883:
29:
1724:
896:
1524:
1719:{\displaystyle {\begin{aligned}\mathbf {J} &=\int _{t_{1}}^{t_{2}}{\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}\,\mathrm {d} t\\&=\int _{\mathbf {p} _{1}}^{\mathbf {p} _{2}}\mathrm {d} \mathbf {p} \\&=\mathbf {p} _{2}-\mathbf {p} _{1}=\Delta \mathbf {p} ,\end{aligned}}}
1876:
1271:
1126:
1516:
1424:
1763:
1041:
1230:
169:
237:
261:
1759:
As a result, an impulse may also be regarded as the change in momentum of an object to which a resultant force is applied. The impulse may be expressed in a simpler form when the mass is constant:
1529:
1175:
1277:
1276:
1273:
1272:
1278:
2245:
1275:
2853:
1062:
1467:
1358:
927:
516:
2238:
635:
2047:, which relates the vehicle's propulsive change in velocity to the engine's specific impulse (or nozzle exhaust velocity) and the vehicle's propellant-
991:
2943:
1190:
608:
1274:
882:
2231:
2141:
3250:
1141:
590:
2009:, and is not physically possible. However, this is a useful model for computing the effects of ideal collisions (such as in videogame
1871:{\displaystyle \mathbf {J} =\int _{t_{1}}^{t_{2}}\mathbf {F} \,\mathrm {d} t=\Delta \mathbf {p} =m\mathbf {v_{2}} -m\mathbf {v_{1}} ,}
1052:
2202:
2183:
920:
2116:
126:
2979:
2954:
2915:
2013:). Additionally, in rocketry, the term "total impulse" is commonly used and is considered synonymous with the term "impulse".
256:
193:
3255:
251:
511:
2257:
1947:
1235:
506:
3245:
1255:
913:
900:
661:
584:
33:
A large force applied for a very short duration, such as a golf shot, is often described as the club giving the ball an
349:
2044:
2027:
The application of Newton's second law for variable mass allows impulse and momentum to be used as analysis tools for
580:
381:
1455:
800:
689:
615:
475:
408:
2060:
2886:
2691:
2545:
1971:
554:
2658:
1247:
830:
674:
2005:
so that the change in momentum produced by the force happens with no change in time. This sort of change is a
2669:
2080:
820:
780:
544:
825:
642:
2804:
2674:
2412:
835:
810:
496:
314:
2063:
defines the impulse of a wave collision. The preservation of momentum in the collision is then called
3126:
3051:
2679:
2451:
2096:
1243:
855:
850:
815:
723:
719:
711:
701:
491:
484:
240:
119:
2857:
2586:
2534:
2254:
1753:
941:
630:
571:
549:
294:
289:
284:
184:
1998:
760:
501:
376:
344:
304:
108:
2829:
2035:-propelled vehicles. In the case of rockets, the impulse imparted can be normalized by unit of
28:
2794:
2630:
2389:
2198:
2179:
2137:
2036:
770:
727:
684:
679:
620:
396:
279:
2963:
2933:
2899:
2618:
2574:
2529:
2075:
2064:
2040:
2022:
1956:
1046:
865:
845:
790:
785:
731:
706:
561:
419:
364:
339:
3208:
3168:
1980:
860:
805:
755:
750:
669:
1055:
states that the rate of change of momentum of an object is equal to the resultant force
3152:
3116:
3041:
2822:
2729:
2709:
2599:
2500:
2195:
Physics for
Scientists and Engineers: Mechanics, Oscillations and Waves, Thermodynamics
2070:
2028:
2010:
1962:
887:
795:
696:
413:
359:
3239:
3026:
2894:
2608:
2172:
2130:
2006:
1986:
1251:
1239:
775:
602:
97:
68:
64:
3101:
2987:
2923:
2648:
2431:
2342:
1121:{\displaystyle \mathbf {F} ={\frac {\mathbf {p} _{2}-\mathbf {p} _{1}}{\Delta t}},}
840:
765:
454:
334:
2469:
2218:
1976:
1259:
2223:
1511:{\displaystyle \mathbf {F} ={\frac {\mathrm {d} \mathbf {p} }{\mathrm {d} t}}.}
2048:
1419:{\displaystyle \mathbf {J} =\int _{t_{1}}^{t_{2}}\mathbf {F} \,\mathrm {d} t,}
1246:
unit of momentum is the kilogram metre per second (kgâ
m/s). The corresponding
625:
299:
2562:
2489:
2477:
647:
2971:
2907:
2866:
2765:
2519:
2378:
2332:
1952:
1300:
is the speed upon impact. To the extent that it bounces back with speed
1180:
959:
566:
449:
424:
85:
1927:
is the final velocity of the object at the end of the time interval, and
3192:
539:
392:
309:
59:
1752:. This is often called the impulse-momentum theorem (analogous to the
3106:
3087:
3075:
3031:
3009:
2463:
2362:
2327:
2086:
2032:
1990:
1966:
598:
444:
354:
101:
93:
72:
1938:
is the initial velocity of the object when the time interval begins.
