951:
1241:
3471:
3455:
3439:
3198:
2739:
1009:
2035:
2532:
964:
3509:
tangential to the curve, respectively orthogonal to the radius in this point. Since in uniform motion the velocity in the tangential direction does not change, the acceleration must be in radial direction, pointing to the center of the circle. This acceleration constantly changes the direction of the velocity to be tangent in the neighboring point, thereby rotating the velocity vector along the circle.
2874:
1398:
2304:
2027:
1206:
2695:
3193:{\displaystyle {\begin{aligned}\mathbf {s} (t)&=\mathbf {s} _{0}+\mathbf {v} _{0}t+{\tfrac {1}{2}}\mathbf {a} t^{2}=\mathbf {s} _{0}+{\tfrac {1}{2}}\left(\mathbf {v} _{0}+\mathbf {v} (t)\right)t\\\mathbf {v} (t)&=\mathbf {v} _{0}+\mathbf {a} t\\{v^{2}}(t)&={v_{0}}^{2}+2\mathbf {a\cdot } ,\end{aligned}}}
1156:) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the vehicle turns, an acceleration occurs toward the new direction and changes its motion vector. The acceleration of the vehicle in its current direction of motion is called a linear (or tangential during
2527:{\displaystyle {\begin{alignedat}{3}\mathbf {a} &={\frac {d\mathbf {v} }{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+v(t){\frac {d\mathbf {u} _{\mathrm {t} }}{dt}}\\&={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }+{\frac {v^{2}}{r}}\mathbf {u} _{\mathrm {n} }\ ,\end{alignedat}}}
3508:
along a circular path, a particle experiences an acceleration resulting from the change of the direction of the velocity vector, while its magnitude remains constant. The derivative of the location of a point on a curve with respect to time, i.e. its velocity, turns out to be always exactly
1164:
to which the passengers on board experience as a force pushing them back into their seats. When changing direction, the effecting acceleration is called radial (or centripetal during circular motions) acceleration, the reaction to which the passengers experience as a
56:
1564:
3845:
2577:
2184:
1193:. Both acceleration and deceleration are treated the same, as they are both changes in velocity. Each of these accelerations (tangential, radial, deceleration) is felt by passengers until their relative (differential) velocity are neutralized in
1977:
1683:
187:
4214:, acceleration 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 acceleration components are defined as
1244:
Acceleration is the rate of change of velocity. At any point on a trajectory, the magnitude of the acceleration is given by the rate of change of velocity in both magnitude and direction at that point. The true acceleration at time
2267:
1388:
2047:
is due to the change in speed of traversal, and points along the curve in the direction of the velocity vector (or in the opposite direction). The normal component (also called centripetal component for circular motion)
1885:
An object moving in a circular motion—such as a satellite orbiting the Earth—is accelerating due to the change of direction of motion, although its speed may be constant. In this case it is said to be undergoing
4799:
is exactly revealed to be an approximation to reality, valid to great accuracy at lower speeds. As the relevant speeds increase toward the speed of light, acceleration no longer follows classical equations.
1473:
4771:
3987:
1849:
1785:
305:
329:
4680:
3751:
2879:
4523:
4446:
2855:
237:
4614:
4393:
4303:
2068:
1919:
1139:
3603:
2690:{\displaystyle \mathbf {a} _{\mathrm {t} }={\frac {dv}{dt}}\mathbf {u} _{\mathrm {t} }\quad {\text{and}}\quad \mathbf {a} _{\mathrm {c} }={\frac {v^{2}}{r}}\mathbf {u} _{\mathrm {n} }}
4095:
3930:
5603:
1599:
4018:
In a nonuniform circular motion, i.e., the speed along the curved path is changing, the acceleration has a non-zero component tangential to the curve, and is not confined to the
1306:
3748:
is a vector from the centre of the circle to the particle with magnitude equal to this distance, and considering the orientation of the acceleration towards the center, yields
3338:
3254:
2812:
4174:
3371:
3287:
5471:
Acceleration
Conversion calculator converts units form meter per second square, kilometre per second square, millimeter per second square & more with metric conversion.
3746:
3415:
3721:
6211:
3480:, not parallel to the radial motion but offset by the angular and Coriolis accelerations, nor tangent to the path but offset by the centripetal and radial accelerations.
5570:
1329:
4200:
4115:
4060:
3629:
2200:
1334:
106:
4135:
4040:
3893:
3867:
3689:
3669:
3649:
3551:
3531:
3391:
3307:
3223:
995:
584:
5596:
703:
4795:
The special theory of relativity describes the behavior of objects traveling relative to other objects at speeds approaching that of light in vacuum.
6301:
5070:
676:
4837:, and said that only observers who feel no force at all—including the force of gravity—are justified in concluding that they are not accelerating.
4685:
3421:
In particular, the motion can be resolved into two orthogonal parts, one of constant velocity and the other according to the above equations. As
1808:
1744:
5379:
2057:
is due to the change in direction of the velocity vector and is normal to the trajectory, pointing toward the center of curvature of the path.
950:
5589:
5389:
5362:
5335:
5308:
5224:
5194:
5167:
5142:
5111:
2309:
5496:
5032:
6618:
4455:
658:
3425:
showed, the net result is parabolic motion, which describes, e.g., the trajectory of a projectile in vacuum near the surface of Earth.
5053:
2764:
in a uniform gravitational field. The acceleration of a falling body in the absence of resistances to motion is dependent only on the
2817:
2715:
Geometrical analysis of three-dimensional space curves, which explains tangent, (principal) normal and binormal, is described by the
5443:
5254:
4790:
4528:
4307:
4217:
1169:. If the speed of the vehicle decreases, this is an acceleration in the opposite direction of the velocity vector (mathematically a
988:
1240:
3938:
6337:
6312:
6273:
5298:
3557:
5063:
2546:
2270:
1877:(m s); or "metre per second per second", as the velocity in metres per second changes by the acceleration value, every second.
1703:
324:
261:
3999:
the centre of the circle, as the net force acting on this particle to keep it in this uniform circular motion. The so-called '
4619:
3899:
3533:, the magnitude of this geometrically caused acceleration (centripetal acceleration) is inversely proportional to the radius
319:
2030:
An oscillating pendulum, with velocity and acceleration marked. It experiences both tangential and centripetal acceleration.
579:
6613:
6608:
5615:
2273:
to the path pointing in the direction of motion at the chosen moment in time. Taking into account both the changing speed
1870:
1094:
31:
574:
4525:
In three-dimensional systems where there is an additional z-axis, the corresponding acceleration component is defined as
1559:{\displaystyle \mathbf {a} =\lim _{{\Delta t}\to 0}{\frac {\Delta \mathbf {v} }{\Delta t}}={\frac {d\mathbf {v} }{dt}}.}
981:
968:
729:
652:
4398:
2859:
Because of the simple analytic properties of the case of constant acceleration, there are simple formulas relating the
417:
4825:
Unless the state of motion of an object is known, it is impossible to distinguish whether an observed force is due to
4211:
1153:
648:
449:
38:
4140:
2716:
201:
5043:
1912:
1907:, for a body with constant mass, the (vector) acceleration of the body's center of mass is proportional to the net
868:
757:
683:
543:
476:
1805:, the derivative of the acceleration function, can be used to find the change of acceleration at a certain time:
1108:
6244:
6049:
5903:
3694:
622:
3840:{\displaystyle \mathbf {a_{c}} =-{\frac {v^{2}}{|\mathbf {r} |}}\cdot {\frac {\mathbf {r} }{|\mathbf {r} |}}\,.}
6016:
5489:
5433:
4871:
1874:
1098:
898:
742:
89:
4065:
2733:
6027:
5540:
4864:
4019:
3470:
2701:
1086:
1048:
888:
848:
612:
1015:
is a sport in which specially-built vehicles compete to be the fastest to accelerate from a standing start.
5352:
2779:
2738:
2062:
1075:
1063:
893:
710:
1286:
6603:
6162:
6032:
5770:
5462:
4834:
2860:
903:
878:
564:
382:
3454:
3438:
2179:{\displaystyle \mathbf {v} (t)=v(t){\frac {\mathbf {v} (t)}{v(t)}}=v(t)\mathbf {u} _{\mathrm {t} }(t),}
1896:, the acceleration of a body relative to a free-fall condition, is measured by an instrument called an
1008:
3314:
3230:
2788:
1972:{\displaystyle \mathbf {F} =m\mathbf {a} \quad \implies \quad \mathbf {a} ={\frac {\mathbf {F} }{m}},}
6484:
6409:
6037:
5809:
4179:
3345:
3261:
1859:
1052:
923:
918:
883:
791:
787:
779:
769:
559:
552:
308:
194:
6215:
5944:
5892:
5612:
5482:
4796:
2765:
2021:
1904:
1893:
1455:
698:
639:
617:
362:
357:
352:
252:
3729:
3398:
4820:
4803:
As speeds approach that of light, the acceleration produced by a given force decreases, becoming
4786:
4449:
4008:
2005:
1688:
1194:
1161:
1028:
828:
569:
444:
412:
372:
6187:
4042:
for the centripetal acceleration. The tangential component is given by the angular acceleration
2704:
and the normal or radial acceleration (or centripetal acceleration in circular motion, see also
6234:
6152:
5988:
5747:
5439:
5385:
5358:
5331:
5325:
5304:
5250:
5220:
5190:
5163:
5138:
5107:
5103:
5097:
5058:
4000:
3992:
3487:
2709:
2564:
2017:
1583:
1311:
1166:
838:
795:
752:
747:
688:
464:
454:
347:
5244:
5231:
5201:
5134:
5128:
4185:
4100:
4045:
3614:
1678:{\displaystyle \mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}.}
6321:
6291:
6257:
5976:
5932:
5887:
5468:
4878:
3870:
3609:
3491:
2769:
1696:
1692:
1044:
933:
913:
858:
853:
799:
774:
629:
487:
432:
407:
182:{\displaystyle \mathbf {a} ={\frac {d\mathbf {v} }{dt}}={\frac {d^{2}\mathbf {x} }{dt^{2}}}}
6566:
6526:
4830:
4804:
4178:
The sign of the tangential component of the acceleration is determined by the sign of the
4012:
3501:
2868:
2705:
1276:
1170:
1157:
928:
873:
823:
818:
737:
2034:
6510:
6474:
6399:
6180:
6087:
6067:
5957:
5858:
5565:
5075:
4808:
4120:
4025:
3878:
3852:
3674:
3654:
3634:
3536:
3516:
3376:
3292:
3208:
2001:
1791:
955:
863:
764:
481:
427:
62:
55:
6597:
6384:
6252:
5966:
1897:
1459:
1250:
843:
670:
5405:
2026:
1173:, if the movement is unidimensional and the velocity is positive), sometimes called
6459:
6345:
6281:
5789:
5700:
5429:
4022:, which directs to the center of the osculating circle, that determines the radius
4004:
908:
833:
522:
2295:, the acceleration of a particle moving on a curved path can be written using the
1062:
acting on that object. The magnitude of an object's acceleration, as described by
1055:). The orientation of an object's acceleration is given by the orientation of the
5214:
5184:
5827:
5037:
4807:
small as light speed is approached; an object with mass can approach this speed
1186:
1149:
1035:
of an object with respect to time. Acceleration is one of several components of
1012:
5581:
1185:
force pushing them forward. Such negative accelerations are often achieved by
5521:
5505:
5271:
4857:
2296:
2262:{\displaystyle \mathbf {u} _{\mathrm {t} }={\frac {\mathbf {v} (t)}{v(t)}}\,,}
1467:
1383:{\displaystyle {\bar {\mathbf {a} }}={\frac {\Delta \mathbf {v} }{\Delta t}}.}
1190:
1036:
693:
367:
4829:
or to acceleration—gravity and inertial acceleration have identical effects.
