939:
3028:
3366:
4198:
952:
2029:
1538:
1389:
4190:
1657:
1964:
1400:
3794:
3001:
1258:
4143:
2172:
2809:
3369:
In a train of identical pulses, the instantaneous power is a periodic function of time. The ratio of the pulse duration to the period is equal to the ratio of the average power to the peak power. It is also called the duty cycle (see text for
2381:
2052:
Power in mechanical systems is the combination of forces and movement. In particular, power is the product of a force on an object and the object's velocity, or the product of a torque on a shaft and the shaft's angular velocity.
2916:
1549:
2495:
3935:
3675:
2723:
1841:
4211:
The activity of a motor is the work done per second, ... Where the joule is employed as the unit of work, the international unit of activity is the joule-per-second, or, as it is commonly called, the watt. (p.
1200:
1826:
225:
3680:
3314:
2924:
3873:
293:
317:
2085:
1253:
2732:
4321:
3102:
4027:
1126:
3597:
1533:{\displaystyle W=\int _{C}\mathbf {F} \cdot d\mathbf {r} =\int _{\Delta t}\mathbf {F} \cdot {\frac {d\mathbf {r} }{dt}}\ dt=\int _{\Delta t}\mathbf {F} \cdot \mathbf {v} \,dt.}
3347:
2269:
2427:
2289:
3482:
1384:{\displaystyle P={\frac {dW}{dt}}={\frac {d}{dt}}\left(\mathbf {F} \cdot \mathbf {x} \right)=\mathbf {F} \cdot {\frac {d\mathbf {x} }{dt}}=\mathbf {F} \cdot \mathbf {v} .}
3560:
4929:
2583:
2852:
2531:
3816:
2008:
3401:
3216:
3177:
3134:
1022:
Specifying power in particular systems may require attention to other quantities; for example, the power involved in moving a ground vehicle is the product of the
4125:
3967:
3502:
3421:
983:
2452:
3878:
572:
3602:
2659:
4314:
691:
1146:
1770:
5019:
664:
1828:
It is the average amount of work done or energy converted per unit of time. Average power is often called "power" when the context makes it clear.
3245:
938:
4307:
646:
1143:
We will now show that the mechanical power generated by a force F on a body moving at the velocity v can be expressed as the product:
175:
1652:{\displaystyle P={\frac {dW}{dt}}={\frac {d}{dt}}\int _{\Delta t}\mathbf {F} \cdot \mathbf {v} \,dt=\mathbf {F} \cdot \mathbf {v} .}
976:
5055:
5030:
4991:
3821:
4110:
2613:
If a mechanical system has no losses, then the input power must equal the output power. This provides a simple formula for the
1543:
312:
249:
1959:{\displaystyle P=\lim _{\Delta t\to 0}P_{\mathrm {avg} }=\lim _{\Delta t\to 0}{\frac {\Delta W}{\Delta t}}={\frac {dW}{dt}}.}
307:
567:
4333:
3045:
1675:
1004:
3972:
1085:
562:
5336:
969:
956:
717:
640:
405:
4042:
3319:
2214:
1222:
636:
437:
3789:{\displaystyle P_{\mathrm {avg} }={\frac {1}{T}}\int _{0}^{T}p(t)\,dt={\frac {\varepsilon _{\mathrm {pulse} }}{T}}.}
2996:{\displaystyle \mathrm {MA} ={\frac {T_{\text{B}}}{T_{\text{A}}}}={\frac {\omega _{\text{A}}}{\omega _{\text{B}}}}.}
2388:
856:
745:
671:
531:
464:
4962:
4767:
4621:
3511:
610:
3027:
5321:
4734:
886:
730:
2547:
5331:
4745:
4131:
876:
836:
600:
2167:{\displaystyle W_{C}=\int _{C}\mathbf {F} \cdot \mathbf {v} \,dt=\int _{C}\mathbf {F} \cdot d\mathbf {x} ,}
1981:
1027:
881:
698:
4880:
4750:
4488:
3567:
3350:
2804:{\displaystyle \mathrm {MA} ={\frac {F_{\text{B}}}{F_{\text{A}}}}={\frac {v_{\text{A}}}{v_{\text{B}}}}.}
891:
866:
552:
370:
4270:
per kilogram, while detonating TNT produces about 4.7 megajoules per kilogram. For the coal value, see
1736:, but because the TNT reaction releases energy more quickly, it delivers more power than the coal. If
5202:
5127:
4755:
4527:
4236:
2919:
2726:
2614:
2602:
1717:
911:
906:
871:
779:
775:
767:
757:
547:
540:
296:
168:
4933:
4662:
4610:
4330:
4052:
3564:
The peak power is not always readily measurable, however, and the measurement of the average power
686:
627:
605:
350:
345:
340:
240:
3365:
3005:
These relations are important because they define the maximum performance of a device in terms of
3426:
2510:
2200:
1071:
1051:
1047:
816:
557:
432:
400:
360:
4905:
2849:
are the torque and angular velocity of the output. If there are no losses in the system, then
4952:
4870:
4706:
4465:
4135:
2506:
826:
783:
740:
735:
676:
452:
442:
335:
5039:
5009:
4975:
4694:
4650:
4605:
4244:
3239:
3219:
2516:
2441:
2204:
1701:
1055:
1043:
1023:
1016:
921:
901:
846:
841:
787:
762:
617:
475:
420:
395:
155:
136:
3801:
4069:
4037:
3377:
3192:
3153:
3110:
2065:
1744:
1075:
916:
861:
811:
806:
725:
4273:
4240:
5326:
5228:
5192:
5117:
4898:
4805:
4785:
4675:
4576:
4290:
3952:
3487:
3406:
3022:
3006:
2534:
2376:{\displaystyle P(t)={\frac {dW}{dt}}=\mathbf {F} \cdot \mathbf {v} =-{\frac {dU}{dt}}.}
1079:
943:
851:
752:
469:
415:
5315:
5102:
4970:
4684:
4064:
3599:
is more commonly performed by an instrument. If one defines the energy per pulse as
2594:
2079:
831:
658:
1831:
Instantaneous power is the limiting value of the average power as the time interval
5177:
5063:
4999:
4724:
4507:
4418:
4047:
896:
821:
510:
390:
55:
4293:. Neither value includes the weight of oxygen from the air used during combustion.
4177:. (p. xxviii) ... ACTIVITY. Power or rate of doing work; unit, the watt. (p. 435)
4545:
4074:
3031:
2911:{\displaystyle P=T_{\text{A}}\omega _{\text{A}}=T_{\text{B}}\omega _{\text{B}},}
4299:
2028:
4139:
4058:
3010:
2057:
1691:
1687:
681:
355:
4638:
4565:
4553:
4267:
2541:
2061:
2012:
In the context of energy conversion, it is more customary to use the symbol
703:
5047:
4983:
4942:
4841:
4595:
4454:
4408:
3231:
2590:
2208:
2037:
1213:
1031:
622:
505:
480:
117:
62:
3034:
photograph of electrical wires of the
Boulder Dam Power Units, 1941–1942
2490:{\displaystyle P(t)={\boldsymbol {\tau }}\cdot {\boldsymbol {\omega }},}
5268:
3235:
3180:
1709:
1059:
595:
448:
365:
130:
41:
3930:{\displaystyle {\frac {P_{\mathrm {avg} }}{P_{0}}}={\frac {\tau }{T}}}
5182:
5163:
5151:
5107:
5085:
4539:
4438:
4403:
4249:
4224:
3670:{\displaystyle \varepsilon _{\mathrm {pulse} }=\int _{0}^{T}p(t)\,dt}
3223:
3145:
2432:
2279:
are the beginning and end of the path along which the work was done.