1997:
The term "impulse" is also used to refer to a fast-acting force or
16:
Integral of a comparatively larger force over a short time interval
3140:
3065:
2999:
2603:
2509:
2504:
2441:
2416:
1269:
434:
429:
371:
89:
1266:
Mathematical derivation in the case of an object of constant mass
3222:
3182:
2755:
2421:
2352:
2317:
439:
402:
2227:
1036:{\displaystyle \mathbf {J} =\mathbf {p} _{2}-\mathbf {p} _{1}.}
1225:{\displaystyle \mathbf {J} =\int \mathbf {F} \,\mathrm {d} t.}
164:{\displaystyle {\mathsf {L}}{\mathsf {M}}{\mathsf {T}}^{-1}}
2156:
See, for example, section 9.2, page 257, of Serway (2004).
1910:
are times when the impulse begins and ends, respectively,
232:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
1761:
1522:
1356:
962:
of an object. If the initial momentum of an object is
2832:
2136:(12th ed.). Pearson Prentice Hall. p. 222.
1766:
1527:
1470:
1361:
1193:
1144:
1065:
994:
196:
129:
118:
107:
79:
58:
42:
21:
2847:
2171:
2129:
1870:
1718:
1510:
1418:
1224:
1170:{\displaystyle \mathbf {J} =\mathbf {F} \Delta t.}
1169:
1120:
1035:
231:
163:
2117:Property Differences In Polymers: Happy/Sad Balls
1179:The impulse delivered by a varying force is the
1049:quantity, so impulse is also a vector quantity.
2239:
2039:expended, to create a performance parameter,
921:
8:
2170:Serway, Raymond A.; Jewett, John W. (2004).
2099:, mathematical abstraction of a pure impulse
1734:is the change in linear momentum from time
1282:The impulse delivered by the "sad" ball is
2246:
2232:
2224:
1942:Impulse has the same units and dimensions
1309:, the "happy" ball delivers an impulse of
928:
914:
175:
27:
2834:
2833:
2831:
1858:
1853:
1840:
1835:
1824:
1810:
1809:
1804:
1796:
1791:
1784:
1779:
1767:
1765:
1704:
1692:
1687:
1677:
1672:
1656:
1651:
1643:
1638:
1636:
1629:
1624:
1622:
1600:
1599:
1588:
1581:
1576:
1573:
1565:
1560:
1553:
1548:
1532:
1528:
1526:
1494:
1487:
1482:
1479:
1471:
1469:
1405:
1404:
1399:
1391:
1386:
1379:
1374:
1362:
1360:
1211:
1210:
1205:
1194:
1192:
1153:
1145:
1143:
1098:
1093:
1083:
1078:
1074:
1066:
1064:
1024:
1019:
1009:
1004:
995:
993:
213:
207:
198:
197:
195:
152:
146:
145:
138:
137:
131:
130:
128:
2266:
2109:
247:
183:
2043:. This fact can be used to derive the
147:
139:
132:
18:
980:, the object has received an impulse
610:Newton's law of universal gravitation
7:
2174:Physics for Scientists and Engineers
1433:is the resultant force applied from
591:Mechanics of planar particle motion
199:
1821:
1811:
1701:
1652:
1601:
1589:
1577:
1495:
1483:
1406:
1212:
1158:
1106:
14:
2001:. This type of impulse is often
1859:
1855:
1841:
1837:
1825:
1805:
1768:
1705:
1688:
1673:
1657:
1639:
1625:
1582:
1533:
1488:
1472:
1400:
1363:
1206:
1195:
1154:
1146:
1094:
1079:
1067:
1020:
1005:
996:
895:
894:
881:
214:
2270:Linear/translational quantities
2197:(5th ed.). W. H. Freeman.