5920:
5847:
5835:
4202:), and the tangent is always directed at right angles to the radius vector.
2761:
2560:
1397:
1020:
715:
17:
5189:(2nd, illustrated, reprinted ed.). John Wiley & Sons. p. 39.
2760:
A frequently cited example of uniform acceleration is that of an object in
6329:
6265:
6224:
6123:
5877:
5736:
5690:
5550:
5544:
5535:
5517:
5406:"The Feynman Lectures on Physics Vol. I Ch. 9: Newton's Laws of Dynamics"
2864:
2754:
2038:
Components of acceleration for a curved motion. The tangential component
1707:
1463:
1280:
1032:
634:
517:
492:
3490:. Notice the setup is not restricted to 2d space, but may represent the
6550:
5048:
4826:
3991:
This acceleration and the mass of the particle determine the necessary
3422:
1205:
1182:
1145:
607:
460:
377:
84:
3726:
Expressing centripetal acceleration vector in polar components, where
6464:
6445:
6433:
6389:
6367:
5821:
5720:
5685:
1863:
1040:
666:
512:
422:
2757:
of an object changes by an equal amount in every equal time period.
1085:, depending on the materials out of which it is made — magnitude is
5378:
David C. Cassidy; Gerald James Holton; F. James
Rutherford (2002).
30:
This article is about acceleration in physics. For other uses, see
6498:
6423:
6357:
5961:
5867:
5862:
5799:
5774:
5554:
3631:, the centripetal acceleration is directly proportional to radius
2783:
2737:
2033:
2025:
1908:
1396:
1239:
1071:
1059:
1007:
502:
497:
439:
5435:
The Fabric of the Cosmos: Space, Time, and the
Texture of Reality
5219:(1st0, illustrated ed.). John Wiley & Sons. p. 36.
1732:; that is, the area under the curve of an acceleration vs. time (
6580:
6540:
6113:
5779:
5710:
5675:
2299:
of differentiation for the product of two functions of time as:
1991:
1866:
1082:
507:
470:
5585:
5478:
3494:
plane in a point of an arbitrary curve in any higher dimension.
1181:, and passengers experience the reaction to deceleration as an
2742:
Calculation of the speed difference for a uniform acceleration
1582:, with respect to time, acceleration can be thought of as the
5474:
5354:
Physics for you: revised national curriculum edition for GCSE
4766:{\displaystyle |a|={\sqrt {a_{x}^{2}+a_{y}^{2}+a_{z}^{2}}}.}
3982:{\displaystyle \mathbf {a_{c}} =-\omega ^{2}\mathbf {r} \,.}
4395:
The two-dimensional acceleration vector is then defined as
2000:
is the center-of-mass acceleration. As speeds approach the
3553:
of the circle, and increases as the square of this speed:
1844:{\displaystyle \mathbf {\Delta a} =\int \mathbf {j} \,dt.}
1780:{\displaystyle \mathbf {\Delta v} =\int \mathbf {a} \,dt.}
1566:
As acceleration is defined as the derivative of velocity,
1436:
and the integral of the velocity is the distance function
1422:
the integral of the acceleration is the velocity function
65:), objects attracted by Earth gain speed at a steady rate.
5243:
Raymond A. Serway; Chris Vuille; Jerry S. Faughn (2008).
300:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
4616:
The three-dimensional acceleration vector is defined as
4003:', appearing to act outward on the body, is a so-called
2061:
The velocity of a particle moving on a curved path as a
5040:: making the connection between space and time explicit
4675:{\displaystyle {\textbf {a}}=<a_{x},a_{y},a_{z}>}
3897:
3555:
1917:
1742:
1576:
and velocity is defined as the derivative of position,
104:
2982:
2937:
1113:
6190:
4688:
4622:
4531:
4458:
4401:
4310:
4220:
4188:
4143:
4123:
4103:
4068:
4048:
4028:
3941:
3902:
3881:
3855:
3754:
3732:
3697:
3677:
3657:
3637:
3617:
3560:
3539:
3519:
3401:
3379:
3348:
3317:
3295:
3264:
3233:
3211:
2877:
2820:
2791:
2580:
2307:
2203:
2071:
1922:
1811:
1747:
1602:
1476:
1337:
1314:
1289:
1111:
264:
204:
109:
5300:
Mathematical
Techniques for Engineers and Scientists
1209:Kinematic quantities of a classical particle: mass
193:
95:
83:
71:
48:
6205:
4765:
4674:
4608:
4518:{\displaystyle |a|={\sqrt {a_{x}^{2}+a_{y}^{2}}}.}
4517:
4440:
4387:
4297:
4194:
4168:
4129:
4109:
4089:
4054:
4034:
4011:of the body in circular motion, due to the body's
3981:
3924:
3887:
3861:
3839:
3740:
3715:
3683:
3663:
3643:
3623:
3597:
3545:
3525:
3409:
3385:
3365:
3332:
3301:
3281:
3248:
3217:
3192:
2849:
2806:
2689:
2526:
2261:
2178:
1971:
1843:
1779:
1677:
1558:
1382:
1323:
1300:
1275:An object's average acceleration over a period of
1133:
299:
231:
181:
4441:{\displaystyle {\textbf {a}}=<a_{x},a_{y}>}
2197:equal to the speed of travel along the path, and
37:"Accelerate" redirects here. For other uses, see
4847:Conversions between common units of acceleration
1486:
4448:. The magnitude of this vector is found by the
2850:{\displaystyle \mathbf {F_{g}} =m\mathbf {g} .}
1740:) graph corresponds to the change of velocity.
232:{\displaystyle {\mathsf {L}}{\mathsf {T}}^{-2}}
4609:{\displaystyle a_{z}=dv_{z}/dt=d^{2}z/dt^{2}.}
4388:{\displaystyle a_{y}=dv_{y}/dt=d^{2}y/dt^{2}.}
4298:{\displaystyle a_{x}=dv_{x}/dt=d^{2}x/dt^{2},}
2753:acceleration is a type of motion in which the
1911:vector (i.e. sum of all forces) acting on it (
1454:Instantaneous acceleration, meanwhile, is the
5597:
5490:
5357:(4th ed.). Nelson Thornes. p. 135.
5330:. New Delhi: S. Chand & Co. p. 337.
5297:Larry C. Andrews; Ronald L. Phillips (2003).
1470:of the velocity vector with respect to time:
989:
8:
5216:Physics, Volume One: Chapters 1-17, Volume 1
5213:John D. Cutnell; Kenneth W. Johnson (2014).
4015:, a vector tangent to the circle of motion.
3651:. This is due to the dependence of velocity
3289:is the displacement from the origin at time
3256:is the initial displacement from the origin,
1890:(directed towards the center) acceleration.
1197:to the acceleration due to change in speed.
1134:{\displaystyle \mathrm {\tfrac {m}{s^{2}}} }
3598:{\displaystyle a_{c}={\frac {v^{2}}{r}}\,.}
5604:
5590:
5582:
5497:
5483:
5475:
2549:to the particle's trajectory (also called
2018:Centripetal force § Local coordinates
1944:
1940:
996:
982:
243:
54:
6192:
6191:
6189:
4752:
4747:
4734:
4729:
4716:
4711:
4705:
4697:
4689:
4687:
4663:
4650:
4637:
4624:
4623:
4621:
4597:
4585:
4576:
4558:
4552:
4536:
4530:
4504:
4499:
4486:
4481:
4475:
4467:
4459:
4457:
4429:
4416:
4403:
4402:
4400:
4376:
4364:
4355:
4337:
4331:
4315:
4309:
4286:
4274:
4265:
4247:
4241:
4225:
4219:
4187:
4148:
4142:
4122:
4102:
4076:
4075:
4067:
4047:
4027:
3975:
3970:
3964:
3947:
3942:
3940:
3909:
3901:
3880:
3854:
3833:
3825:
3820:
3815:
3809:
3807:
3796:
3791:
3786:
3779:
3773:
3760:
3755:
3753:
3733:
3731:
3696:
3676:
3656:
3636:
3616:
3591:
3580:
3574:
3565:
3559:
3538:
3518:
3448:, always points radially from the origin.
3402:
3400:
3378:
3349:
3347:
3324:
3319:
3316:
3294:
3265:
3263:
3240:
3235:
3232:
3210:
3174:
3169:
3151:
3140:
3128:
3121:
3116:
3092:
3087:
3075:
3066:
3061:
3039:
3013:
3004:
2999:
2981:
2972:
2967:
2957:
2948:
2936:
2924:
2919:
2909:
2904:
2882:
2878:
2876:
2839:
2826:
2821:
2819:
2797:
2792:
2790:
2680:
2679:
2674:
2662:
2656:
2646:
2645:
2640:
2633:
2625:
2624:
2619:
2598:
2588:
2587:
2582:
2579:
2507:
2506:
2501:
2489:
2483:
2473:
2472:
2467:
2446:
2418:
2417:
2412:
2405:
2383:
2382:
2377:
2356:
2330:
2324:
2312:
2308:
2306:
2255:
2224:
2221:
2211:
2210:
2205:
2202:
2157:
2156:
2151:
2104:
2101:
2072:
2070:
1956:
1954:
1946:
1934:
1923:
1921:
1831:
1826:
1812:
1810:
1767:
1762:
1748:
1746:
1663:
1649:
1643:
1636:
1617:
1611:
1603:
1601:
1537:
1531:
1512:
1506:
1490:
1489:
1477:
1475:
1361:
1355:
1341:
1339:
1338:
1336:
1313:
1308:, divided by the duration of the period,
1293:
1288:
1122:
1112:
1110:
281:
275:
266:
265:
263:
220:
214:
213:
206:
205:
203:
170:
156:
150:
143:
124:
118:
110:
108:
5624:
5324:Ch V Ramana Murthy; NC Srinivas (2001).