2045:
1039:
1035:
1000:
654:
500:
410:
149:
92:
70:
2718:{\displaystyle P=F_{\text{B}}v_{\text{B}}=F_{\text{A}}v_{\text{A}},}
5216:
5141:
5075:
4679:
4585:
4580:
4517:
4492:
3364:
3141:
3026:
2041:
2027:
1683:
1012:
490:
485:
427:
111:
66:
2813:
The similar relationship is obtained for rotating systems, where
1195:{\displaystyle P={\frac {dW}{dt}}=\mathbf {F} \cdot \mathbf {v} }
5298:
5258:
4831:
4497:
4428:
4393:
3184:
3137:
1821:{\displaystyle P_{\mathrm {avg} }={\frac {\Delta W}{\Delta t}}.}
1748:
1729:
1708:, a logarithmic measure relative to a reference of 1 milliwatt,
1679:
1008:
495:
458:
220:{\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-3}}
98:
46:
4303:
3354:
1733:
1713:
1705:
1697:
3423:, like a train of identical pulses, the instantaneous power
1397:, then the work is expressed in terms of the line integral:
3309:{\displaystyle P=I\cdot V=I^{2}\cdot R={\frac {V^{2}}{R}},}
1046:
of its output shaft. Likewise, the power dissipated in an
3868:{\displaystyle P_{0}\tau =\varepsilon _{\mathrm {pulse} }}
2729:
of the system (output force per input force) is given by
1974:
is constant, the amount of work performed in time period
1674:
The dimension of power is energy divided by time. In the
288:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
3009:
determined by its physical dimensions. See for example
1696:
equals about 745.7 watts. Other units of power include
16:
Amount of energy transferred or converted per unit time
3429:
1686:
per second. Other common and traditional measures are
1659:
Hence the formula is valid for any general situation.
1074:
with respect to time at which work is done; it is the
4908:
3975:
3955:
3881:
3824:
3804:
3683:
3605:
3570:
3514:
3490:
3409:
3380:
3322:
3248:
3195:
3156:
3113:
3048:
2927:
2855:
2831:
are the torque and angular velocity of the input and
2735:
2662:
2550:
2519:
2455:
2391:
2292:
2217:
2088:
1984:
1844:
1773:
1552:
1403:
1261:
1225:
1149:
1088:
252:
178:
3183:(or voltage drop) across the component, measured in
4094:David Halliday; Robert Resnick (1974). "6. Power".
3969:; the power emitted by a source can be written as:
2431:In rotational systems, power is the product of the
2207:(and remembering that force is the negative of the
1732:releases more energy than detonating a kilogram of
167:
76:
53:
40:
28:
23:
4923:
4021:
3961:
3929:
3867:
3810:
3788:
3669:
3591:
3554:
3496:
3476:
3415:
3395:
3341:
3308:
3210:
3171:
3128:
3096:
2995:
2910:
2803:
2717:
2577:
2525:
2489:
2421:
2375:
2263:
2166:
2002:
1958:
1820:
1651:
1532:
1383:
1247:
1194:
1120:
287:
219:
3528:
1892:
1852:
1248:{\displaystyle W=\mathbf {F} \cdot \mathbf {x} }
2056:Mechanical power is also described as the time
1003:transferred or converted per unit time. In the
2656:. If there are no losses in the system, then
4315:
4255:If the watt is assumed as unit of activity...
2385:In one dimension, this can be simplified to:
1728:As a simple example, burning one kilogram of
1690:(hp), comparing to the power of a horse; one
977:
8:
4191:"Electrical Calculations for Rallway Motors"
2629:acting on a point that moves with velocity
2620:Let the input power to a device be a force
4322:
4308:
4300:
4130:(7th revised ed.). Washington, D.C.:
3949:Power is related to intensity at a radius
1662:In older works, power is sometimes called
984:
970:
231:
4910:
4909:
4907:
4248:
4007:
3974:
3954:
3917:
3906:
3889:
3888:
3882:
3880:
3846:
3845:
3829:
3823:
3803:
3759:
3758:
3752:
3742:
3724:
3719:
3705:
3689:
3688:
3682:
3660:
3642:
3637:
3611:
3610:
3604:
3576:
3575:
3569:
3519:
3513:
3489:
3468:
3463:
3445:
3428:
3408:
3379:
3329:
3321:
3292:
3286:
3271:
3247:
3194:
3155:
3112:
3047:
2982:
2972:
2966:
2955:
2945:
2939:
2928:
2926:
2899:
2889:
2876:
2866:
2854:
2790:
2780:
2774:
2763:
2753:
2747:
2736:
2734:
2706:
2696:
2683:
2673:
2661:
2647:acts on a point that moves with velocity
2549:
2518:
2479:
2471:
2454:
2390:
2350:
2339:
2331:
2308:
2291:
2222:
2216:
2156:
2145:
2139:
2125:
2120:
2112:
2106:
2093:
2087:
1983:
1933:
1910:
1895:
1875:
1874:
1855:
1843:
1795:
1779:
1778:
1772:
1767:over that period is given by the formula
1641:
1633:
1623:
1618:
1610:
1601:
1582:
1559:
1551:
1520:
1515:
1507:
1498:
1466:
1460:
1452:
1443:
1431:
1420:
1414:
1402:
1395:variable over a three-dimensional curve C
1373:
1365:
1346:
1340:
1332:
1319:
1311:
1291:
1268:
1260:
1255:. In this case, power can be written as:
1240:
1232:
1224:
1187:
1179:
1156:
1148:
1095:
1087:
269:
263:
254:
253:
251:
208:
202:
201:
194:
188:
187:
180:
179:
177:
4342:
4055:– in the radiative sense, power per area
3136:is the instantaneous power, measured in
2074:on an object that travels along a curve
4086:
3937:are equal. These ratios are called the
2480:
2472:
2282:The power at any point along the curve
1058:flowing through the element and of the
303:
239:
4151:is the time rate of doing work, or if
3484:is also a periodic function of period
1034:of the vehicle. The output power of a
203:
189:
181:
20:
3042:delivered to a component is given by
1724:Average power and instantaneous power
666:Newton's law of universal gravitation
7:
4146:from the original on 23 April 2020.
3097:{\displaystyle P(t)=I(t)\cdot V(t),}
4289:For the TNT value, see the article
4266:Burning coal produces around 15-30
4022:{\displaystyle P(r)=I(4\pi r^{2}).}
3038:The instantaneous electrical power
1121:{\displaystyle P={\frac {dW}{dt}},}
647:Mechanics of planar particle motion
255:
4201:from the original on 23 April 2020
3896:
3893:
3890:
3859:
3856:
3853:
3850:
3847:
3772:
3769:
3766:
3763:
3760:
3696:
3693:
3690:
3624:
3621:
3618:
3615:
3612:
3592:{\displaystyle P_{\mathrm {avg} }}
3583:
3580:
3577:
2932:
2929:
2740:
2737:
1921:
1913:
1896:
1882:
1879:
1876:
1856:
1806:
1798:
1786:
1783:
1780:
1602:
1499:
1444:
14:
4124:Fowle, Frederick E., ed. (1921).