1890:is the resultant force applied,
1458:, force is related to momentum
971:, and a subsequent momentum is
1262:-foot per second (slugâ
ft/s).
1:
2275:Angular/rotational quantities
2178:(6th ed.). Brooks/Cole.
2128:Hibbeler, Russell C. (2010).
1948:International System of Units
1053:Newtonâs second law of motion
517:Koopmanâvon Neumann mechanics
1256:British Gravitational System
1254:-second (lbfâ
s), and in the
1134:delivered by a steady force
585:Non-inertial reference frame
2045:Tsiolkovsky rocket equation
512:Appell's equation of motion
382:Inertial frame of reference
3272:
3251:Vector physical quantities
2848:{\displaystyle {\dot {m}}}
2272:
2020:
1916:is the mass of the object,
2546:specific angular momentum
2274:
2269:
2264:
1972:English engineering units
26:
2067:. Applications include:
1248:English engineering unit
1244:dimensionally equivalent
675:Rotating reference frame
507:HamiltonâJacobi equation
2670:rotational acceleration
2081:Acousto-optic modulator
1238:unit of impulse is the
1138:acting for time Ît is:
616:Newton's laws of motion
476:Newton's laws of motion
2849:
1872:
1720:
1512:
1420:
1327:
1226:
1187:with respect to time:
1171:
1122:
1059:acting on the object:
1037:
643:Simple harmonic motion
556:Euler's laws of motion
350:D'Alembert's principle
233:
165:
3256:Mechanical quantities
2850:
2193:Tipler, Paul (2004).
2132:Engineering Mechanics
2061:Waveâparticle duality
2021:Further information:
1873:
1721:
1513:
1421:
1281:
1227:
1172:
1123:
1038:
497:Hamiltonian mechanics
315:Statistical mechanics
234:
166:
2830:
2680:angular acceleration
2452:angular displacement
2097:Dirac delta function
1946:as momentum. In the
1764:
1525:
1468:
1359:
1191:
1142:
1063:
992:
720:Angular acceleration
712:Rotational frequency
492:Lagrangian mechanics
485:Analytical mechanics
241:Second law of motion
194:
127:
3246:Classical mechanics
2770:weighted position:
2587:rotational velocity
2535:kinematic viscosity
2255:Classical mechanics
1803:
1754:work-energy theorem
1650:
1572:
1456:Newton's second law
1398:
1336:produced from time
958:) is the change in
942:classical mechanics
572:Harmonic oscillator
550:Equations of motion
185:Classical mechanics
179:Part of a series on
2845:
1868:
1775:
1716:
1714:
1618:
1544:
1508:
1416:
1370:
1328:
1258:, the unit is the
1222:
1167:
1118:
1033:
888:Physics portal
502:Routhian mechanics
377:Frame of reference
229:
161:
96:in SI base units,
3233:
3232:
3228:
3227:
2842:
2795:moment of inertia
2143:978-0-13-607791-6
1597:
1503:
1354:is defined to be
1279:
1113:
938:
937:
685:Centrifugal force
680:Centripetal force
636:Euler's equations
621:Relative velocity
397:Moment of inertia
227:
201:
174:
173:
3263:
3220:
3216:
3204:
3200:
3180:
3176:
3164:
3160:
3138:
3134:
3124:
3114:
3099:
3095:
3085:
3063:
3059:
3049:
3039:
3024:
3020:
3007:
2983:
2977:
2969:
2958:
2952:
2941:
2934:angular momentum
2919:
2913:
2905:
2890:
2884:
2874:
2861:
2855:
2854:
2852:
2851:
2846:
2844:
2843:
2835:
2808:
2802:
2786:
2763:
2744:
2739:
2717:
2695:
2689:
2672:
2656:
2634:
2628:
2619:angular velocity
