
1263:
1262:
1255:
1242:
1236:
1233:
1223:
1217:
1211:
1190:
1183:
1171:
1158:
1153:
1148:
1145:
1144:instantaneous
1137:
1133:
1132:
1127:
1123:
1122:
1117:
1116:
1110:
1101:
1088:
1082:
1074:
1065:
1056:
1033:
1010:
999:
995:
980:
978:
977:
972:
968:
967:metric system
964:
958:
956:
952:
949:
945:
942:
937:
935:
931:
927:
923:
919:
915:
904:
899:
897:
892:
890:
885:
884:
882:
881:
875:
865:
862:
857:
851:
850:
849:
848:
840:
837:
835:
832:
830:
827:
825:
822:
820:
817:
815:
812:
810:
807:
805:
802:
800:
797:
795:
792:
790:
787:
785:
782:
780:
777:
775:
772:
770:
767:
765:
762:
760:
757:
755:
752:
750:
747:
745:
742:
740:
737:
735:
732:
730:
727:
725:
722:
721:
714:
713:
706:
702:
698:
694:
691:
690:
686:
683:
681:
678:
676:
673:
671:
668:
664:
661:
660:
659:
656:
654:
651:
649:
646:
644:
641:
640:
636:
631:
630:
622:
619:
617:
614:
610:
607:
605:
602:
601:
600:
597:
595:
592:
590:
587:
585:
580:
577:
573:
570:
569:
565:
562:
559:
555:
551:
550:
546:
543:
541:
538:
536:
533:
531:
526:
524:
521:
519:
516:
514:
511:
510:
503:
502:
491:
488:
486:
483:
481:
478:
476:
473:
471:
468:
466:
463:
462:
460:
459:
454:
451:
450:
445:
444:
438:
437:
429:
426:
424:
421:
419:
416:
414:
411:
409:
406:
404:
401:
399:
396:
394:
390:
388:
385:
383:
379:
377:
374:
371:
367:
363:
361:
358:
356:
353:
351:
348:
346:
343:
339:
336:
334:
331:
330:
329:
326:
324:
321:
319:
316:
314:
311:
309:
306:
305:
298:
297:
289:
286:
284:
281:
279:
276:
274:
271:
269:
266:
264:
261:
259:
256:
254:
251:
250:
243:
242:
236:
233:
231:
228:
226:
223:
222:
220:
219:
215:
196:
193:
183:
177:
163:
162:
159:
156:
155:
151:
150:
143:
140:
137:
135:
131:
128:
124:
121:
119:
112:
109:
105:
102:
96:
92:
91:
79:
73:
67:
63:
57:
50:
45:
40:
37:
33:
19:
7352:
7336:
7312:
7296:
7270:
7260:
7250:
7231:
7220:
7219:
7195:
7185:
7175:
7153:
7143:
7088:
7077:
7020:
7010:
6938:
6922:
6919:
6915:
6911:
6899:
6874:
6873:
6869:angular jerk
6853:
6824:
6823:
6792:
6788:acceleration
6763:
6762:
6752:
6731:
6730:
6718:
6706:
6689:
6678:
6663:
6658:
6653:
6633:
6596:
6595:
6585:
6565:
6552:displacement
6545:
6539:
6533:
6522:
6496:
6476:
6461:
6445:
6438:
6342:Acceleration
6331:
6322:Displacement
6210:
6203:
6180:
6173:
6165:
6160:
6149:. Retrieved
6145:
6136:
6125:
6102:
6095:
6072:
6065:
6044:
6021:
6014:
5991:
5984:
5961:
5928:
5921:
5898:
5891:
5868:
5861:
5838:
5831:
5808:
5801:
5778:
5771:
5760:. Retrieved
5756:
5747:
5724:
5641:is known as
5610:
5479:
5251:
5107:radial speed
5106:
5104:
4981:
4972:
4966:
4960:
4809:
4717:
4648:
4597:
4594:
4520:
4460:
4409:
4358:
4351:
4236:
4224:
4165:
4164:
4159:
4158:
4093:
4088:
4087:
4082:
4081:
4076:
4070:
4069:
4053:
3979:
3965:
3957:
3884:
3880:
3871:
3639:
3626:
3563:
3553:
3508:
3487:
3478:
3477:
3472:
2979:
2978:
2972:
2971:
2966:
2965:
2958:
2951:
2950:
2944:
2937:
2936:
2890:
2884:
2833:
2826:
2821:
2820:
2817:
2759:
2754:
2753:
2749:line tangent
2737:acceleration
2734:
2515:
2508:
2501:
2494:
2165:
2158:
2154:
2147:
2140:
2133:
2128:
2124:
2117:
2110:
2103:
1949:
1942:
1935:
1928:
1925:
1725:
1721:
1714:
1707:
1700:
1695:
1691:
1684:
1677:
1670:
1656:
1642:
1636:
1633:
1629:
1478:
1470:
1466:
1460:
1458:
1427:
1418:
1413:
1411:
1402:
1398:
1396:
1390:
1386:
1382:
1378:
1357:
1304:
1299:
1298:
1291:
1286:
1285:
1274:
1273:
1267:
1260:
1259:
1256:
1151:
1146:
1143:
1141:
1134:(the yellow
1130:
1129:
1120:
1119:
1114:
1113:
993:
991:
976:acceleration
974:
938:
913:
912:
703: /
699: /
697:displacement
695: /
556: /
518:Displacement
456:
447:
441:Formulations
428:Virtual work
422:
368: /
308:Acceleration
301:Fundamentals
141:
138:
89:
88:
77:
71:
65:
36:
6609:solid angle
5111:dot product
4102:relative to
1652:secant line
1385:, velocity
1381:, position
839:von Neumann
506:Core topics
99:Other units
7395:Kinematics
7379:Categories
7344:m s, N m s
7320:m s,
7266:Lagrangian
7191:Lagrangian
6431:Dimensions
6419:Dimensions
6287:Kinematics
6151:2024-01-04
6058:atmosphere
5762:2024-01-05
5740:References
5399:such that
4984:transverse
4938:See also:
1412:To have a
1157:derivative
983:Definition
930:kinematics
774:d'Alembert
754:Maupertuis
717:Scientists
599:Rigid body
273:Kinematics
18:Velocities
7360:ms,
6979:˙
6702:frequency
6629:frequency
6299:Integrate
5530:ω
5426:×
5407:ω
5372:ω
5363:^
5354:⋅
5313:×
5267:ω
5234:^
5183:^
5174:⋅
5142:⋅
4312:−
4267:−
4261:−
4205:−
4140:−
4012:−
3997:γ
3762:ρ
3712:ρ
3450:⋅
3410:∴
3381:−
3334:⋅
3270:⋅
3245:⋅
3181:⋅
3126:⋅
3093:⋅
3042:¯
2849:∫
2708:−
2665:∑
2644:−
2615:⋯
2537:¯
2450:⋯
2351:⋯
2287:⋯
2230:⋯
2179:¯
2058:∑
2022:⋯
1971:¯
1895:⋯
1828:⋯
1747:¯
1598:−
1538:∫
1522:Δ
1512:Δ
1500:¯
1326:∫
1209:Δ
1199:Δ
1188:→
1181:Δ
1080:Δ
1072:Δ
1060:¯
1031:Δ
1008:Δ
955:magnitude
819:Liouville
701:frequency
621:Vibration
338:potential
263:Continuum
258:Celestial
235:Textbooks
134:Dimension
7385:Velocity
7304:m s, N s
7127:J s
7123:m s
7098:m s
7059:m s
7030:m s
7006:momentum
6659:velocity
6529:position
6518:distance
6472:absement
6397:SI units
6332:Velocity
6326:Distance
6317:Absement
5695:Rapidity
5657:See also
4870:for the
4092:; these
3515:momentum
3513:defines
3505:Momentum
3475:= |
2514:= ... =
1948:= ... =
1403:velocity
1281:integral
1147:velocity
944:quantity
914:Velocity
874:Category
799:Hamilton
784:Lagrange
779:Clairaut
744:Horrocks
705:velocity
675:Pendulum
663:reactive
635:Rotation
604:dynamics
554:Inertial
540:Friction
423:Velocity
398:Momentum
278:Kinetics
268:Dynamics
246:Branches
230:Timeline
42:Velocity
7332:rotatum
7111:actergy
7047:actergy
7016:impulse
6936::
6687::
6617:rad, sr
5565:is mass
4910:-, and
3968:is the
3960:is the
3855:is the
3822:is the
3776:density
3774:is the
2747:of the
2743:is the
1720:, ...,
1690:, ...,
1440:(m/s).