3374:In the case of a periodic signal
2211:of the potential energy) yields:
2190:is the velocity along this path.
1042:that the motor generates and the
3798:One may define the pulse length
3342:{\displaystyle R={\frac {V}{I}}}
2638:and the output power be a force
2340:
2332:
2264:{\displaystyle W_{C}=U(A)-U(B),}
2157:
2146:
2121:
2113:
1642:
1634:
1619:
1611:
1516:
1508:
1467:
1453:
1432:
1421:
1374:
1366:
1347:
1333:
1320:
1312:
1241:
1233:
1188:
1180:
951:
950:
937:
270:
4346:Linear/translational quantities
4111:The Feynman Lectures on Physics
4061:– for linear, two-port networks
2540:In fluid power systems such as
2199:is derivable from a potential (
1678:(SI), the unit of power is the
1544:fundamental theorem of calculus
4013:
3994:
3985:
3979:
3739:
3733:
3657:
3651:
3546:
3543:
3537:
3531:
3464:
3459:
3453:
3446:
3439:
3433:
3390:
3384:
3205:
3199:
3166:
3160:
3123:
3117:
3088:
3082:
3073:
3067:
3058:
3052:
2560:
2554:
2465:
2459:
2422:{\displaystyle P(t)=F\cdot v.}
2401:
2395:
2302:
2296:
2255:
2249:
2240:
2234:
1902:
1862:
1219:, the work done is defined as
1:
4351:Angular/rotational quantities
2544:actuators, power is given by
1747:performed during a period of
1676:International System of Units
1005:International System of Units
573:Koopman–von Neumann mechanics
3477:{\textstyle p(t)=|s(t)|^{2}}
641:Non-inertial reference frame
4127:Smithsonian Physical Tables
4108:Chapter 13, § 3, pp 13-2,3
4043:Orders of magnitude (power)
3555:{\displaystyle P_{0}=\max.}
1682:(W), which is equal to one
1007:, the unit of power is the
568:Appell's equation of motion
438:Inertial frame of reference
5353:
4924:{\displaystyle {\dot {m}}}
4348:
3677:then the average power is
3020:
2036:is needed to lift 75
4622:specific angular momentum
4350:
4345:
4340:
4225:"Societies and Academies"
3361:Peak power and duty cycle
4274:"Energy Density of Coal"
3222:through it, measured in
2578:{\displaystyle P(t)=pQ,}
2286:is the time derivative:
1393:If instead the force is
1212:is applied throughout a
731:Rotating reference frame
563:Hamilton–Jacobi equation
4746:rotational acceleration
4272:Fisher, Juliya (2003).
4235:(1700): 118–120. 1902.
4132:Smithsonian Institution
4096:Fundamentals of Physics
1030:on the wheels, and the
1015:per second. Power is a
672:Newton's laws of motion
532:Newton's laws of motion
4925:
4023:
3963:
3931:
3869:
3812:
3790:
3671:
3593:
3556:
3508:is simply defined by:
3498:
3478:
3417:
3397:
3371:
3343:
3310:
3230:If the component is a
3212:
3173:
3130:
3098:
3035:
2997:
2912:
2805:
2719:
2579:
2527:
2526:{\displaystyle \cdot }
2491:
2423:
2377:
2265:
2168:
2049:
2004:
1960:
1822:
1716:per hour (BTU/h), and
1653:
1534:
1385:
1249:
1196:
1122:
1054:is the product of the
1038:is the product of the
699:Simple harmonic motion
612:Euler's laws of motion
406:D'Alembert's principle
289:
221:
4926:
4189:Heron, C. A. (1906).
4024:
3964:
3932:
3870:
3813:
3811:{\displaystyle \tau }
3791:
3672:
3594:
3557:
3499:
3479:
3418:
3398:
3368:
3351:electrical resistance
3344:
3311:
3213:
3174:
3131:
3099:
3030:
2998:
2913:
2806:
2720:
2580:
2528:
2492:
2424:
2378:
2266:
2203:), then applying the
2169:
2031:
2005:
2003:{\displaystyle W=Pt.}
1978:can be calculated as
1961:
1823:
1718:tons of refrigeration
1693:mechanical horsepower
1654:
1535:
1386:
1250:
1197:
1123:
553:Hamiltonian mechanics
371:Statistical mechanics
290:
222:
4906:
4756:angular acceleration
4528:angular displacement
4278:The Physics Factbook
4157:represents work and
3973:
3953:
3941:of the pulse train.
3879:
3822:
3802:
3681:
3603:
3568:
3512:
3488:
3427:
3407:
3396:{\displaystyle s(t)}
3378:
3320:
3246:
3234:with time-invariant
3211:{\displaystyle I(t)}
3193:
3181:potential difference
3172:{\displaystyle V(t)}
3154:
3129:{\displaystyle P(t)}
3111:
3046:
2925:
2920:mechanical advantage
2853:
2733:
2727:mechanical advantage
2660:
2615:mechanical advantage
2609:Mechanical advantage
2605:in m/s in SI units.
2603:volumetric flow rate
2548:
2517:
2453:
2389:
2290:
2215:
2086:
1982:
1842:
1771:
1758:, the average power
1700:per second (erg/s),
1550:
1401:
1259:
1223:
1147:
1086:
1062:across the element.
776:Angular acceleration
768:Rotational frequency
548:Lagrangian mechanics
541:Analytical mechanics
297:Second law of motion
250:
176:
5337:Physical quantities
4846:weighted position:
4663:rotational velocity
4611:kinematic viscosity
4331:Classical mechanics
4241:1902Natur..66R.118.
3875:so that the ratios
3729:
3647:
628:Harmonic oscillator
606:Equations of motion
241:Classical mechanics
235:Part of a series on
4921:
4019:
3959:
3927:
3865:
3808:
3786:
3715:
3667:
3633:
3589:
3552:
3494:
3474:
3413:
3393:
3372:
3339:
3306:
3208:
3169:
3126:
3094:
3036:
2993:
2908:
2801:
2715:
2575:
2523:
2511:radians per second
2487:
2419:
2373:
2261:
2164:
2050:
2000:
1956:
1909:
1869:
1818:
1649:
1530:
1381:
1245:
1192:
1118:
1048:electrical element
944:Physics portal
558:Routhian mechanics
433:Frame of reference
285:
217:
57:SI base units
5309:
5308:
5304:
5303:
4918:
4871:moment of inertia
4149:Power or Activity
3962:{\displaystyle r}
3925:
3912:
3781:
3713:
3497:{\displaystyle T}
3416:{\displaystyle T}
3337:
3301:
2988:
2985:
2975:
2961:
2958:
2948:
2918:which yields the
2902:
2892:
2879:
2869:
2796:
2793:
2783:
2769:
2766:
2756:
2709:
2699:
2686:
2676:
2507:angular frequency
2368:
2326:
2180:defines the path
2034:metric horsepower
1951:
1928:
1891:
1851:
1838:approaches zero.