2616:
2597:
2596:
2583:
2582:
2575:rotational speed
2571:
2570:
2553:
2542:
2527:
2517:
2498:
2497:
2480:
2475:
2461:
2449:
2429:
2410:
2409:
2403:
2397:
2386:
2360:
2340:
2325:
2309:
2302:
2267:
2248:
2241:
2234:
2225:
2208:
2189:
2177:
2157:
2154:
2148:
2147:
2135:
2125:
2119:
2114:
2076:Nonlinear optics
2041:specific impulse
2023:Specific impulse
1993:
1984:
1969:
1960:
1945:
1937:
1926:
1915:
1909:
1900:
1889:
1878:
1875:
1874:
1869:
1864:
1863:
1862:
1846:
1845:
1844:
1828:
1814:
1808:
1802:
1801:
1800:
1790:
1789:
1788:
1771:
1751:
1742:
1733:
1726:
1723:
1722:
1717:
1715:
1708:
1697:
1696:
1691:
1682:
1681:
1676:
1664:
1660:
1655:
1649:
1648:
1647:
1642:
1635:
1634:
1633:
1628:
1611:
1604:
1598:
1596:
1592:
1586:
1585:
1580:
1574:
1571:
1570:
1569:
1559:
1558:
1557:
1536:
1517:
1515:
1514:
1509:
1504:
1502:
1498:
1492:
1491:
1486:
1480:
1475:
1463:
1450:
1441:
1432:
1426:
1423:
1422:
1417:
1409:
1403:
1397:
1396:
1395:
1385:
1384:
1383:
1366:
1353:
1344:
1335:
1325:
1308:
1299:
1290:
1280:
1231:
1229:
1228:
1223:
1215:
1209:
1198:
1186:
1176:
1174:
1173:
1168:
1157:
1149:
1137:
1133:
1127:
1125:
1124:
1119:
1114:
1112:
1104:
1103:
1102:
1097:
1088:
1087:
1082:
1075:
1070:
1058:
1042:
1040:
1039:
1034:
1029:
1028:
1023:
1014:
1013:
1008:
999:
985:
979:
970:
953:
930:
923:
916:
903:
898:
897:
890:
886:
885:
791:Johann Bernoulli
786:Daniel Bernoulli
707:Tangential speed
611:
587:
562:Fictitious force
557:
409:Mechanical power
399:
340:Angular momentum
238:
236:
235:
230:
228:
226:
218:
217:
208:
203:
202:
176:
170:
168:
167:
162:
160:
159:
151:
150:
143:
142:
136:
135:
31:
19:
3271:
3270:
3266:
3265:
3264:
3262:
3261:
3260:
3236:
3235:
3234:
3229:
3218:
3217:
3212:
3202:
3201:
3196:
3178:
3177:
3172:
3162:
3161:
3156:
3136:
3135:
3130:
3120:
3110:
3097:
3096:
3091:
3079:
3061:
3060:
3055:
3045:
3035:
3022:
3021:
3019:
3013:
3003:
2981:
2978:
2975:
2967:
2956:
2953:
2947:
2944:angular impulse
2937:
2917:
2914:
2911:
2903:
2888:
2885:
2880:
2870:
2859:
2856:
2828:
2827:
2826:
2806:
2803:
2798:
2771:
2764:
2759:
2742:
2740:
2733:
2718:
2713:
2693:
2690:
2683:
2673:
2668:
2657:
2652:
2632:
2629:
2622:
2612:
2598:
2590:
2585:
2578:
2573:
2566:
2561:
2554:
2549:
2544:
2538:
2528:
2523:
2513:
2499:
2493:
2488:
2476:
2473:
2468:
2462:
2455:
2445:
2430:
2425:
2415:
2405:
2399:
2393:
2388:
2382:
2361:
2356:
2341:
2336:
2326:
2321:
2305:
2298:
2260:
2252:
2215:
2205:
2192:
2186:
2169:
2166:
2161:
2160:
2155:
2151:
2144:
2127:
2126:
2122:
2115:
2111:
2106:
2057:
2025:
2019:
2011:physics engines
1985:
1975:
1961:
1951:
1943:
1936:
1930:
1925:
1919:
1913:
1908:
1902:
1899:
1893:
1885:
1854:
1836:
1792:
1780:
1762:
1760:
1750:
1744:
1741:
1735:
1728:
1713:
1712:
1686:
1671:
1662:
1661:
1637:
1623:
1609:
1608:
1587:
1575:
1561:
1549:
1537:
1523:
1521:
1493:
1481:
1466:
1465:
1459:
1449:
1443:
1440:
1434:
1428:
1387:
1375:
1357:
1355:
1352:
1346:
1343:
1337:
1331:
1324:
1310:
1307:
1301:
1298:
1292:
1289:
1283:
1270:
1268:
1242:(Nâ
s), and the
1189:
1188:
1184:
1140:
1139:
1135:
1131:
1130:so the impulse
1105:
1092:
1077:
1076:
1061:
1060:
1056:
1018:
1003:
990:
989:
981:
978:
972:
969:
963:
949:
948:(symbolized by
934:
893:
880:
879:
872:
871:
870:
745:
737:
736:
716:
670:Circular motion
664:
654:
653:
652:
609:
579:
576:
555:
534:
526:
525:
522:
521:
479:
469:
461:
460:
459:
418:
414:Mechanical work
407:
391:
329:
321:
320:
319:
274:
266:
243:
219:
209:
192:
191:
144:
125:
124:
82:
45:
38:
17:
12:
11:
5:
3269:
3267:
3259:
3258:
3253:
3248:
3238:
3237:
3231:
3230:
3226:
3225:
3206:
3190:
3188:
3185:
3166:
3150:
3148:
3144:
3143:
3104:
3073:
3071:
3068:
3029:
3017:
2997:
2995:
2991:
2990:
2961:
2931:
2929:
2926:
2897:
2864:
2841:
2838:
2823:Mass flow rate
2820:
2816:
2815:
2813:
2811:
2792:
2789:
2787:
2768:
2753:
2749:
2748:
2746:
2727:
2725:
2722:
2720:
2707:
2705:
2701:
2700:
2698:
2677:
2666:
2663:
2661:
2646:
2644:
2640:
2639:
2637:
2606:
2559:
2556:
2532:
2507:
2486:
2482:
2481:
2466:
2439:
2437:
2434:
2419:
2376:
2374:
2370:
2369:
2367:
2365:
2350:
2347:
2345:
2330:
2315:
2311:
2310:
2303:
2296:
2293:
2290:
2287:
2284:
2281:
2277:
2276:
2273:
2271:
2265:
2262:
2261:
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2065:phase matching
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1045:Momentum is a
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44:Common symbols
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24:
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15:
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4:
3:
2:
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3159:
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3133:
3128:
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3118:
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2723:
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2716:
2711:
2708:
2706:
2703:
2702:
2699:
2697:
2688:
2687:
2681:
2678:
2676:
2671:
2667:
2664:
2662:
2660:
2655:
2650:
2647:
2645:
2642:
2641:
2638:
2636:
2627:
2626:
2620:
2615:
2610:
2609:angular speed
2607:
2605:
2601:
2595:
2594:
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2576:
2569:
2564:
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2204:0-7167-0809-4
2200:
2196:
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2185:0-534-40842-7
2181:
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2017:Variable mass
2016:
2014:
2012:
2008:
2004:
2000:
1995:
1992:
1988:
1982:
1978:
1973:
1968:
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1954:
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1933:
1929:
1922:
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1912:
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1832:
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1776:
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1757:
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1410:
1392:
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1376:
1371:
1367:
1349:
1340:
1334:
1321:
1317:
1313:
1304:
1295:
1286:
1265:
1263:
1261:
1257:
1253:
1249:
1245:
1241:
1240:newton second
1237:
1232:
1219:
1216:
1202:
1199:
1183:of the force
1182:
1177:
1164:
1161:
1150:
1128:
1115:
1109:
1099:
1089:
1084:
1071:
1054:
1050:
1048:
1043:
1030:
1025:
1015:
1010:
1000:
987:
984:
975:
966:
961:
957:
952:
947:
943:
931:
926:
924:
919:
917:
912:
911:
909:
908:
902:
892:
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884:
878:
877:
876:
875:
867:
864:
862:
859:
857:
854:
852:
849:
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844:
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834:
832:
829:
827:
824:
822:
819:
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814:
812:
809:
807:
804:
802:
799:
797:
794:
792:
789:
787:
784:
782:
779:
777:
774:
772:
769:
767:
764:
762:
759:
757:
754:
752:
749:
748:
741:
740:
733:
729:
725:
721:
718:
717:
713:
710:
708:
705:
703:
700:
698:
695:
691:
688:
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678:
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649:
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641:
637:
634:
632:
629:
628:
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624:
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619:
617:
614:
612:
607:
604:
600:
597:
596:
592:
589:
586:
582:
578:
577:
573:
570:
568:
565:
563:
560:
558:
553:
551:
548:
546:
543:
541:
538:
537:
530:
529:
518:
515:
513:
510:
508:
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503:
500:
498:
495:
493:
490:
489:
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486:
481:
478:
477:
472:
471:
465:
464:
456:
453:
451:
448:
446:
443:
441:
438:
436:
433:
431:
428:
426:
423:
421:
417:
415:
412:
410:
406:
404:
401:
398:
394:
390:
388:
385:
383:
380:
378:
375:
373:
370:
366:
363:
361:
358:
357:
356:
353:
351:
348:
346:
343:
341:
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333:
332:
325:
324:
316:
313:
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308:
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301:
298:
296:
293:
291:
288:
286:
283:
281:
278:
277:
270:
269:
263:
260:
258:
255:
253:
250:
249:
246:
242:
223:
220:
210:
204:
190:
189:
186:
182:
178:
177:
156:
153:
123:
121:
117:
113:
110:
106:
103:
99:
95:
91:
87:
84:
78:
74:
70:
66:
65:newton-second
63:
61:
57:
54:
50:
47:
41:
36:
30:
25:
20:
3213:
3197:
3173:
3157:
3131:
3121:
3111:
3092:
3081:
3080:
3056:
3046:
3036:
3014:
3004:
2949:
2938:
2881:
2876:
2871:
2799:
2783:
2780:
2776:
2772:
2760:
2735:
2734:
2730:angular jerk
2714:
2685:
2684:
2653:
2649:acceleration
2624:
2623:
2613:
2592:
2591:
2579:
2567:
2550:
2539:
2524:
2514:
2494:
2457:
2456:
2446:
2426:
2413:displacement
2406:
2400:
2394:
2383:
2357:
2337:
2322:
2306:
2299:
2194:
2173:
2164:Bibliography
2152:
2131:
2123:
2112:
2026:
2002:
1996:
1950:, these are
1941:
1931:
1920:
1903:
1894:
1886:
1880:
1758:
1745:
1736:
1730:
1519:
1460:
1453:
1444:
1435:
1429:
1347:
1338:
1332:
1329:
1319:
1315:
1311:
1302:
1293:
1284:
1233:
1178:
1129:
1051:
1044:
988:
982:
973:
964:
955:
950:
945:
939:
730: /
726: /
724:displacement
722: /
583: /
545:Displacement
483:
474:
468:Formulations
455:Virtual work
395: /
386:
335:Acceleration
328:Fundamentals
60:SI unit
52:
48:
34:
2470:solid angle
2007:step change