1434:seconds
1126:tangent
916:is the
834:Koopman
794:Poisson
789:Laplace
734:Huygens
729:Galileo
574: (
513:Damping
366:Inertia
360:Impulse
333:kinetic
283:Statics
253:Applied
225:History
7246:energy
7227:moment
7215:torque
7171:energy
7149:weight
7121:
7103:action
7096:
7057:
7039:action
7028:
6999:
6946:
6918:⟩ = ∑
6882:
6833:
6772:
6218:
6188:
6110:
6080:
6029:
5999:
5969:
5936:
5906:
5876:
5846:
5816:
5786:
5731:
5542:where
5198:where
5038:where
4942:; and
4850:, and
4079:vector
3956:where
3751:where
3625:where
3552:where
3483:|
3470:where
2857:
2153:,...,
2123:,...,
1430:metres
1407:scalar
1334:
948:scalar
941:vector
926:object
924:of an
922:motion
872:
824:Appell
809:Cauchy
804:Jacobi
749:Halley
739:Newton
724:Kepler
576:linear
572:Motion
418:Torque
393:Moment
328:Energy
318:Couple
7348:power
7308:power
7278:m s,
7239:m s,
7203:m s,
7164:m s,
7139:force
6649:speed
6581:angle
6336:Speed
5718:Notes
5647:orbit
4664:=<
4476:=<
3826:, and
3485:etc.
2934:with
2745:slope
1424:Units
1399:speed
1369:Speed
969:) as
959:speed
918:speed
829:Gibbs
814:Routh
769:Euler
408:Speed
403:Space
345:Force
7292:yank
7256:work
7181:work
6895:mass
6849:jerk
6561:area
6492:time
6457:time
6347:Jerk
6216:ISBN
6186:ISBN
6108:ISBN
6078:ISBN
6048:For
6027:ISBN
5997:ISBN
5967:ISBN
5934:ISBN
5904:ISBN
5874:ISBN
5844:ISBN
5814:ISBN
5784:ISBN
5729:ISBN
5105:The
4703:>
4502:>
4169:is:
3964:and
3859:– a
3646:drag
3564:The
3492:and
2948:and
1640:vs.
1401:and
1265:vs.
1142:The
1136:area
992:The
413:Time
376:Mass
108:ft/s
7326:MLT
7241:N m
7209:MLT
7162:kg
7067:MLT
7063:J s
7034:N s
6880:rad
6858:m s
6831:rad
6798:m s
6770:rad
6694:m s
6669:m s
6603:rad
6482:m s
4961:In
4890:-,
4518:as
4301:rel
4250:rel
3980:In
3640:In
2961:= 0
2492:If
1926:If
1176:lim
114:In
104:mph
7381::
7358:kg
7350::
7342:kg
7334::
7318:kg
7310::
7302:kg
7294::
7286:MT
7276:kg
7268::
7264:,
7258::
7254:,
7248::
7237:kg
7229::
7225:,
7217::
7201:kg
7193::
7189:,
7183::
7179:,
7173::
7151::
7147:,
7141::
7133:MT
7125:,
7119:kg
7113::
7109:,
7107:𝒮
7105::
7094:kg
7085::
7081:,
7075::
7061:,
7055:kg
7049::
7045:,
7043:𝒮
7041::
7032:,
7026:kg
7018::
7014:,
7008::
6997:kg
6964::
6958:MT
6944:kg
6930:ML
6905:kg
6897::
6871::
6851::
6821::
6790::
6760::
6756:,
6750::
6743:Hz
6741:,
6728::
6723:,
6716::
6711:,
6704::
6676::
6661::
6657:,
6651::
6644:Hz
6642:,
6631::
6611::
6593::
6589:,
6583::
6563::
6550:,
6543:,
6537:,
6531::
6526:,
6520::
6494::
6474::
6459::
6301:…
6297:←
6144:.
5951:^
5755:.
5653:.
4830:,
3887:is
3644:,
2984:/2
2977:+
2970:=
2507:=
2500:=
2146:,
2139:,
2116:,
2109:,
1941:=
1934:=
1713:,
1706:,
1683:,
1676:,
1000:,
979:.