1813:
1743:is the amount of
1595:
1577:
1484:
1480:
1360:
1304:
1286:
1174:
1113:
999:is the amount of
994:
993:
741:Centrifugal force
736:Centripetal force
692:Euler's equations
677:Relative velocity
453:Moment of inertia
283:
257:
230:
229:
5344:
5296:
5292:
5280:
5276:
5256:
5252:
5240:
5236:
5214:
5210:
5200:
5190:
5175:
5171:
5161:
5139:
5135:
5125:
5115:
5100:
5096:
5083:
5059:
5053:
5045:
5034:
5028:
5017:
5010:angular momentum
4995:
4989:
4981:
4966:
4960:
4950:
4937:
4931:
4930:
4928:
4927:
4922:
4920:
4919:
4911:
4884:
4878:
4862:
4839:
4820:
4815:
4793:
4771:
4765:
4748:
4732:
4710:
4704:
4695:angular velocity
4692:
4673:
4672:
4659:
4658:
4651:rotational speed
4647:
4646:
4629:
4618:
4603:
4593:
4574:
4573:
4556:
4551:
4537:
4525:
4505:
4486:
4485:
4479:
4473:
4462:
4436:
4416:
4401:
4385:
4378:
4343:
4324:
4317:
4310:
4301:
4294:
4288:
4286:
4284:
4264:
4258:
4257:
4252:
4250:10.1038/066118b0
4221:
4215:
4214:
4208:
4206:
4195:Purdue Eng. Rev.
4186:
4180:
4179:
4176:
4162:
4156:
4121:
4115:
4106:
4100:
4099:
4091:
4028:
4026:
4025:
4020:
4012:
4011:
3968:
3966:
3965:
3960:
3936:
3934:
3933:
3928:
3926:
3918:
3913:
3911:
3910:
3901:
3900:
3899:
3883:
3874:
3872:
3871:
3866:
3864:
3863:
3862:
3834:
3833:
3817:
3815:
3814:
3809:
3795:
3793:
3792:
3787:
3782:
3777:
3776:
3775:
3753:
3728:
3723:
3714:
3706:
3701:
3700:
3699:
3676:
3674:
3673:
3668:
3646:
3641:
3629:
3628:
3627:
3598:
3596:
3595:
3590:
3588:
3587:
3586:
3561:
3559:
3558:
3553:
3524:
3523:
3503:
3501:
3500:
3495:
3483:
3481:
3480:
3475:
3473:
3472:
3467:
3449:
3422:
3420:
3419:
3414:
3402:
3400:
3399:
3394:
3348:
3346:
3345:
3340:
3338:
3330:
3315:
3313:
3312:
3307:
3302:
3297:
3296:
3287:
3276:
3275:
3217:
3215:
3214:
3209:
3178:
3176:
3175:
3170:
3135:
3133:
3132:
3127:
3103:
3101:
3100:
3095:
3017:Electrical power
3002:
3000:
2999:
2994:
2989:
2987:
2986:
2983:
2977:
2976:
2973:
2967:
2962:
2960:
2959:
2956:
2950:
2949:
2946:
2940:
2935:
2917:
2915:
2914:
2909:
2904:
2903:
2900:
2894:
2893:
2890:
2881:
2880:
2877:
2871:
2870:
2867:
2848:
2839:
2830:
2821:
2810:
2808:
2807:
2802:
2797:
2795:
2794:
2791:
2785:
2784:
2781:
2775:
2770:
2768:
2767:
2764:
2758:
2757:
2754:
2748:
2743:
2724:
2722:
2721:
2716:
2711:
2710:
2707:
2701:
2700:
2697:
2688:
2687:
2684:
2678:
2677:
2674:
2655:
2646:
2637:
2628:
2600:
2588:
2584:
2582:
2581:
2576:
2532:
2530:
2529:
2524:
2504:
2496:
2494:
2493:
2488:
2483:
2475:
2448:
2442:angular velocity
2439:
2428:
2426:
2425:
2420:
2382:
2380:
2379:
2374:
2369:
2367:
2359:
2351:
2343:
2335:
2327:
2325:
2317:
2309:
2285:
2278:
2274:
2270:
2268:
2267:
2262:
2227:
2226:
2205:gradient theorem
2198:
2189:
2183:
2179:
2173:
2171:
2170:
2165:
2160:
2149:
2144:
2143:
2124:
2116:
2111:
2110:
2098:
2097:
2078:is given by the
2077:
2073:
2068:done by a force
2024:Mechanical power
2019:
2015:
2009:
2007:
2006:
2001:
1977:
1973:
1965:
1963:
1962:
1957:
1952:
1950:
1942:
1934:
1929:
1927:
1919:
1911:
1908:
1887:
1886:
1885:
1868:
1837:
1827:
1825:
1824:
1819:
1814:
1812:
1804:
1796:
1791:
1790:
1789:
1766:
1757:
1742:
1658:
1656:
1655:
1650:
1645:
1637:
1622:
1614:
1609:
1608:
1596:
1594:
1583:
1578:
1576:
1568:
1560:
1539:
1537:
1536:
1531:
1519:
1511:
1506:
1505:
1482:
1481:
1479:
1471:
1470:
1461:
1456:
1451:
1450:
1435:
1424:
1419:
1418:
1390:
1388:
1387:
1382:
1377:
1369:
1361:
1359:
1351:
1350:
1341:
1336:
1328:
1324:
1323:
1315:
1305:
1303:
1292:
1287:
1285:
1277:
1269:
1254:
1252:
1251:
1246:
1244:
1236:
1201:
1199:
1198:
1193:
1191:
1183:
1175:
1173:
1165:
1157:
1139:
1135:
1131:
1127:
1125:
1124:
1119:
1114:
1112:
1104:
1096:
1044:angular velocity
1024:aerodynamic drag
986:
979:
972:
959:
954:
953:
946:
942:
941:
847:Johann Bernoulli
842:Daniel Bernoulli
763:Tangential speed
667:
643:
618:Fictitious force
613:
465:Mechanical power
455:
396:Angular momentum
294:
292:
291:
286:
284:
282:
274:
273:
264:
259:
258:
232:
226:
224:
223:
218:
216:
215:
207:
206:
199:
198:
193:
192:
185:
184:
160:
141:
122:
103:
80:other quantities
78:Derivations from
58:
36:
21:
5352:
5351:
5347:
5346:
5345:
5343:
5342:
5341:
5322:Power (physics)
5312:
5311:
5310:
5305:
5294:
5293:
5288:
5278:
5277:
5272:
5254:
5253:
5248:
5238:
5237:
5232:
5212:
5211:
5206:
5196:
5186:
5173:
5172:
5167:
5155:
5137:
5136:
5131:
5121:
5111:
5098:
5097:
5095:
5089:
5079:
5057:
5054:
5051:
5043:
5032:
5029:
5023:
5020:angular impulse
5013:
4993:
4990:
4987:
4979:
4964:
4961:
4956:
4946:
4935:
4932:
4904:
4903:
4902:
4882:
4879:
4874:
4847:
4840:
4835:
4818:
4816:
4809:
4794:
4789:
4769:
4766:
4759:
4749:
4744:
4733:
4728:
4708:
4705:
4698:
4688:
4674:
4666:
4661:
4654:
4649:
4642:
4637:
4630:
4625:
4620:
4614:
4604:
4599:
4589:
4575:
4569:
4564:
4552:
4549:
4544:
4538:
4531:
4521:
4506:
4501:
4491:
4481:
4475:
4469:
4464:
4458:
4437:
4432:
4417:
4412:
4402:
4397:
4381:
4374:
4336:
4328:
4298:
4297:
4282:
4280:
4271:
4265:
4261:
4223:
4222:
4218:
4204:
4202:
4188:
4187:
4183:
4164:
4158:
4152:
4123:
4122:
4118:
4107:
4103:
4093:
4092:
4088:
4083:
4070:Signal strength
4038:Simple machines
4034:
4003:
3971:
3970:
3951:
3950:
3947:
3902:
3884:
3877:
3876:
3841:
3825:
3820:
3819:
3800:
3799:
3754:
3684:
3679:
3678:
3606:
3601:
3600:
3571:
3566:
3565:
3515:
3510:
3509:
3486:
3485:
3462:
3425:
3424:
3405:
3404:
3376:
3375:
3363:
3318:
3317:
3288:
3267:
3244:
3243:
3191:
3190:
3152:
3151:
3109:
3108:
3044:
3043:
3025:
3019:
3007:velocity ratios
2978:
2968:
2951:
2941:
2923:
2922:
2895:
2885:
2872:
2862:
2851:
2850:
2847:
2841:
2838:
2832:
2829:
2823:
2820:
2814:
2786:
2776:
2759:
2749:
2731:
2730:
2702:
2692:
2679:
2669:
2658:
2657:
2654:
2648:
2645:
2639:
2636:
2630:
2627:
2621:
2617:of the system.