5133:. Barron's Educational Series. pp.
5071:Space travel using constant acceleration
4844:
4090:{\displaystyle \alpha ={\dot {\omega }}}
3875:with respect to a point at the distance
1862:of velocity (L/T) divided by time, i.e.
1204:
1066:, is the combined effect of two causes:
5102:. Courier Dover Publications. pp.
5088:
3925:{\displaystyle \omega ={\frac {v}{r}}.}
3464:, always tangent to the path of motion.
2012:Tangential and centripetal acceleration
1074:acting onto that object — magnitude is
315:
251:
4682:with its magnitude being determined by
215:
207:
45:
3869:of a particle may be expressed as an
1986:is the net force acting on the body,
678:Newton's law of universal gravitation
7:
5033:Acceleration (differential geometry)
3417:is the uniform rate of acceleration.
1466:, instantaneous acceleration is the
1458:of the average acceleration over an
4625:
4404:
1301:{\displaystyle \Delta \mathbf {v} }
659:Mechanics of planar particle motion
267:
5465:Simple acceleration unit converter
5054:Orders of magnitude (acceleration)
2681:
2647:
2626:
2589:
2508:
2474:
2419:
2384:
2212:
2158:
1519:
1509:
1491:
1462:interval of time. In the terms of
1368:
1358:
1315:
1290:
1119:
1115:
25:
5162:. BiblioBazaar, LLC. p. 43.
4791:Acceleration (special relativity)
3849:As usual in rotations, the speed
1695:quantities can be substituted by
3971:
3948:
3944:
3821:
3810:
3792:
3761:
3757:
3734:
3469:
3453:
3437:
3403:
3350:
3333:{\displaystyle \mathbf {v} _{0}}
3320:
3266:
3249:{\displaystyle \mathbf {s} _{0}}
3236:
3170:
3152:
3141:
3076:
3062:
3040:
3014:
3000:
2968:
2949:
2920:
2905:
2883:
2840:
2827:
2823:
2807:{\displaystyle \mathbf {F_{g}} }
2798:
2794:
2675:
2641:
2620:
2583:
2502:
2468:
2413:
2378:
2331:
2313:
2225:
2206:
2152:
2105:
2073:
1957:
1947:
1935:
1924:
1827:
1816:
1813:
1763:
1752:
1749:
1650:
1618:
1604:
1538:
1513:
1478:
1362:
1342:
1294:
1070:the net balance of all external
963:
962:
949:
282:
157:
125:
111:
5628:Linear/translational quantities
5410:www.feynmanlectures.caltech.edu
5064:Shock and vibration data logger
4169:{\displaystyle a_{t}=r\alpha .}
3504:, that is moving with constant
3366:{\displaystyle \mathbf {v} (t)}
3282:{\displaystyle \mathbf {s} (t)}
2638:
2632:
1945:
1939:
1704:fundamental theorem of calculus
5183:P. Smith; R. C. Smith (1991).
4698:
4690:
4468:
4460:
3826:
3816:
3797:
3787:
3360:
3354:
3276:
3270:
3180:
3162:
3156:
3148:
3105:
3099:
3050:
3044:
3024:
3018:
2893:
2887:
2814:acting on a body is given by:
2402:
2396:
2284:and the changing direction of
2249:
2243:
2235:
2229:
2170:
2164:
2147:
2141:
2129:
2123:
2115:
2109:
2098:
2092:
2083:
2077:
1941:
1790:Likewise, the integral of the
1498:
1346:
1047:quantities (in that they have
1:
5633:Angular/rotational quantities
5067:measuring 3-axis acceleration
2863:, initial and time-dependent
1710:of the acceleration function
585:Koopman–von Neumann mechanics
32:Acceleration (disambiguation)
4212:Cartesian coordinate systems
3741:{\displaystyle \mathbf {r} }
3410:{\displaystyle \mathbf {a} }
1873:unit of acceleration is the
1689:motion is in a straight line
1078:to this net resulting force;
653:Non-inertial reference frame
5384:. Birkhäuser. p. 146.
5303:. SPIE Press. p. 164.
5160:The Principles of Mechanics
5127:Lehrman, Robert L. (1998).
5099:Relativity and Common Sense
4062:, i.e., the rate of change
3716:{\displaystyle v=\omega r.}
3486:Kinematic vectors in plane
2776:acceleration due to gravity
2065:of time can be written as:
2008:become increasingly large.
1154:inertial frame of reference
580:Appell's equation of motion
450:Inertial frame of reference
39:Accelerate (disambiguation)
6635:
6619:Vector physical quantities
6206:{\displaystyle {\dot {m}}}
5630:
5246:College Physics, Volume 10
5044:Gravitational acceleration
4818:
4784:
2867:, and acceleration to the
2731:
2015:
1706:, it can be seen that the
1393:Instantaneous acceleration
36:
29:
27:Rate of change of velocity
5904:specific angular momentum
5632:
5627:
5622:
5531:
5512:
4876:
4869:
4862:
4855:
4852:
1721:is the velocity function
1408:an acceleration function
1249:is found in the limit as
1201:Definition and properties
1097:unit for acceleration is
53:
3373:is the velocity at time
3340:is the initial velocity,
1875:metre per second squared
1687:(Here and elsewhere, if
1324:{\displaystyle \Delta t}
1099:metre per second squared
743:Rotating reference frame
575:Hamilton–Jacobi equation
6028:rotational acceleration
5469:Acceleration Calculator
5463:Acceleration Calculator
5438:. Vintage. p. 67.
5249:. Cengage. p. 32.
5096:Bondi, Hermann (1980).
4811:, but never reach it.
4195:{\displaystyle \alpha }
4110:{\displaystyle \omega }
4055:{\displaystyle \alpha }
3624:{\displaystyle \omega }
2702:tangential acceleration
1572:, with respect to time
684:Newton's laws of motion
544:Newton's laws of motion
6207:
5351:Keith Johnson (2001).
4776:Relation to relativity
4767:
4676:
4610:
4519:
4442:
4389:
4299:
4196:
4170:
4131:
4111:
4091:
4056:
4036:
3983:
3926:
3889:
3863:
3841:
3742:
3717:
3685:
3665:
3645:
3625:
3599:
3547:
3527:
3411:
3387:
3367:
3334:
3303:
3283:
3250:
3219:
3194:
2851:
2808:
2743:
2717:Frenet–Serret formulas
2691:
2545:is the unit (inward)
2528:
2263:
2180:
2058:
2031:
1973:
1845:
1781:
1679:
1560:
1451:
1384:
1325:
1302:
1272:
1232:
1152:(zero velocity, in an
1135:
1087:inversely proportional
1016:
711:Simple harmonic motion
624:Euler's laws of motion
418:D'Alembert's principle
301:
233:
183:
6208:
5381:Understanding physics
4835:equivalence principle
4768:
4677:
4611:
4520:
4443:
4390:
4300:
4210:In multi-dimensional
4197:
4171:
4132:
4112:
4097:of the angular speed
4092:
4057:
4037:
3984:
3927:
3890:
3864:
3842:
3743:
3718:
3686:
3666:
3646:
3626:
3600:
3548:
3528:
3412:
3388:
3368:
3335:
3304:
3284:
3251:
3220:
3195:
2852:
2809:
2741:
2734:Torricelli's equation
2692:
2559:is its instantaneous
2529:
2264:
2181:
2037:
2029:
1974:
1858:Acceleration has the
1846:
1782:
1680:
1561:
1400:
1385:
1326:
1303:
1243:
1208:
1136:
1089:to the object's mass.
1076:directly proportional
1011:
565:Hamiltonian mechanics
383:Statistical mechanics
302:
234:
184:
6614:Kinematic properties
6609:Dynamics (mechanics)
6188:
6038:angular acceleration
5810:angular displacement
5158:Crew, Henry (2008).
5130:Physics the Easy Way
4686:
4620:
4529:
4456:
4399:
4308:
4218:
4186:
4180:angular acceleration
4141:
4121:
4101:
4066:
4046:
4026:
3939:
3900:
3879:
3853:
3752:
3730:
3695:
3675:
3655:
3635:
3615:
3558:
3537:
3517:
3476:Acceleration vector
3399:
3377:
3346:
3315:
3293:
3262:
3231:
3225:is the elapsed time,
3209:
2875:
2818:
2789:
2728:Uniform acceleration
2578:
2551:the principal normal
2305:
2201:
2069:
2006:relativistic effects
1920:
1809:
1745:
1600:
1474:
1335:
1312:
1287:
1236:Average acceleration
1160:) acceleration, the
1144:For example, when a
1109:
1043:. Accelerations are
788:Angular acceleration
780:Rotational frequency
560:Lagrangian mechanics
553:Analytical mechanics
309:Second law of motion
262:
202:
107:
6128:weighted position:
5945:rotational velocity
5893:kinematic viscosity
5613:Classical mechanics
5327:Applied Mathematics
5270:Weisstein, Eric W.
4849:
4797:Newtonian mechanics
4757:
4739:
4721:
4509:
4491:
4007:experienced in the
2780:Newton's Second Law
2766:gravitational field
2561:radius of curvature
2271:unit vector tangent
2022:Tangential velocity
1913:Newton's second law
1905:classical mechanics
1894:Proper acceleration
1699:in the equations.)