963:SI
106:,
86:,
75:,
69:,
7362:W
7353:P
7337:P
7322:W
7313:P
7297:Y
7280:J
7271:L
7261:W
7251:E
7232:M
7221:τ
7205:J
7196:L
7186:W
7176:E
7166:N
7157:g
7154:F
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7115:ℵ
7089:L
7087:Δ
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7051:ℵ
7021:J
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6914:⟨
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6900:m
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6835:s
6825:α
6814:s
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6764:ω
6753:ω
6739:s
6732:n
6719:n
6707:f
6697:T
6690:h
6682:,
6679:ν
6664:v
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6634:f
6624:T
6613:Ω
6597:θ
6586:θ
6575:1
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6502:s
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6439:θ
6434:1
6428:L
6425:L
6422:1
6386:e
6379:t
6372:v
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6334:(
6328:)
6324:(
6305:→
6279:e
6272:t
6265:v
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6248:(
6224:.
6194:.
6154:.
6116:.
6086:.
6060:.
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5822:.
5792:.
5765:.
5735:.
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5592:|
5587:r
5582:|
5578:=
5575:r
5553:m
5525:2
5521:r
5517:m
5514:=
5509:T
5505:v
5501:r
5498:m
5495:=
5492:L
5466:.
5458:2
5453:|
5447:r
5442:|
5435:|
5430:v
5422:r
5417:|
5410:=
5386:|
5381:r
5376:|
5369:=
5360:t
5350:v
5346:=
5339:|
5334:r
5329:|
5322:|
5317:v
5309:r
5304:|
5297:=
5292:T
5288:v
5231:r
5207:r
5180:r
5170:v
5166:=
5160:|
5156:r
5152:|
5146:r
5138:v
5131:=
5126:R
5122:v
5087:R
5082:v
5056:T
5051:v
5024:R
5019:v
5014:+
5009:T
5004:v
4999:=
4995:v
4918:z
4898:y
4878:x
4858:w
4838:v
4818:u
4796:.
4789:2
4784:z
4780:v
4776:+
4771:2
4766:y
4762:v
4758:+
4753:2
4748:x
4744:v
4738:=
4734:|
4730:v
4726:|
4698:z
4694:v
4690:,
4685:y
4681:v
4677:,
4672:x
4668:v
4659:v
4635:.
4632:t
4629:d
4625:/
4621:z
4618:d
4615:=
4610:z
4606:v
4581:.
4574:2
4569:y
4565:v
4561:+
4556:2
4551:x
4547:v
4541:=
4537:|
4533:v
4529:|
4497:y
4493:v
4489:,
4484:x
4480:v
4471:v
4447:.
4444:t
4441:d
4437:/
4433:y
4430:d
4427:=
4422:y
4418:v
4396:,
4393:t
4390:d
4386:/
4382:x
4379:d
4376:=
4371:x
4367:v
4327:,
4324:)
4321:w
4318:+
4315:(
4309:v
4306:=
4297:v
4276:,
4273:)
4270:w
4264:(
4258:v
4255:=
4246:v
4209:v
4201:w
4197:=
4192:A
4184:B
4179:v
4166:v
4160:w
4144:w
4136:v
4132:=
4127:B
4119:A
4114:v
4089:w
4083:v
4054:c
4032:2
4028:c
4022:2
4018:v
4009:1
4005:1
4000:=
3966:g
3958:G
3944:,
3939:r
3936:g
3933:2
3928:=
3922:r
3918:M
3915:G
3912:2
3905:=
3900:e
3896:v
3885:M
3881:r
3863:.
3841:D
3837:C
3810:A
3788:v
3738:A
3732:D
3728:C
3721:2
3717:v
3705:2
3702:1
3695:=
3689:D
3685:F
3661:D
3657:F
3630:k
3627:E
3610:2
3606:v
3602:m
3596:2
3593:1
3587:=
3582:k
3578:E
3554:m
3538:v
3534:m
3531:=
3527:p
3479:v
3473:v
3458:)
3454:x
3446:a
3442:(
3439:2
3436:+
3431:2
3427:u
3423:=
3418:2
3414:v
3389:2
3385:u
3376:2
3372:v
3368:=
3363:2
3359:t
3353:2
3349:a
3345:+
3342:)
3338:u
3330:a
3326:(
3323:t
3320:2
3317:=
3314:)
3309:2
3305:t
3300:a
3293:2
3290:1
3284:+
3281:t
3277:u
3273:(
3267:)
3263:a
3259:2
3256:(
3253:=
3249:x
3242:)
3238:a
3234:2
3231:(
3210:2
3206:t
3200:2
3196:a
3192:+
3189:)
3185:u
3177:a
3173:(
3170:t
3167:2
3164:+
3159:2
3155:u
3151:=
3148:)
3145:t
3141:a
3137:+
3133:u
3129:(
3123:)
3120:t
3116:a
3112:+
3108:u
3104:(
3101:=
3097:v
3089:v
3085:=
3080:2
3076:v
3051:.