2611:
2598:
2586:
2546:
2545:
2515:
2514:
2498:
2451:
2450:
2444:
2435:
2387:
2386:
2360:
2352:
2318:
2310:
2288:
2287:
2283:
2276:
2272:
2218:
2213:
2212:
2194:
2185:
2181:
2175:
2135:
2102:
2089:
2084:
2083:
2075:
2069:
2026:
2017:
2013:
1980:
1979:
1975:
1969:
1943:
1935:
1920:
1912:
1870:
1840:
1839:
1832:
1805:
1797:
1774:
1769:
1768:
1765:
1759:
1752:
1737:
1726:
1672:
1597:
1587:
1569:
1561:
1548:
1547:
1546:, we know that
1494:
1472:
1462:
1439:
1410:
1399:
1398:
1352:
1342:
1310:
1306:
1296:
1278:
1270:
1257:
1256:
1221:
1220:
1166:
1158:
1145:
1144:
1137:
1133:
1129:
1105:
1097:
1084:
1083:
1076:time derivative
1068:
1011:, equal to one
990:
949:
936:
935:
928:
927:
926:
801:
793:
792:
772:
726:Circular motion
720:
710:
709:
708:
665:
635:
632:
611:
590:
582:
581:
578:
577:
535:
525:
517:
516:
515:
474:
470:Mechanical work
463:
447:
385:
377:
376:
375:
330:
322:
299:
275:
265:
248:
247:
200:
186:
174:
173:
163:
144:
125:
106:
87:
81:
79:
56:
34:
31:
17:
12:
11:
5:
5350:
5348:
5340:
5339:
5334:
5332:Temporal rates
5329:
5324:
5314:
5313:
5307:
5306:
5302:
5301:
5282:
5266:
5264:
5261:
5242:
5226:
5224:
5220:
5219:
5180:
5149:
5147:
5144:
5105:
5093:
5073:
5071:
5067:
5066:
5037:
5007:
5005:
5002:
4973:
4940:
4917:
4914:
4899:Mass flow rate
4896:
4892:
4891:
4889:
4887:
4868:
4865:
4863:
4844:
4829:
4825:
4824:
4822:
4803:
4801:
4798:
4796:
4783:
4781:
4777:
4776:
4774:
4753:
4742:
4739:
4737:
4722:
4720:
4716:
4715:
4713:
4682:
4635:
4632:
4608:
4583:
4562:
4558:
4557:
4542:
4515:
4513:
4510:
4495:
4452:
4450:
4446:
4445:
4443:
4441:
4426:
4423:
4421:
4406:
4391:
4387:
4386:
4379:
4372:
4369:
4366:
4363:
4360:
4357:
4353:
4352:
4349:
4347:
4341:
4338:
4337:
4329:
4327:
4326:
4319:
4312:
4304:
4296:
4295:
4291:TNT equivalent
4259:
4216:
4181:
4116:
4114:Volume I, 1963
4101:
4085:
4084:
4082:
4079:
4078:
4077:
4072:
4067:
4062:
4056:
4050:
4045:
4040:
4033:
4030:
4018:
4015:
4010:
4006:
4002:
3999:
3996:
3993:
3990:
3987:
3984:
3981:
3978:
3958:
3946:
3943:
3924:
3921:
3916:
3909:
3905:
3898:
3895:
3892:
3887:
3861:
3858:
3855:
3852:
3849:
3844:
3840:
3837:
3832:
3828:
3807:
3785:
3780:
3774:
3771:
3768:
3765:
3762:
3757:
3751:
3748:
3745:
3741:
3738:
3735:
3732:
3727:
3722:
3718:
3712:
3709:
3704:
3698:
3695:
3692:
3687:
3666:
3663:
3659:
3656:
3653:
3650:
3645:
3640:
3636:
3632:
3626:
3623:
3620:
3617:
3614:
3609:
3585:
3582:
3579:
3574:
3551:
3548:
3545:
3542:
3539:
3536:
3533:
3530:
3527:
3522:
3518:
3493:
3471:
3466:
3461:
3458:
3455:
3452:
3448:
3444:
3441:
3438:
3435:
3432:
3412:
3392:
3389:
3386:
3383:
3362:
3359:
3353:, measured in
3336:
3333:
3328:
3325:
3305:
3300:
3295:
3291:
3285:
3282:
3279:
3274:
3270:
3266:
3263:
3260:
3257:
3254:
3251:
3228:
3227:
3207:
3204:
3201:
3198:
3188:
3168:
3165:
3162:
3159:
3149:
3125:
3122:
3119:
3116:
3093:
3090:
3087:
3084:
3081:
3078:
3075:
3072:
3069:
3066:
3063:
3060:
3057:
3054:
3051:
3023:Electric power
3021:Main article:
3018:
3015:
2992:
2981:
2971:
2965:
2954:
2944:
2938:
2934:
2931:
2907:
2898:
2888:
2884:
2875:
2865:
2861:
2858:
2845:
2836:
2827:
2818:
2800:
2789:
2779:
2773:
2762:
2752:
2746:
2742:
2739:
2714:
2705:
2695:
2691:
2682:
2672:
2668:
2665:
2652:
2643:
2634:
2625:
2610:
2607:
2574:
2571:
2568:
2565:
2562:
2559:
2556:
2553:
2535:scalar product
2522:
2509:, measured in
2486:
2482:
2478:
2474:
2470:
2467:
2464:
2461:
2458:
2418:
2415:
2412:
2409:
2406:
2403:
2400:
2397:
2394:
2372:
2366:
2363:
2358:
2355:
2349:
2346:
2342:
2338:
2334:
2330:
2324:
2321:
2316:
2313:
2307:
2304:
2301:
2298:
2295:
2260:
2257:
2254:
2251:
2248:
2245:
2242:
2239:
2236:
2233:
2230:
2225:
2221:
2163:
2159:
2155:
2152:
2148:
2142:
2138:
2134:
2131:
2128:
2123:
2119:
2115:
2109:
2105:
2101:
2096:
2092:
2025:
2022:
1999:
1996:
1993:
1990:
1987:
1955:
1949:
1946:
1941:
1938:
1932:
1926:
1923:
1918:
1915:
1907:
1904:
1901:
1898:
1894:
1890:
1884:
1881:
1878:
1873:
1867:
1864:
1861:
1858:
1854:
1850:
1847:
1817:
1811:
1808:
1803:
1800:
1794:
1788:
1785:
1782:
1777:
1763:
1725:
1722:
1671:
1668:
1648:
1644:
1640:
1636:
1632:
1629:
1626:
1621:
1617:
1613:
1607:
1604:
1600:
1593:
1590:
1586:
1581:
1575:
1572:
1567:
1564:
1558:
1555:
1529:
1526:
1523:
1518:
1514:
1510:
1504:
1501:
1497:
1493:
1490:
1487:
1478:
1475:
1469:
1465:
1459:
1455:
1449:
1446:
1442:
1438:
1434:
1430:
1427:
1423:
1417:
1413:
1409:
1406:
1380:
1376:
1372:
1368:
1364:
1358:
1355:
1349:
1345:
1339:
1335:
1331:
1327:
1322:
1318:
1314:
1309:
1302:
1299:
1295:
1290:
1284:
1281:
1276:
1273:
1267:
1264:
1243:
1239:
1235:
1231:
1228:
1190:
1186:
1182:
1178:
1172:
1169:
1164:
1161:
1155:
1152:
1117:
1111:
1108:
1103:
1100:
1094:
1091:
1067:
1064:
1028:traction force
992:
991:
989:
988:
981:
974:
966:
963:
962:
961:
960:
947:
930:
929:
925:
924:
919:
914:
909:
904:
899:
894:
889:
884:
879:
874:
869:
864:
859:
854:
849:
844:
839:
834:
829:
824:
819:
814:
809:
803:
802:
799:
798:
795:
794:
791:
790:
771:
770:
765:
760:
755:
753:Coriolis force
750:
749:
748:
738:
733:
728:
722:
721:
716:
715:
712:
711:
707:
706:
701:
696:
695:
694:
689:
679:
674:
669:
662:
651:
650:
649:
644:
631:
630:
625:
620:
615:
608:
603:
598:
592:
591:
588:
587:
584:
583:
580:
579:
576:
575:
570:
565:
560:
555:
550:
544:
538:
536:
529:
526:
523:
522:
519:
518:
514:
513:
508:
503:
498:
493:
488:
483:
478:
472:
467:
461:
456:
445:
440:
435:
430:
425:
424:
423:
418:
408:
403:
398:
393:
387:
386:
383:
382:
379:
378:
374:
373:
368:
363:
358:
353:
348:
343:
338:
332:
331:
328:
327:
324:
323:
321:
320:
315:
310:
304:
301:
300:
295:
281:
278:
272:
268:
262:
244:
243:
237:
236:
228:
227:
214:
211:
205:
197:
191:
183:
171:
165:
164:
162:
161:
142:
123:
104:
84:
82:
77:
74:
73:
60:
51:
50:
44:
38:
37:
32:
30:Common symbols
29:
26:
25:
15:
13:
10:
9:
6:
4:
3:
2:
5349:
5338:
5335:
5333:
5330:
5328:
5325:
5323:
5320:
5319:
5317:
5300:
5291:
5286:
5283:
5275:
5270:
5267:
5265:
5262:
5260:
5251:
5246:
5243:
5235:
5230:
5227:
5225:
5222:
5221:
5218:
5209:
5204:
5199:
5194:
5189:
5184:
5181:
5179:
5170:
5165:
5160:
5159:
5153:
5150:
5148:
5145:
5143:
5134:
5129:
5124:
5119:
5114:
5109:
5106:
5104:
5092:
5087:
5082:
5077:
5074:
5072:
5069:
5068:
5065:
5061:
5049:
5041:
5038:
5036:
5027:
5021:
5016:
5011:
5008:
5006:
5003:
5001:
4997:
4985:
4977:
4974:
4972:
4968:
4959:
4954:
4949:
4944:
4941:
4939:
4915:
4912:
4900:
4897:
4894:
4893:
4890:
4888:
4886:
4877:
4872:
4869:
4866:
4864:
4861:
4858:
4854:
4850:
4845:
4843:
4838:
4833:
4830:
4827:
4826:
4823:
4814:
4813:
4807:
4804:
4802:
4799:
4797:
4792:
4787:
4784:
4782:
4779:
4778:
4775:
4773:
4764:
4763:
4757:
4754:
4752:
4747:
4743:
4740:
4738:
4736:
4731:
4726:
4723:
4721:
4718:
4717:
4714:
4712:
4703:
4702:
4696:
4691:
4686:
4685:angular speed
4683:
4681:
4677:
4671:
4670:
4664:
4657:
4652:
4645:
4640:
4636:
4633:
4628:
4623:
4617:
4612:
4609:
4607:
4602:
4597:
4592:
4587:
4584:
4582:
4578:
4572:
4567:
4563:
4560:
4559:
4555:
4547:
4543:
4541:
4536:
4535:
4529:
4524:
4519:
4516:
4514:
4511:
4509:
4504:
4499:
4496:
4494:
4490:
4484:
4478:
4472:
4467:
4461:
4456:
4453:
4451:
4448:
4447:
4444:
4442:
4440:
4435:
4430:
4427:
4424:
4422:
4420:
4415:
4410:
4407:
4405:
4400:
4395:
4392:
4389:
4388:
4384:
4380:
4377:
4373:
4370:
4367:
4364:
4361:
4358:
4355:
4354:
4344:
4339:
4335:
4332:
4325:
4320:
4318:
4313:
4311:
4306:
4305:
4302:
4292:
4279:
4275:
4269:
4263:
4260:
4256:
4251:
4246:
4242:
4238:
4234:
4230:
4226:
4220:
4217:
4213:
4200:
4196:
4192:
4185:
4182:
4178:
4175:
4171:
4167:
4161:
4155:
4150:
4145:
4141:
4137:
4133:
4129:
4128:
4120:
4117:
4113:
4112:
4105:
4102:
4097:
4090:
4087:
4080:
4076:
4073:
4071:
4068:
4066:
4065:Power density
4063:
4060:
4057:
4054:
4051:
4049:
4046:
4044:
4041:
4039:
4036:
4035:
4031:
4029:
4016:
4008:
4004:
4000:
3997:
3991:
3988:
3982:
3976:
3956:
3945:Radiant power
3944:
3942:
3940:
3922:
3919:
3914:
3907:
3903:
3885:
3842:
3838:
3835:
3830:
3826:
3805:
3796:
3783:
3778:
3755:
3749:
3746:
3743:
3736:
3730:
3725:
3720:
3716:
3710:
3707:
3702:
3685:
3664:
3661:
3654:
3648:
3643:
3638:
3634:
3630:
3607:
3572:
3562:
3549:
3540:
3534:
3525:
3520:
3516:
3507:
3491:
3469:
3456:
3450:
3442:
3436:
3430:
3410:
3387:
3381:
3370:definitions).