1974:, they are
1520:Therefore,
866:von Neumann
533:Core topics
81:Other units
3240:Categories
3205:m s, N m s
3181:m s,
3127:Lagrangian
3052:Lagrangian
2292:Dimensions
2280:Dimensions
2089:scattering
2049:mass ratio
2037:propellant
801:d'Alembert
781:Maupertuis
744:Scientists
626:Rigid body
300:Kinematics
3221:ms,
2840:˙
2563:frequency
2490:frequency
2085:Electron
2003:idealized
1848:−
1822:Δ
1777:∫
1702:Δ
1684:−
1620:∫
1546:∫
1372:∫
1203:∫
1159:Δ
1107:Δ
1090:−
1016:−
846:Liouville
728:frequency
648:Vibration
365:potential
290:Continuum
285:Celestial
262:Textbooks
154:−
120:Dimension
109:Conserved
3165:m s, N s
2988:J s
2984:m s
2959:m s
2920:m s
2891:m s
2867:momentum
2520:velocity
2390:position
2379:distance
2333:absement
2258:SI units
2219:Dynamics
2055:See also
1330:Impulse
1291:, where
1181:integral
960:momentum
901:Category
826:Hamilton
811:Lagrange
806:Clairaut
771:Horrocks
732:velocity
702:Pendulum
690:reactive
662:Rotation
631:dynamics
581:Inertial
567:Friction
450:Velocity
425:Momentum
305:Kinetics
295:Dynamics
273:Branches
257:Timeline
3193:rotatum
2972:actergy
2908:actergy
2877:impulse
2797::
2548::
2478:rad, sr
1250:is the
946:impulse
861:Koopman
821:Poisson
816:Laplace
761:Huygens
756:Galileo
601: (
540:Damping
393:Inertia
387:Impulse
360:kinetic
310:Statics
280:Applied
252:History
35:impulse
22:Impulse
3107:energy
3088:moment
3076:torque
3032:energy
3010:weight
2982:
2964:action
2957:
2918:
2900:action
2889:
2860:
2807:
2779:â© = â
2743:
2694:
2633:
2201:
2182:
2140:
2087:phonon
2033:rocket
1999:impact
1881:where
1727:where
1427:where
1314:Δ
1047:vector
899:
851:Appell
836:Cauchy
831:Jacobi
776:Halley
766:Newton
751:Kepler
603:linear
599:Motion
445:Torque
420:Moment
355:Energy
345:Couple
3209:power
3169:power
3139:m s,
3100:m s,
3064:m s,
3025:m s,
3000:force
2510:speed
2442:angle
2104:Notes
2031:- or
1970:. In
1944:(MLT)
1454:From
1252:pound
856:Gibbs
841:Routh
796:Euler
435:Speed
430:Space
372:Force
3153:yank
3117:work
3042:work
2756:mass
2710:jerk
2422:area
2353:time
2318:time
2199:ISBN
2180:ISBN
2138:ISBN
1981:ft/s
1977:slug
1901:and
1260:slug
1234:The
440:Time
403:Mass
3187:MLT
3102:N m
3070:MLT
3023:kg
2928:MLT
2924:J s
2895:N s
2741:rad
2719:m s
2692:rad
2659:m s
2631:rad
2555:m s
2530:m s
2464:rad
2343:m s
2029:jet
1987:lbf
1957:m/s
1756:).
1743:to
1464:by
1442:to
1345:to
1318:= 2
956:Imp
954:or
940:In
114:yes
98:lbf
53:Imp
3242::
3219:kg
3211::
3203:kg
3195::
3179:kg
3171::
3163:kg
3155::
3147:MT
3137:kg
3129::
3125:,
3119::
3115:,
3109::
3098:kg
3090::
3086:,
3078::
3062:kg
3054::
3050:,
3044::
3040:,
3034::
3012::
3008:,
3002::
2994:MT
2986:,
2980:kg
2974::
2970:,
2968:đź
2966::
2955:kg
2946::
2942:,
2936::
2922:,
2916:kg
2910::
2906:,
2904:đź
2902::
2893:,
2887:kg
2879::
2875:,
2869::
2858:kg
2825::
2819:MT
2805:kg
2791:ML
2766:kg
2758::
2732::
2712::
2682::
2651::
2621::
2617:,
2611::
2604:Hz
2602:,
2589::
2584:,
2577::
2572:,
2565::
2537::
2522::
2518:,
2512::
2505:Hz
2503:,
2492::
2472::
2454::
2450:,
2444::
2424::
2411:,
2404:,
2398:,
2392::
2387:,
2381::
2355::
2335::
2320::
2051:.