1064:Newton's Second Law
640:Harmonic oscillator
618:Equations of motion
253:Classical mechanics
247:Part of a series on
6203:
5571:Higher derivatives
5278:. Wolfram Research
5232:Extract of page 36
5202:Extract of page 39
4845:
4821:General relativity
4815:General relativity
4787:Special relativity
4781:Special relativity
4763:
4743:
4725:
4707:
4672:
4606:
4515:
4495:
4477:
4438:
4385:
4295:
4206:Coordinate systems
4192:
4166:
4127:
4107:
4087:
4052:
4032:
4009:frame of reference
3979:
3922:
3885:
3859:
3837:
3738:
3713:
3681:
3661:
3641:
3621:
3595:
3543:
3523:
3513:For a given speed
3407:
3383:
3363:
3330:
3299:
3279:
3246:
3215:
3190:
3188:
2991:
2946:
2847:
2804:
2744:
2687:
2524:
2522:
2259:
2176:
2059:
2032:
1969:
1841:
1777:
1675:
1556:
1505:
1452:
1402:From bottom to top
1380:
1331:. Mathematically,
1321:
1298:
1273:
1233:
1131:
1129:
1017:
956:Physics portal
570:Routhian mechanics
445:Frame of reference
297:
229:
179:
90:m/s, m·s, m s
6591:
6590:
6586:
6585:
6200:
6153:moment of inertia
5579:
5578:
5391:978-0-387-98756-9
5364:978-0-7487-6236-1
5337:978-81-219-2082-7
5310:978-0-8194-4506-3
5276:Wolfram MathWorld
5226:978-1-118-83688-0
5196:978-0-471-92737-2
5169:978-0-559-36871-4
5144:978-0-7641-0236-3
5113:978-0-486-24021-3
5059:Shock (mechanics)
5023:
5022:
4758:
4627:
4510:
4406:
4130:{\displaystyle r}
4117:times the radius
4084:
4035:{\displaystyle r}
4001:centrifugal force
3993:centripetal force
3917:
3888:{\displaystyle r}
3862:{\displaystyle v}
3831:
3802:
3684:{\displaystyle r}
3664:{\displaystyle v}
3644:{\displaystyle r}
3589:
3546:{\displaystyle r}
3526:{\displaystyle v}
3488:polar coordinates
3386:{\displaystyle t}
3302:{\displaystyle t}
3218:{\displaystyle t}
2990:
2945:
2712:), respectively.
2710:centripetal force
2671:
2636:
2616:
2571:. The components
2565:osculating circle
2516:
2498:
2464:
2434:
2374:
2344:
2253:
2133:
1994:of the body, and
1964:
1670:
1631:
1584:second derivative
1551:
1526:
1485:
1375:
1349:
1279:is its change in
1167:centrifugal force
1128:
1031:of change of the
1006:
1005:
753:Centrifugal force
748:Centripetal force
704:Euler's equations
689:Relative velocity
465:Moment of inertia
295:
269:
242:
241:
177:
138:
16:(Redirected from
6626:
6578:
6574:
6562:
6558:
6538:
6534:
6522:
6518:
6496:
6492:
6482:
6472:
6457:
6453:
6443:
6421:
6417:
6407:
6397:
6382:
6378:
6365:
6341:
6335:
6327:
6316:
6310:
6299:
6292:angular momentum
6277:
6271:
6263:
6248:
6242:
6232:
6219:
6213:
6212:
6210:
6209:
6204:
6202:
6201:
6193:
6166:
6160:
6144:
6121:
6102:
6097:
6075:
6053:
6047:
6030:
6014:
5992:
5986:
5977:angular velocity
5974:
5955:
5954:
5941:
5940:
5933:rotational speed
5929:
5928:
5911:
5900:
5885:
5875:
5856:
5855:
5838:
5833:
5819:
5807:
5787:
5768:
5767:
5761:
5755:
5744:
5718:
5698:
5683:
5667:
5660:
5625:
5606:
5599:
5592:
5583:
5499:
5492:
5485:
5476:
5450:
5449:
5426:
5420:
5419:
5417:
5416:
5402:
5396:
5395:
5375:
5369:
5368:
5348:
5342:
5341:
5321:
5315:
5314:
5294:
5288:
5287:
5285:
5283:
5267:
5261:
5260:
5240:
5234:
5230:
5210:
5204:
5200:
5180:
5174:
5173:
5155:
5149:
5148:
5124:
5118:
5117:
5093:
5014:
5013:
5006:
5001:
4985:
4984:
4972:
4971:
4964:
4954:
4953:
4946:
4945:
4933:
4923:
4921:
4918:
4911:
4906:
4905:
4879:Standard gravity
4850:
4848:
4833:called this the
4772:
4770:
4769:
4764:
4759:
4756:
4751:
4738:
4733:
4720:
4715:
4706:
4701:
4693:
4681:
4679:
4678:
4673:
4668:
4667:
4655:
4654:
4642:
4641:
4629:
4628:
4615:
4613:
4612:
4607:
4602:
4601:
4589:
4581:
4580:
4562:
4557:
4556:
4541:
4540:
4524:
4522:
4521:
4516:
4511:
4508:
4503:
4490:
4485:
4476:
4471:
4463:
4450:distance formula
4447:
4445:
4444:
4439:
4434:
4433:
4421:
4420:
4408:
4407:
4394:
4392:
4391:
4386:
4381:
4380:
4368:
4360:
4359:
4341:
4336:
4335:
4320:
4319:
4304:
4302:
4301:
4296:
4291:
4290:
4278:
4270:
4269:
4251:
4246:
4245:
4230:
4229:
4201:
4199:
4198:
4193:
4175:
4173:
4172:
4167:
4153:
4152:
4136:
4134:
4133:
4128:
4116:
4114:
4113:
4108:
4096:
4094:
4093:
4088:
4086:
4085:
4077:
4061:
4059:
4058:
4053:
4041:
4039:
4038:
4033:
4020:principal normal
3988:
3986:
3985:
3980:
3974:
3969:
3968:
3953:
3952:
3951:
3932:
3929:
3928:
3923:
3918:
3910:
3894:
3892:
3891:
3886:
3868:
3866:
3865:
3860:
3846:
3844:
3843:
3838:
3832:
3830:
3829:
3824:
3819:
3813:
3808:
3803:
3801:
3800:
3795:
3790:
3784:
3783:
3774:
3766:
3765:
3764:
3747:
3745:
3744:
3739:
3737:
3722:
3720:
3719:
3714:
3690:
3688:
3687:
3682:
3670:
3668:
3667:
3662:
3650:
3648:
3647:
3642:
3630:
3628:
3627:
3622:
3610:angular velocity
3605:
3602:
3601:
3596:
3590:
3585:
3584:
3575:
3570:
3569:
3552:
3550:
3549:
3544:
3532:
3530:
3529:
3524:
3492:osculating plane
3473:
3460:Velocity vector
3457:
3444:Position vector
3441:
3416:
3414:
3413:
3408:
3406:
3392:
3390:
3389:
3384:
3372:
3370:
3369:
3364:
3353:
3339:
3337:
3336:
3331:
3329:
3328:
3323:
3308:
3306:
3305:
3300:
3288:
3286:
3285:
3280:
3269:
3255:
3253:
3252:
3247:
3245:
3244:
3239:
3224:
3222:
3221:
3216:
3199:
3197:
3196:
3191:
3189:
3179:
3178:
3173:
3155:
3147:
3133:
3132:
3127:
3126:
3125:
3098:
3097:
3096:
3079:
3071:
3070:
3065:
3043:
3031:
3027:
3017:
3009:
3008:
3003:
2992:
2983:
2977:
2976:
2971:
2962:
2961:
2952:
2947:
2938:
2929:
2928:
2923:
2914:
2913:
2908:
2886:
2856:
2854:
2853:
2848:
2843:
2832:
2831:
2830:
2813:
2811:
2810:
2805:
2803:
2802:
2801:
2772:
2696:
2694:
2693:
2688:
2686:
2685:
2684:
2678:
2672:
2667:
2666:
2657:
2652:
2651:
2650:
2644:
2637:
2634:
2631:
2630:
2629:
2623:
2617:
2615:
2607:
2599:
2594:
2593:
2592:
2586:
2570:
2558:
2544:
2533:
2531:
2530:
2525:
2523:
2514:
2513:
2512:
2511:
2505:
2499:
2494:
2493:
2484:
2479:
2478:
2477:
2471:
2465:
2463:
2455:
2447:
2439:
2435:
2433:
2425:
2424:
2423:
2422:
2416:
2406:
2389:
2388:
2387:
2381:
2375:
2373:
2365:
2357:
2349:
2345:
2343:
2335:
2334:
2325:
2316:
2294:
2283:
2268:
2266:
2265:
2260:
2254:
2252:
2238:
2228:
2222:
2217:
2216:
2215:
2209:
2196:
2185:
2183:
2182:
2177:
2163:
2162:
2161:
2155:
2134:
2132:
2118:
2108:
2102:
2076:
2056:
2046:
1999:
1989:
1985:
1979:
1976:
1975:
1970:
1965:
1960:
1955:
1950:
1938:
1927:
1850:
1848:
1847:
1842:
1830:
1819:
1804:
1787:
1784:
1783:
1778:
1766:
1755:
1739:
1735:
1731:
1720:
1684:
1682:
1681:
1676:
1671:
1669:
1668:
1667:
1654:
1653:
1648:
1647:
1637:
1632:
1630:
1622:
1621:
1612:
1607:
1595:
1592:with respect to
1591:
1581:
1575:
1571:
1565:
1563:
1562:
1557:
1552:
1550:
1542:
1541:
1532:
1527:
1525:
1517:
1516:
1507:
1504:
1497:
1481:
1446:
1432:
1418:
1389:
1387:
1386:
1381:
1376:
1374:
1366:
1365:
1356:
1351:
1350:
1345:
1340:
1330:
1328:
1327:
1322:
1307:
1305:
1304:
1299:
1297:
1270:
1259:
1248:
1230:
1224:
1218:
1212:
1158:circular motions
1140:
1138:
1137:
1132:
1130:
1127:
1126:
1114:
1104:
998:
991:
984:
971:
966:
965:
958:
954:
953:
859:Johann Bernoulli
854:Daniel Bernoulli
775:Tangential speed
679:
655:
630:Fictitious force
625:
477:Mechanical power
467:
408:Angular momentum
306:
304:
303:
298:
296:
294:
286:
285:
276:
271:
270:
244:
238:
236:
235:
230:
228:
227:
219:
218:
211:
210:
189:
186:
185:
180:
178:
176:
175:
174:
161:
160:
155:
154:
144:
139:
137:
129:
128:
119:
114:
99:other quantities
97:Derivations from
58:
46:
21:
6634:
6633:
6629:
6628:
6627:
6625:
6624:
6623:
6594:
6593:
6592:
6587:
6576:
6575:
6570:
6560:
6559:
6554:
6536:
6535:
6530:
6520:
6519:
6514:
6494:
6493:
6488:
6478:
6468:
6455:
6454:
6449:
6437:
6419:
6418:
6413:
6403:
6393:
6380:
6379:
6377:
6371:
6361:
6339:
6336:
6333:
6325:
6314:
6311:
6305:
6302:angular impulse
6295:
6275:
6272:
6269:
6261:
6246:
6243:
6238:
6228:
6217:
6214:
6186:
6185:
6184:
6164:
6161:
6156:
6129:
6122:
6117:
6100:
6098:
6091:
6076:
6071:
6051:
6048:
6041:
6031:
6026:
6015:
6010:
5990:
5987:
5980:
5970:
5956:
5948:
5943:
5936:
5931:
5924:
5919:
5912:
5907:
5902:
5896:
5886:
5881:
5871:
5857:
5851:
5846:
5834:
5831:
5826:
5820:
5813:
5803:
5788:
5783:
5773:
5763:
5757:
5751:
5746:
5740:
5719:
5714:
5699:
5694:
5684:
5679:
5663:
5656:
5618:
5610:
5580:
5575:
5527:
5508:
5503:
5459:
5454:
5453:
5446:
5428:
5427:
5423:
5414:
5412:
5404:
5403:
5399:
5392:
5377:
5376:
5372:
5365:
5350:
5349:
5345:
5338:
5323:
5322:
5318:
5311:
5296:
5295:
5291:
5281:
5279:
5269:
5268:
5264:
5257:
5242:
5241:
5237:
5227:
5212:
5211:
5207:
5197:
5182:
5181:
5177:
5170:
5157:
5156:
5152:
5145:
5126:
5125:
5121:
5114:
5095:
5094:
5090:
5085:
5080:
5066:
5028:
5011:
5009:
5004:
4999:
4996:
4982:
4980:
4969:
4967:
4962:
4951:
4949:
4943:
4941:
4931:
4919:
4916:
4914:
4909:
4903:
4901:
4893:1 Gal, or cm/s
4887:
4846:
4843:
4831:Albert Einstein
4823:
4817:
4805:infinitesimally
4793:
4785:Main articles:
4783:
4778:
4684:
4683:
4659:
4646:
4633:
4618:
4617:
4593:
4572:
4548:
4532:
4527:
4526:
4454:
4453:
4425:
4412:
4397:
4396:
4372:
4351:
4327:
4311:
4306:
4305:
4282:
4261:
4237:
4221:
4216:
4215:
4208:
4184:
4183:
4144:
4139:
4138:
4119:
4118:
4099:
4098:
4064:
4063:
4044:
4043:
4024:
4023:
4013:linear momentum
3960:
3943:
3937:
3936:
3898:
3896:
3877:
3876:
3851:
3850:
3814:
3785:
3775:
3756:
3750:
3749:
3728:
3727:
3693:
3692:
3673:
3672:
3653:
3652:
3633:
3632:
3613:
3612:
3576:
3561:
3556:
3554:
3535:
3534:
3515:
3514:
3502:circular motion
3498:
3497:
3496:
3495:
3483:
3482:
3481:
3474:
3466:
3465:
3458:
3450:
3449:
3442:
3431:
3429:Circular motion
3397:
3396:
3375:
3374:
3344:
3343:
3318:
3313:
3312:
3291:
3290:
3260:
3259:
3234:
3229:
3228:
3207:
3206:
3187:
3186:
3168:
3117:
3115:
3108:
3088:
3084:
3083:
3060:
3053:
3036:
3035:
2998:
2997:
2993:
2966:
2953:
2918:
2903:
2896:
2873:
2872:
2822:
2816:
2815:
2793:
2787:
2786:
2770:
2736:
2730:
2725:
2706:circular motion
2700:are called the
2673:
2658:
2639:
2618:
2608:
2600:
2581:
2576:
2575:
2568:
2563:based upon the
2554:
2543:
2537:
2521:
2520:
2500:
2485:
2466:
2456:
2448:
2437:
2436:
2426:
2411:
2407:
2376:
2366:
2358:
2347:
2346:
2336:
2326:
2317:
2303:
2302:
2293:
2285:
2274:
2239:
2223:
2204:
2199:
2198:
2187:
2150:
2119:
2103:
2067:
2066:
2055:
2049:
2045:
2039:
2024:
2014:
1995:
1987:
1981:
1918:
1916:
1883:
1856:
1807:
1806:
1795:
1743:
1741:
1737:
1733:
1722:
1711:
1659:
1655:
1639:
1638:
1623:
1613:
1598:
1597:
1593:
1587:
1577:
1573:
1567:
1543:
1533:
1518:
1508:
1472:
1471:
1450:
1437:
1423:
1409:
1395:
1367:
1357:
1333:
1332:
1310:
1309:
1285:
1284:
1261:
1253:
1246:
1238:
1226:
1225:, acceleration
1220:
1214:
1210:
1203:
1118:
1107:
1106:
1102:
1039:, the study of
1002:
961:
948:
947:
940:
939:
938:
813:
805:
804:
784:
738:Circular motion
732:
722:
721:
720:
677:
647:
644:
623:
602:
594:
593:
590:
589:
547:
537:
529:
528:
527:
486:
482:Mechanical work
475:
459:
397:
389:
388:
387:
342:
334:
311:
287:
277:
260:
259:
212:
200:
199:
166:
162:
146:
145:
130:
120:
105:
103:
100:
98:
74:
67:
66:
42:
35:
28:
23:
22:
15:
12:
11:
5:
6632:
6630:
6622:
6621:
6616:
6611:
6606:
6596:
6595:
6589:
6588:
6584:
6583:
6564:
6548:
6546:
6543:
6524:
6508:
6506:
6502:
6501:
6462:
6431:
6429:
6426:
6387:
6375:
6355:
6353:
6349:
6348:
6319:
6289:
6287:
6284:
6255:
6222:
6199:
6196:
6181:Mass flow rate
6178:
6174:
6173:
6171:
6169:
6150:
6147:
6145:
6126:
6111:
6107:
6106:
6104:
6085:
6083:
6080:
6078:
6065:
6063:
6059:
6058:
6056:
6035:
6024:
6021:
6019:
6004:
6002:
5998:
5997:
5995:
5964:
5917:
5914:
5890:
5865:
5844:
5840:
5839:
5824:
5797:
5795:
5792:
5777:
5734:
5732:
5728:
5727:
5725:
5723:
5708:
5705:
5703:
5688:
5673:
5669:
5668:
5661:
5654:
5651:
5648:
5645:
5642:
5639:
5635:
5634:
5631:
5629:
5623:
5620:
5619:
5611:
5609:
5608:
5601:
5594:
5586:
5577:
5576:
5574:
5573:
5568:
5563:
5558:
5548:
5538:
5532:
5529:
5528:
5526:
5525:
5513:
5510:
5509:
5504:
5502:
5501:
5494:
5487:
5479:
5473:
5472:
5466:
5458:
5457:External links
5455:
5452:
5451:
5444:
5421:
5397:
5390:
5370:
5363:
5343:
5336:
5316:
5309:
5289:
5262:
5255:
5235:
5225:
5205:
5195:
5175:
5168:
5150:
5143:
5119:
5112:
5087:
5086:
5084:
5081:
5079:
5078:
5076:Specific force
5073:
5068:
5061:
5056:
5051:
5046:
5041:
5035:
5029:
5027:
5024:
5021:
5020:
5015:
5007:
5002:
4997:
4994:
4987:
4986:
4978:
4973:
4965:
4960:
4956:
4955:
4947:
4939:
4934:
4929:
4925:
4924:
4912:
4907:
4899:
4894:
4890:
4889:
4885:
4875:
4868:
4861:
4854:
4842:
4839:
4819:Main article:
4816:
4813:
4809:asymptotically
4782:
4779:
4777:
4774:
4762:
4755:
4750:
4746:
4742:
4737:
4732:
4728:
4724:
4719:
4714:
4710:
4704:
4700:
4696:
4692:
4671:
4666:
4662:
4658:
4653:
4649:
4645:
4640:
4636:
4632:
4605:
4600:
4596:
4592:
4588:
4584:
4579:
4575:
4571:
4568:
4565:
4561:
4555:
4551:
4547:
4544:
4539:
4535:
4514:
4507:
4502:
4498:
4494:
4489:
4484:
4480:
4474:
4470:
4466:
4462:
4437:
4432:
4428:
4424:
4419:
4415:
4411:
4384:
4379:
4375:
4371:
4367:
4363:
4358:
4354:
4350:
4347:
4344:
4340:
4334:
4330:
4326:
4323:
4318:
4314:
4294:
4289:
4285:
4281:
4277:
4273:
4268:
4264:
4260:
4257:
4254:
4250:
4244:
4240:
4236:
4233:
4228:
4224:
4207:
4204:
4191:
4165:
4162:
4159:
4156:
4151:
4147:
4126:
4106:
4083:
4080:
4074:
4071:
4051:
4031:
3978:
3973:
3967:
3963:
3959:
3956:
3950:
3946:
3921:
3916:
3913:
3908:
3905:
3884:
3858:
3836:
3828:
3823:
3818:
3812:
3806:
3799:
3794:
3789:
3782:
3778:
3772:
3769:
3763:
3759:
3736:
3724:
3723:
3712:
3709:
3706:
3703:
3700:
3680:
3671:on the radius
3660:
3640:
3620:
3606:
3594:
3588:
3583:
3579:
3573:
3568:
3564:
3542:
3522:
3485:
3484:
3475:
3468:
3467:
3459:
3452:
3451:
3443:
3436:
3435:
3434:
3433:
3432:
3430:
3427:
3419:
3418:
3405:
3394:
3382:
3362:
3359:
3356:
3352:
3341:
3327:
3322:
3310:
3298:
3278:
3275:
3272:
3268:
3257:
3243:
3238:
3226:
3214:
3185:
3182:
3177:
3172:
3167:
3164:
3161:
3158:
3154:
3150:
3146:
3143:
3139:
3136:
3131:
3124:
3120:
3114:
3111:
3109:
3107:
3104:
3101:
3095:
3091:
3086:
3085:
3082:
3078:
3074:
3069:
3064:
3059:
3056:
3054:
3052:
3049:
3046:
3042:
3038:
3037:
3034:
3030:
3026:
3023:
3020:
3016:
3012:
3007:
3002:
2996:
2989:
2986:
2980:
2975:
2970:
2965:
2960:
2956:
2951:
2944:
2941:
2935:
2932:
2927:
2922:
2917:
2912:
2907:
2902:
2899:
2897:
2895:
2892:
2889:
2885:
2881:
2880:
2846:
2842:
2838:
2835:
2829:
2825:
2800:
2796:
2729:
2726:
2724:
2721:
2698:
2697:
2683:
2677:
2670:
2665:
2661:
2655:
2649:
2643:
2628:
2622:
2614:
2611:
2606:
2603:
2597:
2591:
2585:
2541:
2519:
2510:
2504:
2497:
2492:
2488:
2482:
2476:
2470:
2462:
2459:
2454:
2451:
2445:
2442:
2440:
2438:
2432:
2429:
2421:
2415:
2410:
2404:
2401:
2398:
2395:
2392:
2386:
2380:
2372:
2369:
2364:
2361:
2355:
2352:
2350:
2348:
2342:
2339:
2333:
2329:
2323:
2320:
2318:
2315:
2311:
2310:
2289:
2258:
2251:
2248:
2245:
2242:
2237:
2234:
2231:
2227:
2220:
2214:
2208:
2175:
2172:
2169:
2166:
2160:
2154:
2149:
2146:
2143:
2140:
2137:
2131:
2128:
2125:
2122:
2117:
2114:
2111:
2107:
2100:
2097:
2094:
2091:
2088:
2085:
2082:
2079:
2075:
2053:
2043:
2013:
2010:
2002:speed of light
1968:
1963:
1959:
1953:
1949:
1943:
1937:
1933:
1930:
1926:
1882:
1879:
1855:
1852:
1840:
1837:
1834:
1829:
1825:
1822:
1818:
1815:
1776:
1773:
1770:
1765:
1761:
1758:
1754:
1751:
1674:
1666:
1662:
1658:
1652:
1646:
1642:
1635:
1629:
1626:
1620:
1616:
1610:
1606:
1555:
1549:
1546:
1540:
1536:
1530:
1524:
1521:
1515:
1511:
1503:
1500:
1496:
1493:
1488:
1484:
1480:
1449:
1448:
1434:
1420:
1405:
1394:
1391:
1379:
1373:
1370:
1364:
1360:
1354:
1348:
1344:
1320:
1317:
1296:
1292:
1237:
1234:
1202:
1199:
1148:starts from a
1125:
1121:
1117:
1091:
1090:
1081:that object's
1079:
1004:
1003:
1001:
1000:
993:
986:
978:
975:
974:
973:
972:
959:
942:
941:
937:
936:
931:
926:
921:
916:
911:
906:
901:
896:
891:
886:
881:
876:
871:
866:
861:
856:
851:
846:
841:
836:
831:
826:
821:
815:
814:
811:
810:
807:
806:
803:
802:
783:
782:
777:
772:
767:
765:Coriolis force
762:
761:
760:
750:
745:
740:
734:
733:
728:
727:
724:
723:
719:
718:
713:
708:
707:
706:
701:
691:
686:
681:
674:
663:
662:
661:
656:
643:
642:
637:
632:
627:
620:
615:
610:
604:
603:
600:
599:
596:
595:
592:
591:
588:
587:
582:
577:
572:
567:
562:
556:
550:
548:
541:
538:
535:
534:
531:
530:
526:
525:
520:
515:
510:
505:
500:
495:
490:
484:
479:
473:
468:
457:
452:
447:
442:
437:
436:
435:
430:
420:
415:
410:
405:
399:
398:
395:
394:
391:
390:
386:
385:
380:
375:
370:
365:
360:
355:
350:
344:
343:
340:
339:
336:
335:
333:
332:
327:
322:
316:
313:
312:
307:
293:
290:
284:
280:
274:
256:
255:
249:
248:
240:
239:
226:
223:
217:
209:
197:
191:
190:
173:
169:
165:
159:
153:
149:
142:
136:
133:
127:
123:
117:
113:
101:
96:
93:
92:
87:
81:
80:
75:
73:Common symbols
72:
69:
68:
63:air resistance
61:In vacuum (no
60:
59:
51:
50:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6631:
6620:
6617:
6615:
6612:
6610:
6607:
6605:
6602:
6601:
6599:
6582:
6573:
6568:
6565:
6557:
6552:
6549:
6547:
6544:
6542:
6533:
6528:
6525:
6517:
6512:
6509:
6507:
6504:
6503:
6500:
6491:
6486:
6481:
6476:
6471:
6466:
6463:
6461:
6452:
6447:
6442:
6441:
6435:
6432:
6430:
6427:
6425:
6416:
6411:
6406:
6401:
6396:
6391:
6388:
6386:
6374:
6369:
6364:
6359:
6356:
6354:
6351:
6350:
6347:
6343:
6331:
6323:
6320:
6318:
6309:
6303:
6298:
6293:
6290:
6288:
6285:
6283:
6279:
6267:
6259:
6256:
6254:
6250:
6241:
6236:
6231:
6226:
6223:
6221:
6197:
6194:
6182:
6179:
6176:
6175:
6172:
6170:
6168:
6159:
6154:
6151:
6148:
6146:
6143:
6140:
6136:
6132:
6127:
6125:
6120:
6115:
6112:
6109:
6108:
6105:
6096:
6095:
6089:
6086:
6084:
6081:
6079:
6074:
6069:
6066:
6064:
6061:
6060:
6057:
6055:
6046:
6045:
6039:
6036:
6034:
6029:
6025:
6022:
6020:
6018:
6013:
6008:
6005:
6003:
6000:
5999:
5996:
5994:
5985:
5984:
5978:
5973:
5968:
5967:angular speed
5965:
5963:
5959:
5953:
5952:
5946:
5939:
5934:
5927:
5922:
5918:
5915:
5910:
5905:
5899:
5894:
5891:
5889:
5884:
5879:
5874:
5869:
5866:
5864:
5860:
5854:
5849:
5845:
5842:
5841:
5837:
5829:
5825:
5823:
5818:
5817:
5811:
5806:
5801:
5798:
5796:
5793:
5791:
5786:
5781:
5778:
5776:
5772:
5766:
5760:
5754:
5749:
5743:
5738:
5735:
5733:
5730:
5729:
5726:
5724:
5722:
5717:
5712:
5709:
5706:
5704:
5702:
5697:
5692:
5689:
5687:
5682:
5677:
5674:
5671:
5670:
5666:
5662:
5659:
5655:
5652:
5649:
5646:
5643:
5640:
5637:
5636:
5626:
5621:
5617:
5614:
5607:
5602:
5600:
5595:
5593:
5588:
5587:
5584:
5572:
5569:
5567:
5564:
5562:
5559:
5556:
5552:
5549:
5546:
5542:
5539:
5537:
5534:
5533:
5530:
5523:
5522:Differentiate
5519:
5515:
5514:
5511:
5507:
5500:
5495:
5493:
5488:
5486:
5481:
5480:
5477:
5470:
5467:
5464:
5461:
5460:
5456:
5447:
5445:0-375-72720-5
5441:
5437:
5436:
5431:
5430:Greene, Brian
5425:
5422:
5411:
5407:
5401:
5398:
5393:
5387:
5383:
5382:
5374:
5371:
5366:
5360:
5356:
5355:
5347:
5344:
5339:
5333:
5329:
5328:
5320:
5317:
5312:
5306:
5302:
5301:
5293:
5290:
5277:
5273:
5266:
5263:
5258:
5256:9780495386933
5252:
5248:
5247:
5239:
5236:
5233:
5228:
5222:
5218:
5217:
5209:
5206:
5203:
5198:
5192:
5188:
5187:
5179:
5176:
5171:
5165:
5161:
5154:
5151:
5146:
5140:
5136:
5132:
5131:
5123:
5120:
5115:
5109:
5105:
5101:
5100:
5092:
5089:
5082:
5077:
5074:
5072:
5069:
5065:
5062:
5060:
5057:
5055:
5052:
5050:
5047:
5045:
5042:
5039:
5036:
5034:
5031:
5030:
5025:
5019:
5016:
5008:
5003:
4998:
4993:
4989:
4988:
4979:
4977:
4974:
4966:
4961:
4958:
4957:
4948:
4940:
4938:
4935:
4930:
4927:
4926:
4913:
4908:
4900:
4898:
4895:
4892:
4891:
4884:
4880:
4873:
4866:
4859:
4851:
4840:
4838:
4836:
4832:
4828:
4822:
4814:
4812:
4810:
4806:
4801:
4798:
4792:
4788:
4780:
4775:
4773:
4760:
4753:
4748:
4744:
4740:
4735:
4730:
4726:
4722:
4717:
4712:
4708:
4702:
4694:
4669:
4664:
4660:
4656:
4651:
4647:
4643:
4638:
4634:
4630:
4603:
4598:
4594:
4590:
4586:
4582:
4577:
4573:
4569:
4566:
4563:
4559:
4553:
4549:
4545:
4542:
4537:
4533:
4512:
4505:
4500:
4496:
4492:
4487:
4482:
4478:
4472:
4464:
4451:
4435:
4430:
4426:
4422:
4417:
4413:
4409:
4382:
4377:
4373:
4369:
4365:
4361:
4356:
4352:
4348:
4345:
4342:
4338:
4332:
4328:
4324:
4321:
4316:
4312:
4292:
4287:
4283:
4279:
4275:
4271:
4266:
4262:
4258:
4255:
4252:
4248:
4242:
4238:
4234:
4231:
4226:
4222:
4213:
4205:
4203:
4189:
4181:
4176:
4163:
4160:
4157:
4154:
4149:
4145:
4124:
4104:
4081:
4078:
4072:
4069:
4049:
4029:
4021:
4016:
4014:
4010:
4006:
4002:
3998:
3994:
3989:
3976:
3965:
3961:
3957:
3954:
3933:
3931:
3919:
3914:
3911:
3906:
3903:
3882:
3874:
3873:
3872:angular speed
3856:
3847:
3834:
3804:
3780:
3776:
3770:
3767:
3710:
3707:
3704:
3701:
3698:
3678:
3658:
3638:
3618:
3611:
3607:
3604:
3592:
3586:
3581:
3577:
3571:
3566:
3562:
3540:
3520:
3512:
3511:
3510:
3507:
3503:
3493:
3489:
3479:
3472:
3463:
3456:
3447:
3440:
3428:
3426:
3424:
3395:
3380:
3357:
3342:
3325:
3311:
3296:
3273:
3258:
3241:
3227:
3212:
3205:
3204:
3203:
3200:
3183:
3175:
3165:
3159:
3144:
3137:
3134:
3129:
3122:
3118:
3112:
3110:
3102:
3093:
3089:
3080:
3072:
3067:
3057:
3055:
3047:
3032:
3028:
3021:
3010:
3005:
2994:
2987:
2984:
2978:
2973:
2963:
2958:
2954:
2942:
2939:
2933:
2930:
2925:
2915:
2910:
2900:
2898:
2890:
2870:
2866:
2862:
2857:
2844:
2836:
2833:
2785:
2781:
2777:
2774:(also called
2773:
2767:
2763:
2758:
2756:
2752:
2748:
2740:
2735:
2727:
2723:Special cases
2722:
2720:
2718:
2713:
2711:
2707:
2703:
2668:
2663:
2659:
2653:
2612:
2609:
2604:
2601:
2595:
2574:
2573:
2572:
2566:
2562:
2557:
2552:
2548:
2547:normal vector
2540:
2534:
2517:
2495:
2490:
2486:
2480:
2460:
2457:
2452:
2449:
2443:
2441:
2430:
2427:
2408:
2399:
2393:
2390:
2370:
2367:
2362:
2359:
2353:
2351:
2340:
2337:
2327:
2321:
2319:
2300:
2298:
2292:
2288:
2281:
2277:
2272:
2256:
2246:
2240:
2232:
2218:
2194:
2190:
2173:
2167:
2144:
2138:
2135:
2126:
2120:
2112:
2095:
2089:
2086:
2080:
2064:
2052:
2042:
2036:
2028:
2023:
2019:
2011:
2009:
2007:
2003:
1998:
1993:
1984:
1978:
1966:
1961:
1951:
1931:
1928:
1914:
1910:
1906:
1901:
1899:
1898:accelerometer
1895:
1891:
1889:
1880:
1878:
1876:
1872:
1868:
1865:
1861:
1853:
1851:
1838:
1835:
1832:
1823:
1820:
1802:
1798:
1793:
1788:
1786:
1774:
1771:
1768:
1759:
1756:
1729:
1725:
1718:
1714:
1709:
1705:
1700:
1698:
1694:
1690:
1685:
1672:
1664:
1660:
1656:
1644:
1640:
1633:
1627:
1624:
1614:
1608:
1590:
1585:
1580:
1570:
1553:
1547:
1544:
1534:
1528:
1522:
1501:
1494:
1482:
1469:
1465:
1461:
1460:infinitesimal
1457:
1444:
1440:
1435:
1430:
1426:
1421:
1416:
1412:
1407:
1406:
1403:
1399:
1392:
1390:
1377:
1371:
1352:
1318:
1282:
1278:
1269:
1265:
1257:
1252:
1251:time interval
1242:
1235:
1229:
1223:
1217:
1207:
1200:
1198:
1196:
1192:
1188:
1184:
1180:
1176:
1172:
1168:
1163:
1159:
1155:
1151:
1147:
1142:
1123:
1100:
1096:
1088:
1084:
1080:
1077:
1073:
1069:
1068:
1067:
1065:
1061:
1058:
1054:
1050:
1046:
1042:
1038:
1034:
1030:
1026:
1022:
1014:
1010:
999:
994:
992:
987:
985:
980:
979:
977:
976:
970:
960:
957:
952:
946:
945:
944:
943:
935:
932:
930:
927:
925:
922:
920:
917:
915:
912:
910:
907:
905:
902:
900:
897:
895:
892:
890:
887:
885:
882:
880:
877:
875:
872:
870:
867:
865:
862:
860:
857:
855:
852:
850:
847:
845:
842:
840:
837:
835:
832:
830:
827:
825:
822:
820:
817:
816:
809:
808:
801:
797:
793:
789:
786:
785:
781:
778:
776:
773:
771:
768:
766:
763:
759:
756:
755:
754:
751:
749:
746:
744:
741:
739:
736:
735:
731:
726:
725:
717:
714:
712:
709:
705:
702:
700:
697:
696:
695:
692:
690:
687:
685:
682:
680:
675:
672:
668:
665:
664:
660:
657:
654:
650:
646:
645:
641:
638:
636:
633:
631:
628:
626:
621:
619:
616:
614:
611:
609:
606:
605:
598:
597:
586:
583:
581:
578:
576:
573:
571:
568:
566:
563:
561:
558:
557:
555:
554:
549:
546:
545:
540:
539:
533:
532:
524:
521:
519:
516:
514:
511:
509:
506:
504:
501:
499:
496:
494:
491:
489:
485:
483:
480:
478:
474:
472:
469:
466:
462:
458:
456:
453:
451:
448:
446:
443:
441:
438:
434:
431:
429:
426:
425:
424:
421:
419:
416:
414:
411:
409:
406:
404:
401:
400:
393:
392:
384:
381:
379:
376:
374:
371:
369:
366:
364:
361:
359:
356:
354:
351:
349:
346:
345:
338:
337:
331:
328:
326:
323:
321:
318:
317:
314:
310:
291:
288:
278:
272:
258:
257:
254:
250:
246:
245:
224:
221:
198:
196:
192:
188:
171:
167:
163:
151:
147:
140:
134:
131:
121:
115:
102:
94:
91:
88:
86:
82:
79:
76:
70:
64:
57:
52:
47:
44:
40:
33:
19:
6604:Acceleration
6571:
6555:
6531:
6515:
6489:
6479:
6469:
6450:
6439:
6438:
6414:
6404:
6394:
6372:
6362:
6307:
6296:
6239:
6229:
6157:
6141:
6138:
6134:
6130:
6118:
6093:
6092:
6088:angular jerk
6072:
6043:
6042:
6011:
6007:acceleration
6006:
5982:
5981:
5971:
5950:
5949:
5937:
5925:
5908:
5897:
5882:
5872:
5852:
5815:
5814:
5804:
5784:
5771:displacement
5764:
5758:
5752:
5741:
5715:
5695:
5680:
5664:
5657:
5561:Acceleration
5560:
5541:Displacement
5434:
5424:
5413:. Retrieved
5409:
5400:
5380:
5373:
5353:
5346:
5326:
5319:
5299:
5292:
5280:. Retrieved
5275:
5272:"Chain Rule"
5265:
5245:
5238:
5215:
5208:
5185:
5178:
5159:
5153:
5129:
5122:
5098:
5091:
5017:
4991:
4975:
4936:
4896:
4882:
4824:
4802:
4794:
4209:
4177:
4017:
4005:pseudo force
3996:
3990:
3934:
3871:
3848:
3725:
3608:For a given
3505:
3499:
3477:
3461:
3445:
3420:
3201:
2869:time elapsed
2861:displacement
2858:
2775:
2759:
2750:
2746:
2745:
2714:
2699:
2555:
2550:
2538:
2535:
2301:
2290:
2286:
2279:
2275:
2192:
2188:
2060:
2050:
2040:
1996:
1982:
1902:
1892:
1887:
1884:
1857:
1800:
1796:
1789:
1727:
1723:
1716:
1712:
1701:
1686:
1588:
1578:
1568:
1453:
1442:
1438:
1428:
1424:
1414:
1410:
1401:
1274:
1267:
1263:
1255:
1227:
1221:
1215:
1178:
1175:deceleration
1174:
1143:
1092:
1056:
1025:acceleration
1024:
1018:
798: /
794: /
792:displacement
790: /
651: /
613:Displacement
551:
542:
536:Formulations
523:Virtual work
463: /
403:Acceleration
402:
396:Fundamentals
85:SI unit
77:
49:Acceleration
43:
18:Accelerating
5828:solid angle
5038:Four-vector
4860:, or cm/s)
4853:Base value
4841:Conversions
4137:. That is,
3995:, directed
3500:In uniform
1888:centripetal
1881:Other forms
1219:, velocity
1213:, position
1189:burning in
1187:retrorocket
1179:retardation
1013:Drag racing
934:von Neumann
601:Core topics
6598:Categories
6563:m s, N m s
6539:m s,
6485:Lagrangian
6410:Lagrangian
5650:Dimensions
5638:Dimensions
5506:Kinematics
5415:2024-01-04
5083:References
2865:velocities
2732:See also:
2297:chain rule
2016:See also:
1860:dimensions
1468:derivative
1191:spacecraft
1150:standstill
1037:kinematics
869:d'Alembert
849:Maupertuis
812:Scientists
694:Rigid body
368:Kinematics
6579:ms,
6198:˙
5921:frequency
5848:frequency
5518:Integrate
5186:Mechanics
4190:α
4161:α
4105:ω
4082:˙
4079:ω
4070:α
4050:α
3962:ω
3958:−
3904:ω
3805:⋅
3771:−
3705:ω
3619:ω
3166:−
3145:⋅
2768:strength
2762:free fall
1942:⟹
1824:∫
1814:Δ
1794:function
1760:∫
1750:Δ
1520:Δ
1510:Δ
1499:→
1492:Δ
1369:Δ
1359:Δ
1347:¯
1316:Δ
1291:Δ
1195:reference
1053:direction
1049:magnitude
1021:mechanics
914:Liouville
796:frequency
716:Vibration
433:potential
358:Continuum
353:Celestial
330:Textbooks
222:−
195:Dimension
6523:m s, N s
6346:J s
6342:m s
6317:m s
6278:m s
6249:m s
6225:momentum
5878:velocity
5748:position
5737:distance
5691:absement
5616:SI units
5551:Velocity
5545:Distance
5536:Absement
5282:2 August
5026:See also
2755:velocity
2751:constant
2567:at time
2063:function
1990:is the
1708:integral
1464:calculus
1281:velocity
1183:inertial
1171:negative
1162:reaction
1033:velocity
969:Category
894:Hamilton
879:Lagrange
874:Clairaut
839:Horrocks
800:velocity
770:Pendulum
758:reactive
730:Rotation
699:dynamics
649:Inertial
635:Friction
518:Velocity
493:Momentum
373:Kinetics
363:Dynamics
341:Branches
325:Timeline
6551:rotatum
6330:actergy
6266:actergy
6235:impulse
6155::
5906::
5836:rad, sr
5049:Inertia
5005:32.1740
5000:980.665
4932:30.4800
4928:1 ft/s
4827:gravity
3423:Galileo
2747:Uniform
2553:), and
1702:By the
1697:scalars
1146:vehicle
1027:is the
929:Koopman
889:Poisson
884:Laplace
829:Huygens
824:Galileo
669: (
608:Damping
461:Inertia
455:Impulse
428:kinetic
378:Statics
348:Applied
320:History
6465:energy
6446:moment
6434:torque
6390:energy
6368:weight
6340:
6322:action
6315:
6276:
6258:action
6247:
6218:
6165:
6137:⟩ = ∑
6101:
6052:
5991:
5442:
5388:
5361:
5334:
5307:
5253:
5223:
5193:
5166:
5141:
5110:
4959:1 m/s
3997:toward
3202:where
2778:). By
2536:where
2515:
2020:, and
1980:where
1869:. The
1693:vector
1072:forces
1045:vector
1041:motion
967:
919:Appell
904:Cauchy
899:Jacobi
844:Halley
834:Newton
819:Kepler
671:linear
667:Motion
513:Torque
488:Moment
423:Energy
413:Couple
6567:power
6527:power
6497:m s,
6458:m s,
6422:m s,
6383:m s,
6358:force
5868:speed
5800:angle
5555:Speed
5010:9.806
4981:0.101
4968:3.280
4950:0.031
4942:0.304
4915:1.019
4902:0.032
4631:=<
4410:=<
3935:Thus
3506:speed
3393:, and
2784:force
2186:with
1909:force
1854:Units
1456:limit
1060:force
924:Gibbs
909:Routh
864:Euler
503:Speed
498:Space
440:Force
6511:yank
6475:work
6400:work
6114:mass
6068:jerk
5780:area
5711:time
5676:time
5566:Jerk
5440:ISBN
5386:ISBN
5359:ISBN
5332:ISBN
5305:ISBN
5284:2016
5251:ISBN
5221:ISBN
5191:ISBN
5164:ISBN
5139:ISBN
5108:ISBN
4952:0810
4910:0.01
4904:8084
4865:ft/s
4789:and
4670:>
4436:>
2782:the
2708:and
1992:mass
1792:jerk
1736:vs.