3367:
3360:
3358:
3356:
3352:
3334:
3331:
3326:
3323:
3303:
3298:
3293:
3289:
3283:
3280:
3277:
3272:
3268:
3264:
3261:
3258:
3255:
3252:
3249:
3242:ratio, then:
3241:
3237:
3233:
3225:
3221:
3202:
3196:
3189:
3186:
3182:
3163:
3157:
3150:
3147:
3143:
3139:
3120:
3114:
3107:
3106:
3105:
3091:
3085:
3079:
3076:
3070:
3064:
3061:
3055:
3049:
3041:
3033:
3029:
3024:
3016:
3014:
3012:
3008:
3003:
2990:
2979:
2969:
2963:
2952:
2942:
2936:
2921:
2905:
2896:
2886:
2882:
2873:
2863:
2859:
2856:
2844:
2835:
2826:
2817:
2811:
2798:
2787:
2777:
2771:
2760:
2750:
2744:
2728:
2712:
2703:
2693:
2689:
2680:
2670:
2666:
2663:
2651:
2642:
2633:
2624:
2618:
2616:
2608:
2606:
2604:
2596:
2592:
2572:
2569:
2566:
2563:
2557:
2551:
2543:
2538:
2536:
2520:
2512:
2508:
2503:
2502:
2484:
2476:
2468:
2462:
2456:
2447:
2443:
2438:
2434:
2429:
2416:
2413:
2410:
2407:
2404:
2398:
2392:
2383:
2370:
2364:
2361:
2356:
2353:
2347:
2344:
2336:
2328:
2322:
2319:
2314:
2311:
2305:
2299:
2293:
2280:
2258:
2252:
2246:
2243:
2237:
2231:
2228:
2223:
2219:
2210:
2206:
2202:
2197:
2193:If the force
2191:
2188:
2178:
2161:
2153:
2150:
2140:
2136:
2132:
2129:
2126:
2117:
2107:
2103:
2099:
2094:
2090:
2081:
2080:line integral
2072:
2067:
2063:
2060:of work. In
2059:
2054:
2047:
2043:
2039:
2035:
2030:
2023:
2021:
2010:
1997:
1994:
1991:
1988:
1985:
1972:
1966:
1953:
1947:
1944:
1939:
1936:
1930:
1924:
1916:
1905:
1899:
1888:
1871:
1865:
1859:
1848:
1845:
1836:
1829:
1815:
1809:
1801:
1792:
1775:
1762:
1756:
1750:
1746:
1741:
1735:
1731:
1723:
1721:
1719:
1715:
1711:
1707:
1703:
1699:
1695:
1694:
1689:
1685:
1681:
1677:
1669:
1667:
1665:
1660:
1646:
1638:
1630:
1627:
1624:
1615:
1605:
1598:
1591:
1588:
1584:
1579:
1573:
1570:
1565:
1562:
1556:
1553:
1545:
1540:
1527:
1524:
1521:
1512:
1502:
1495:
1491:
1488:
1485:
1476:
1473:
1463:
1457:
1447:
1440:
1436:
1428:
1425:
1415:
1411:
1407:
1404:
1396:
1391:
1378:
1370:
1362:
1356:
1353:
1343:
1337:
1329:
1325:
1316:
1307:
1300:
1297:
1293:
1288:
1282:
1279:
1274:
1271:
1265:
1262:
1237:
1229:
1226:
1218:
1215:
1211:
1207:
1202:
1184:
1176:
1170:
1167:
1162:
1159:
1153:
1150:
1141:
1136:is work, and
1115:
1109:
1106:
1101:
1098:
1092:
1089:
1081:
1077:
1073:
1070:Power is the
1065:
1063:
1061:
1057:
1053:
1049:
1045:
1041:
1037:
1033:
1029:
1025:
1020:
1018:
1014:
1010:
1006:
1002:
998:
987:
982:
980:
975:
973:
968:
967:
965:
964:
958:
948:
945:
940:
934:
933:
932:
931:
923:
920:
918:
915:
913:
910:
908:
905:
903:
900:
898:
895:
893:
890:
888:
885:
883:
880:
878:
875:
873:
870:
868:
865:
863:
860:
858:
855:
853:
850:
848:
845:
843:
840:
838:
835:
833:
830:
828:
825:
823:
820:
818:
815:
813:
810:
808:
805:
804:
797:
796:
789:
785:
781:
777:
774:
773:
769:
766:
764:
761:
759:
756:
754:
751:
747:
744:
743:
742:
739:
737:
734:
732:
729:
727:
724:
723:
719:
714:
713:
705:
702:
700:
697:
693:
690:
688:
685:
684:
683:
680:
678:
675:
673:
670:
668:
663:
660:
656:
653:
652:
648:
645:
642:
638:
634:
633:
629:
626:
624:
621:
619:
616:
614:
609:
607:
604:
602:
599:
597:
594:
593:
586:
585:
574:
571:
569:
566:
564:
561:
559:
556:
554:
551:
549:
546:
545:
543:
542:
537:
534:
533:
528:
527:
521:
520:
512:
509:
507:
504:
502:
499:
497:
494:
492:
489:
487:
484:
482:
479:
477:
473:
471:
468:
466:
462:
460:
457:
454:
450:
446:
444:
441:
439:
436:
434:
431:
429:
426:
422:
419:
417:
414:
413:
412:
409:
407:
404:
402:
399:
397:
394:
392:
389:
388:
381:
380:
372:
369:
367:
364:
362:
359:
357:
354:
352:
349:
347:
344:
342:
339:
337:
334:
333:
326:
325:
319:
316:
314:
311:
309:
306:
305:
302:
298:
279:
276:
266:
260:
246:
245:
242:
238:
234:
233:
212:
209:
195:
172:
170:
166:
159:
158:
153:
152:
147:
143:
140:
139:
134:
133:
128:
124:
121:
120:
115:
114:
109:
105:
102:
101:
96:
95:
90:
86:
85:
83:
75:
72:
68:
64:
61:
59:
52:
48:
45:
43:
39:
33:
27:
22:
19:
5289:
5284:
5273:
5249:
5244:
5233:
5207:
5197:
5187:
5168:
5157:
5156:
5132:
5122:
5112:
5090:
5080:
5025:
5014:
4957:
4947:
4875:
4859:
4856:
4852:
4848:
4836:
4811:
4810:
4806:angular jerk
4790:
4761:
4760:
4729:
4725:acceleration
4700:
4699:
4689:
4668:
4667:
4655:
4643:
4626:
4615:
4600:
4590:
4570:
4533:
4532:
4522:
4502:
4489:displacement
4482:
4476:
4470:
4459:
4433:
4413:
4398:
4382:
4375:
4281:. Retrieved
4277:
4262:
4254:
4232:
4228:
4219:
4210:
4203:. Retrieved
4197:(2): 77–93.