3048:t
3039:v
3033:=
3030:t
3025:2
3021:)
3017:v
3013:+
3009:u
3005:(
2999:=
2995:x
2982:t
2980:a
2975:t
2973:u
2967:x
2959:t
2952:u
2945:t
2938:v
2922:t
2918:a
2914:+
2910:u
2906:=
2902:v
2891:a
2866:.
2863:t
2860:d
2853:a
2846:=
2842:v
2829:)
2827:t
2825:(
2822:a
2803:.
2797:t
2794:d
2788:v
2784:d
2778:=
2774:a
2762:)
2760:t
2758:(
2755:v
2716:.
2711:1
2703:)
2695:i
2691:v
2687:1
2680:n
2675:1
2672:=
2669:i
2660:(
2655:n
2652:=
2647:1
2639:)
2631:n
2627:v
2623:1
2618:+
2612:+
2605:3
2601:v
2597:1
2592:+
2585:2
2581:v
2577:1
2572:+
2565:1
2561:v
2557:1
2551:(
2546:n
2543:=
2534:v
2516:s
2512:3
2509:s
2505:2
2502:s
2498:1
2495:s
2473:n
2469:v
2463:n
2459:s
2453:+
2447:+
2440:3
2436:v
2430:3
2426:s
2420:+
2413:2
2409:v
2403:2
2399:s
2393:+
2386:1
2382:v
2376:1
2372:s
2362:n
2358:s
2354:+
2348:+
2343:3
2339:s
2335:+
2330:2
2326:s
2322:+
2317:1
2313:s
2306:=
2298:n
2294:t
2290:+
2284:+
2279:3
2275:t
2271:+
2266:2
2262:t
2258:+
2253:1
2249:t
2241:n
2237:s
2233:+
2227:+
2222:3
2218:s
2214:+
2209:2
2205:s
2201:+
2196:1
2192:s
2185:=
2176:v
2159:n
2155:v
2151:3
2148:v
2144:2
2141:v
2137:1
2134:v
2129:n
2125:s
2121:3
2118:s
2114:2
2111:s
2107:1
2104:s
2084:i
2080:v
2073:n
2068:1
2065:=
2062:i
2052:n
2049:1
2044:=
2039:n
2033:n
2029:v
2025:+
2019:+
2014:3
2010:v
2006:+
2001:2
1997:v
1993:+
1988:1
1984:v
1977:=
1968:v
1950:t
1946:3
1943:t
1939:2
1936:t
1932:1
1929:t
1906:n
1902:t
1898:+
1892:+
1887:3
1883:t
1879:+
1874:2
1870:t
1866:+
1861:1
1857:t
1849:n
1845:t
1839:n
1835:v
1831:+
1825:+
1820:3
1816:t
1810:3
1806:v
1802:+
1797:2
1793:t
1787:2
1783:v
1779:+
1774:1
1770:t
1764:1
1760:v
1753:=
1744:v
1726:n
1722:t
1718:3
1715:t
1711:2
1708:t
1704:1
1701:t
1696:n
1692:v
1688:3
1685:v
1681:2
1678:v
1674:1
1671:v
1657:t
1643:t
1637:x
1614:.
1606:0
1602:t
1593:1
1589:t
1583:t
1580:d
1577:)
1574:t
1571:(
1567:v
1559:1
1555:t
1547:0
1543:t
1531:=
1525:t
1516:x
1506:=
1497:v
1479:t
1477:Δ
1473:)
1471:t
1469:(
1467:v
1393:.
1391:a
1387:v
1383:r
1379:m
1343:.
1340:t
1337:d
1330:v
1323:=
1319:s
1307:)
1305:t
1303:(
1300:s
1294:)
1292:t
1290:(
1287:v
1275:s
1268:t
1261:v
1243:.
1237:t
1234:d
1228:s
1224:d
1218:=
1212:t
1203:s
1191:0
1184:t
1172:=
1168:v
1152:t
1131:s
1121:a
1115:v
1089:.
1083:t
1075:s
1066:=
1057:v
1034:t
1011:s
965:(
953:(
902:e
895:t
888:v
578:)
197:t
194:d
188:p
184:d
178:=
173:F
142:T
139:L
127:s
125:/
123:m
90:v
83:→
78:v
72:v
66:v
34:.
20:)
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