1277:time
1093:The
1083:mass
1051:and
1029:rate
508:Time
471:Mass
6545:MLT
6460:N m
6428:MLT
6381:kg
6286:MLT
6282:J s
6253:N s
6099:rad
6077:m s
6050:rad
6017:m s
5989:rad
5913:m s
5888:m s
5822:rad
5701:m s
4983:972
4963:100
4944:800
4872:m/s
4858:Gal
3895:as
2749:or
2635:and
1915:):
1903:In
1586:of
1487:lim
1260:of
1258:→ 0
1177:or
1141:).
1103:m⋅s
1057:net
1019:In
6600::
6577:kg
6569::
6561:kg
6553::
6537:kg
6529::
6521:kg
6513::
6505:MT
6495:kg
6487::
6483:,
6477::
6473:,
6467::
6456:kg
6448::
6444:,
6436::
6420:kg
6412::
6408:,
6402::
6398:,
6392::
6370::
6366:,
6360::
6352:MT
6344:,
6338:kg
6332::
6328:,
6326:𝒮
6324::
6313:kg
6304::
6300:,
6294::
6280:,
6274:kg
6268::
6264:,
6262:𝒮
6260::
6251:,
6245:kg
6237::
6233:,
6227::
6216:kg
6183::
6177:MT
6163:kg
6149:ML
6124:kg
6116::
6090::
6070::
6040::
6009::
5979::
5975:,
5969::
5962:Hz
5960:,
5947::
5942:,
5935::
5930:,
5923::
5895::
5880::
5876:,
5870::
5863:Hz
5861:,
5850::
5830::
5812::
5808:,
5802::
5782::
5769:,
5762:,
5756:,
5750::
5745:,
5739::
5713::
5693::
5678::
5520:…
5516:←
5432:.
5408:.
5274:.
5137:.
5135:27
5106:.
5012:65
4990:1
4970:84
4922:10
4917:72
4888:)
4881:,
4874:)
4867:)
4452:as
3691:.
2871::
2719:.
2269:a
2004:,
1900:.
1871:SI
1691:,
1596::
1404::
1283:,
1266:/Δ
1105:,
1095:SI
1023:,
6581:W
6572:P
6556:P
6541:W
6532:P
6516:Y
6499:J
6490:L
6480:W
6470:E
6451:M
6440:τ
6424:J
6415:L
6405:W
6395:E
6385:N
6376:g
6373:F
6363:F
6334:ℵ
6308:L
6306:Δ
6297:L
6270:ℵ
6240:J
6230:p
6220:s
6195:m
6167:m
6158:I
6142:x
6139:m
6135:x
6133:⟨
6131:M
6119:m
6110:M
6103:s
6094:ζ
6082:T
6073:j
6062:T
6054:s
6044:α
6033:s
6023:T
6012:a
6001:T
5993:s
5983:ω
5972:ω
5958:s
5951:n
5938:n
5926:f
5916:T
5909:h
5901:,
5898:ν
5883:v
5873:v
5859:s
5853:f
5843:T
5832:Ω
5816:θ
5805:θ
5794:1
5790:m
5785:A
5775:m
5765:x
5759:s
5753:r
5742:d
5731:1
5721:s
5716:t
5707:T
5696:A
5686:s
5681:t
5672:T
5665:θ
5658:θ
5653:1
5647:L
5644:L
5641:1
5605:e
5598:t
5591:v
5557:)
5553:(
5547:)
5543:(
5524:→
5498:e
5491:t
5484:v
5448:.
5418:.
5394:.
5367:.
5340:.
5313:.
5286:.
5259:.
5229:.
5199:.
5172:.
5147:.
5116:.
5104:3
5018:1
4995:0
4992:g
4976:1
4937:1
4920:×
4897:1
4886:0
4883:g
4877:(
4870:(
4863:(
4856:(
4761:.
4754:2
4749:z
4745:a
4741:+
4736:2
4731:y
4727:a
4723:+
4718:2
4713:x
4709:a
4703:=
4699:|
4695:a
4691:|
4665:z
4661:a
4657:,
4652:y
4648:a
4644:,
4639:x
4635:a
4626:a
4604:.
4599:2
4595:t
4591:d
4587:/
4583:z
4578:2
4574:d
4570:=
4567:t
4564:d
4560:/
4554:z
4550:v
4546:d
4543:=
4538:z
4534:a
4513:.
4506:2
4501:y
4497:a
4493:+
4488:2
4483:x
4479:a
4473:=
4469:|
4465:a
4461:|
4431:y
4427:a
4423:,
4418:x
4414:a
4405:a
4383:.
4378:2
4374:t
4370:d
4366:/
4362:y
4357:2
4353:d
4349:=
4346:t
4343:d
4339:/
4333:y
4329:v
4325:d
4322:=
4317:y
4313:a
4293:,
4288:2
4284:t
4280:d
4276:/
4272:x
4267:2
4263:d
4259:=
4256:t
4253:d
4249:/
4243:x
4239:v
4235:d
4232:=
4227:x
4223:a
4182:(
4164:.
4158:r
4155:=
4150:t
4146:a
4125:r
4073:=
4030:r
3977:.
3972:r
3966:2
3955:=
3949:c
3945:a
3920:.
3915:r
3912:v
3907:=
3883:r
3857:v
3835:.
3827:|
3822:r
3817:|
3811:r
3798:|
3793:r
3788:|
3781:2
3777:v
3768:=
3762:c
3758:a
3735:r
3711:.
3708:r
3702:=
3699:v
3679:r
3659:v
3639:r
3593:.
3587:r
3582:2
3578:v
3572:=
3567:c
3563:a
3541:r
3521:v
3478:a
3462:v
3446:r
3404:a
3381:t
3361:)
3358:t
3355:(
3351:v
3326:0
3321:v
3309:,
3297:t
3277:)
3274:t
3271:(
3267:s
3242:0
3237:s
3213:t
3184:,
3181:]
3176:0
3171:s
3163:)
3160:t
3157:(
3153:s
3149:[
3142:a
3138:2
3135:+
3130:2
3123:0
3119:v
3113:=
3106:)
3103:t
3100:(
3094:2
3090:v
3081:t
3077:a
3073:+
3068:0
3063:v
3058:=
3051:)
3048:t
3045:(
3041:v
3033:t
3029:)
3025:)
3022:t
3019:(
3015:v
3011:+
3006:0
3001:v
2995:(
2988:2
2985:1
2979:+
2974:0
2969:s
2964:=
2959:2
2955:t
2950:a
2943:2
2940:1
2934:+
2931:t
2926:0
2921:v
2916:+
2911:0
2906:s
2901:=
2894:)
2891:t
2888:(
2884:s
2845:.
2841:g
2837:m
2834:=
2828:g
2824:F
2799:g
2795:F
2771:g
2682:n
2676:u
2669:r
2664:2
2660:v
2654:=
2648:c
2642:a
2627:t
2621:u
2613:t
2610:d
2605:v
2602:d
2596:=
2590:t
2584:a
2569:t
2556:r
2542:n
2539:u
2518:,
2509:n
2503:u
2496:r
2491:2
2487:v
2481:+
2475:t
2469:u
2461:t
2458:d
2453:v
2450:d
2444:=
2431:t
2428:d
2420:t
2414:u
2409:d
2403:)
2400:t
2397:(
2394:v
2391:+
2385:t
2379:u
2371:t
2368:d
2363:v
2360:d
2354:=
2341:t
2338:d
2332:v
2328:d
2322:=
2314:a
2291:t
2287:u
2282:)
2280:t
2278:(
2276:v
2257:,
2250:)
2247:t
2244:(
2241:v
2236:)
2233:t
2230:(
2226:v
2219:=
2213:t
2207:u
2195:)
2193:t
2191:(
2189:v
2174:,
2171:)
2168:t
2165:(
2159:t
2153:u
2148:)
2145:t
2142:(
2139:v
2136:=
2130:)
2127:t
2124:(
2121:v
2116:)
2113:t
2110:(
2106:v
2099:)
2096:t
2093:(
2090:v
2087:=
2084:)
2081:t
2078:(
2074:v
2054:c
2051:a
2044:t
2041:a
1997:a
1988:m
1983:F
1967:,
1962:m
1958:F
1952:=
1948:a
1936:a
1932:m
1929:=
1925:F
1867:T
1864:L
1839:.
1836:t
1833:d
1828:j
1821:=
1817:a
1803:)
1801:t
1799:(
1797:j
1775:.
1772:t
1769:d
1764:a
1757:=
1753:v
1738:t
1734:a
1730:)
1728:t
1726:(
1724:v
1719:)
1717:t
1715:(
1713:a
1673:.
1665:2
1661:t
1657:d
1651:x
1645:2
1641:d
1634:=
1628:t
1625:d
1619:v
1615:d
1609:=
1605:a
1594:t
1589:x
1579:x
1574:t
1569:v
1554:.
1548:t
1545:d
1539:v
1535:d
1529:=
1523:t
1514:v
1502:0
1495:t
1483:=
1479:a
1447:.
1445:)
1443:t
1441:(
1439:s
1433:;
1431:)
1429:t
1427:(
1425:v
1419:;
1417:)
1415:t
1413:(
1411:a
1378:.
1372:t
1363:v
1353:=
1343:a
1319:t
1295:v
1271:.
1268:t
1264:v
1262:Δ
1256:t
1254:Δ
1247:t
1231:.
1228:a
1222:v
1216:r
1211:m
1124:2
1120:s
1116:m
1101:(
997:e
990:t
983:v
673:)
292:t
289:d
283:p
279:d
273:=
268:F
225:2
216:T
208:L
172:2
168:t
164:d
158:x
152:2
148:d
141:=
135:t
132:d
126:v
122:d
116:=
112:a
78:a
41:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