4194:
4184:
4173:
4169:
4165:
4159:
4153:
4148:
4147:
4126:
4119:
4109:
4104:
4095:
4089:
4048:Pulsed power
3948:
3938:
3797:
3563:
3505:
3373:
3229:
3039:
3037:
3004:
2842:
2833:
2824:
2815:
2812:
2649:
2640:
2631:
2622:
2619:
2612:
2597:or N/m, and
2539:
2500:
2499:
2445:
2436:
2430:
2384:
2281:
2201:conservative
2195:
2192:
2186:
2176:
2070:
2055:
2051:
2033:
2016:rather than
2011:
1970:
1967:
1834:
1830:
1760:
1754:
1751:of duration
1739:
1727:
1704:per minute,
1692:
1673:
1663:
1661:
1541:
1394:
1392:
1216:
1209:
1205:
1203:
1142:
1069:
1021:
996:
995:
786: /
782: /
780:displacement
778: /
639: /
601:Displacement
539:
530:
524:Formulations
511:Virtual work
451: /
391:Acceleration
384:Fundamentals
156:
150:
145:
137:
131:
126:
118:
112:
107:
99:
93:
88:
42:SI unit
18:
4546:solid angle
4075:Sound power
3032:Ansel Adams
3011:gear ratios
2533:represents
1968:When power
1702:foot-pounds
922:von Neumann
589:Core topics
5316:Categories
5281:m s, N m s
5257:m s,
5203:Lagrangian
5128:Lagrangian
4368:Dimensions
4356:Dimensions
4268:megajoules
4140:1142734534
4081:References
4059:Power gain
3939:duty cycle
3818:such that
3506:peak power
3403:of period
2058:derivative
2044:in 1
2040:by 1
1712:per hour,
1688:horsepower
1132:is power,
1066:Definition
1019:quantity.
857:d'Alembert
837:Maupertuis
800:Scientists
682:Rigid body
356:Kinematics
5297:ms,
4916:˙
4639:frequency
4566:frequency
4053:Intensity
4001:π
3920:τ
3843:ε
3836:τ
3806:τ
3756:ε
3717:∫
3635:∫
3608:ε
3278:⋅
3259:⋅
3077:⋅
2980:ω
2970:ω
2897:ω
2874:ω
2542:hydraulic
2521:⋅
2481:ω
2477:⋅
2473:τ
2411:⋅
2348:−
2337:⋅
2244:−
2151:⋅
2137:∫
2118:⋅
2104:∫
2062:mechanics
2038:kilograms
1922:Δ
1914:Δ
1903:→
1897:Δ
1863:→
1857:Δ
1807:Δ
1799:Δ
1639:⋅
1616:⋅
1603:Δ
1599:∫
1542:From the
1513:⋅
1500:Δ
1496:∫
1458:⋅
1445:Δ
1441:∫
1426:⋅
1412:∫
1371:⋅
1338:⋅
1317:⋅
1238:⋅
1185:⋅
1140:is time.
902:Liouville
784:frequency
704:Vibration
421:potential
346:Continuum
341:Celestial
318:Textbooks
210:−
169:Dimension
5241:m s, N s
5064:J s
5060:m s
5035:m s
4996:m s
4967:m s
4943:momentum
4596:velocity
4466:position
4455:distance
4409:absement
4334:SI units
4205:23 April
4199:Archived
4144:Archived
4032:See also
3232:resistor
2725:and the
2591:pressure
2209:gradient
1710:calories
1664:activity
1214:distance
1206:constant
1032:velocity
957:Category
882:Hamilton
867:Lagrange
862:Clairaut
827:Horrocks
788:velocity
758:Pendulum
746:reactive
718:Rotation
687:dynamics
637:Inertial
623:Friction
506:Velocity
481:Momentum
361:Kinetics
351:Dynamics
329:Branches
313:Timeline
5269:rotatum
5048:actergy
4984:actergy
4953:impulse
4873::
4624::
4554:rad, sr
4237:Bibcode
4163:power,
3504:. The
3349:is the
3240:current
3236:voltage
3224:amperes
3220:current
3218:is the
3179:is the
2595:pascals
2513:. The
1060:voltage
1056:current
1052:circuit
917:Koopman
877:Poisson
872:Laplace
817:Huygens
812:Galileo
657: (
596:Damping
449:Inertia
443:Impulse
416:kinetic
366:Statics
336:Applied
308:History
5183:energy
5164:moment
5152:torque
5108:energy
5086:weight
5058:
5040:action
5033:
4994:
4976:action
4965:
4936:
4883:
4855:⟩ = ∑
4819:
4770:
4709:
4283:30 May
4229:Nature
4138:
3316:where
3146:second
3142:joules
3104:where
2585:where
2497:where
2433:torque
2271:where
2174:where
2064:, the
2046:second
1483:
1208:force
1128:where
1040:torque
1017:scalar
1001:energy
955:
907:Appell
892:Cauchy
887:Jacobi
832:Halley
822:Newton
807:Kepler
659:linear
655:Motion
501:Torque
476:Moment
411:Energy
401:Couple
5327:Force
5285:power
5245:power
5215:m s,
5176:m s,
5140:m s,
5101:m s,
5076:force
4586:speed
4518:angle
3187:, and
3185:volts
3138:watts
2042:metre
1684:joule
1670:Units
1204:If a
1050:of a
1036:motor
1026:plus
1013:joule
997:Power
912:Gibbs
897:Routh
852:Euler
491:Speed
486:Space
428:Force
24:Power
5229:yank
5193:work
5118:work
4832:mass
4786:jerk
4498:area
4429:time
4394:time
4285:2011
4207:2020
4136:OCLC
3355:ohms
3144:per
2840:and
2822:and
2440:and
2275:and
2184:and
2066:work
2032:One
1749:time
1745:work
1730:coal
1698:ergs
1680:watt
1080:work
1072:rate
1009:watt
496:Time
459:Mass
47:watt
5263:MLT
5178:N m
5146:MLT
5099:kg
5004:MLT
5000:J s
4971:N s
4817:rad
4795:m s
4768:rad
4735:m s
4707:rad
4631:m s
4606:m s
4540:rad
4419:m s
4245:doi
4212:78)
3529:max
3238:to
2601:is
2593:in
2589:is
2505:is
1893:lim
1853:lim
1764:avg
1734:TNT
1714:BTU
1706:dBm
1078:of
54:In
49:(W)
5318::
5295:kg
5287::
5279:kg
5271::
5255:kg
5247::
5239:kg
5231::
5223:MT
5213:kg
5205::
5201:,
5195::
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5185::
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5166::
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4963:kg
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4881:kg
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4842:kg
4834::
4808::
4788::
4758::
4727::
4697::
4693:,
4687::
4680:Hz
4678:,
4665::
4660:,
4653::
4648:,
4641::
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4594:,
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4581:Hz
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4276:.
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148:=
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5217:J
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4958:J
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4751:s
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2100:=
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1989:=
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1849:=
1846:P
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1816:.
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1628:t
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1266:=
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1234:F
1230:=
1227:W
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1177:=
1171:t
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1154:=
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