1994:.
1953:kg
1451:.
1320:mv
1285:mv
1236:SI
986::
944:,
86:kg
51:,
3223:W
3214:P
3198:P
3183:W
3174:P
3158:Y
3141:J
3132:L
3122:W
3112:E
3093:M
3082:Ï
3066:J
3057:L
3047:W
3037:E
3027:N
3018:g
3015:F
3005:F
2976:â”
2950:L
2948:Î
2939:L
2912:â”
2882:J
2872:p
2862:s
2837:m
2809:m
2800:I
2784:x
2781:m
2777:x
2775:âš
2773:M
2761:m
2752:M
2745:s
2736:ζ
2724:T
2715:j
2704:T
2696:s
2686:α
2675:s
2665:T
2654:a
2643:T
2635:s
2625:Ï
2614:Ï
2600:s
2593:n
2580:n
2568:f
2558:T
2551:h
2543:,
2540:Μ
2525:v
2515:v
2501:s
2495:f
2485:T
2474:Ω
2458:Ξ
2447:Ξ
2436:1
2432:m
2427:A
2417:m
2407:x
2401:s
2395:r
2384:d
2373:1
2363:s
2358:t
2349:T
2338:A
2328:s
2323:t
2314:T
2307:Ξ
2300:Ξ
2295:1
2289:L
2286:L
2283:1
2247:e
2240:t
2233:v
2207:.
2188:.
2146:.
1991:s
1989:â
1983:=
1979:â
1967:s
1965:â
1963:N
1959:=
1955:â
1935:1
1932:v
1924:2
1921:v
1914:m
1907:2
1904:t
1898:1
1895:t
1887:F
1866:,
1860:1
1856:v
1851:m
1842:2
1838:v
1833:m
1830:=
1826:p
1819:=
1816:t
1812:d
1806:F
1798:2
1794:t
1786:1
1782:t
1773:=
1769:J
1749:2
1746:t
1740:1
1737:t
1731:p
1729:Î
1710:,
1706:p
1699:=
1694:1
1689:p
1679:2
1674:p
1669:=
1658:p
1653:d
1645:2
1640:p
1631:1
1626:p
1616:=
1606:t
1602:d
1594:t
1590:d
1583:p
1578:d
1567:2
1563:t
1555:1
1551:t
1542:=
1534:J
1506:.
1500:t
1496:d
1489:p
1484:d
1477:=
1473:F
1461:p
1448:2
1445:t
1439:1
1436:t
1430:F
1414:,
1411:t
1407:d
1401:F
1393:2
1389:t
1381:1
1377:t
1368:=
1364:J
1351:2
1348:t
1342:1
1339:t
1333:J
1326:.
1323:0
1316:v
1312:m
1306:0
1303:v
1297:0
1294:v
1288:0
1220:.
1217:t
1213:d
1207:F
1200:=
1196:J
1185:F
1165:.
1162:t
1155:F
1151:=
1147:J
1136:F
1132:J
1116:,
1110:t
1100:1
1095:p
1085:2
1080:p
1072:=
1068:F
1057:F
1031:.
1026:1
1021:p
1011:2
1006:p
1001:=
997:J
983:J
977:2
974:p
968:1
965:p
951:J
929:e
922:t
915:v
605:)
224:t
221:d
215:p
211:d
205:=
200:F
157:1
148:T
140:M
133:L
111:?
102:s
100:â
94:s
92:/
90:m
88:â
75:)
73:s
71:â
69:N
67:(
49:J
37:.
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