1711:"The SI unit of frequency is hertz, the SI unit of angular velocity and angular frequency is radian per second, and the SI unit of activity is becquerel, implying counts per second. Although it is formally correct to write all three of these units as the reciprocal second, the use of the different names emphasizes the different nature of the quantities concerned. It is especially important to carefully distinguish frequencies from angular frequencies, because by definition their numerical values differ by a factor of 2π. Ignoring this fact may cause an error of 2π. Note that in some countries, frequency values are conventionally expressed using “cycle/s” or “cps” instead of the SI unit Hz, although “cycle” and “cps” are not units in the SI. Note also that it is common, although not recommended, to use the term frequency for quantities expressed in rad/s. Because of this, it is recommended that quantities called “frequency”, “angular frequency”, and “angular velocity” always be given explicit units of Hz or rad/s and not s."
940:
1649:, despite some relation between the two concepts. Imagine a merry-go-round with a constant rate of rotation. No matter how close to or far from the axis of rotation you stand, your rotational frequency will remain constant. However, your tangential speed does not remain constant. If you stand two meters from the axis of rotation, your tangential speed will be double the amount if you were standing only one meter from the axis of rotation.
953:
47:
1701:
of a rotating body is defined to be the number of revolutions it makes in a time interval divided by that time interval . The SI unit of this quantity is thus the reciprocal second (s). However, as pointed out in Ref. , the designations “revolutions per second” (r/s) and “revolutions per minute”
1427:
1345:
294:
318:
1357:
1285:
1577:
226:
1188:
is the rate of change of rotational velocity; it has dimension of squared reciprocal time and SI units of squared reciprocal seconds (s); thus, it is a normalized version of
1352:
1624:
1280:
1469:
1601:
1252:
107:
1818:
1764:
1733:
1509:
1489:
1449:
1275:
1228:
984:
1775:
573:
692:
665:
939:
1799:
647:
1113:
1539:
in the SI system. Since 2Ď€ radians or 360 degrees correspond to a cycle, we can convert angular frequency to rotational frequency by
1743:
977:
313:
250:
308:
568:
1862:
1542:
563:
1085:
1029:
970:
957:
718:
641:
406:
637:
438:
857:
746:
672:
532:
465:
611:
887:
731:
1867:
1255:
877:
837:
601:
1053:
882:
699:
1165:
892:
867:
553:
371:
197:
1786:
1190:
1041:
912:
907:
872:
780:
776:
758:
548:
541:
297:
190:
134:
1702:(r/min) are widely used as units for rotational frequency in specifications on rotating machinery."
1673:
1089:
687:
628:
606:
351:
346:
341:
241:
817:
558:
433:
401:
361:
153:
1608:
1872:
1830:
1795:
1739:
1536:
1528:
1061:
1049:
1037:
827:
784:
741:
736:
677:
453:
443:
336:
138:
1454:
1658:
1585:
1208:
1155:
1117:
922:
902:
847:
842:
788:
763:
618:
476:
421:
396:
1761:"The NIST Guide for the Use of the International System of Units, Special Publication 811"
1668:
1663:
1237:
1159:
1151:
917:
862:
812:
807:
726:
92:
31:
1349:
An algebraic rearrangement of this equation allows us to solve for rotational frequency:
17:
1531:
rather than the quantity defined in this article. Angular frequency gives the change in
1842:
1635:
1494:
1474:
1434:
1260:
1213:
944:
852:
753:
470:
416:
1856:
1634:
might turn exactly one complete revolution each second. Its angular frequency is 360
1631:
832:
659:
1760:
1422:{\displaystyle {\begin{aligned}\nu &=v/2\pi r\\\omega &=v/r.\end{aligned}}}
897:
822:
511:
391:
146:
1340:{\displaystyle {\begin{aligned}v&=2\pi r\nu \\v&=r\omega .\end{aligned}}}
1066:
1013:
60:
46:
1678:
1196:
682:
356:
1523:
Rotational frequency can measure, for example, how fast a motor is running.
1021:
704:
1642:
per second (2Ď€ rad/s), while the rotational frequency is 60 rpm.
1814:
1025:
623:
506:
481:
1794:(9th ed.), International Bureau of Weights and Measures, Dec 2022,
1141:
1073:
1033:
596:
449:
366:
117:
1626:
is angular frequency, with unit radian per second or degree per second
1639:
1512:
1471:, as for a wheel, disk, or rigid wand. The direct proportionality of
655:
501:
411:
1646:
1532:
1045:
491:
486:
428:
122:
65:
54:
1815:"ISO 80000-3:2019 Quantities and units — Part 3: Space and time"
496:
459:
58:(in radians per second), is greater than rotational frequency
1515:, because the planets have different rotational frequencies.
1431:
Thus, the tangential speed will be directly proportional to
1070:
1231:
289:{\displaystyle {\textbf {F}}={\frac {d\mathbf {p} }{dt}}}
1451:
when all parts of a system simultaneously have the same
1611:
1588:
1545:
1497:
1477:
1457:
1437:
1355:
1283:
1263:
1240:
1216:
253:
200:
95:
1603:
is rotational frequency, with unit cycles per second
189:
159:
144:
128:
116:
84:
74:
39:
1759:Thompson, Ambler; Taylor, Barry N. (2020-03-04) .
1618:
1595:
1571:
1503:
1483:
1463:
1443:
1421:
1339:
1269:
1246:
1222:
1170:(external axis), the rotation speed may be called
288:
220:
101:
1645:Rotational frequency is not to be confused with
1120:, the reciprocal of rotational frequency is the
1819:International Organization for Standardization
1765:National Institute of Standards and Technology
1059:Rotational frequency can be obtained dividing
978:
8:
1535:per time unit, which is given with the unit
1164:(around an axis internal to the body) and
1158:rotational speed. In the special cases of
985:
971:
232:
45:
1615:
1610:
1592:
1587:
1555:
1544:
1496:
1476:
1456:
1436:
1404:
1373:
1356:
1354:
1284:
1282:
1277:, are related by the following equation:
1262:
1239:
1215:
270:
264:
255:
254:
252:
209:
203:
202:
199:
94:
1732:Atkins, Tony; Escudier, Marcel (2013).
1724:
1690:
1084:rad). It can also be formulated as the
304:
240:
1735:A Dictionary of Mechanical Engineering
204:
36:
667:Newton's law of universal gravitation
7:
1572:{\displaystyle \nu =\omega /2\pi ,}
648:Mechanics of planar particle motion
256:
1140:, with dimension of time (SI unit
1114:International System of Quantities
221:{\displaystyle {\mathsf {T}}^{-1}}
80:rotational speed, rate of rotation
25:
1788:The International System of Units
27:Number of rotations per unit time
952:
951:
938:
271:
1:
574:Koopman–von Neumann mechanics
1086:instantaneous rate of change
642:Non-inertial reference frame
1738:. Oxford University Press.
1638:per second (360°/s), or 2π
1154:whose magnitude equals the
569:Appell's equation of motion
439:Inertial frame of reference
1889:
1697:"The rotational frequency
1527:is sometimes used to mean
29:
1619:{\displaystyle \omega \,}
44:
18:Rotation period (physics)
1234:), rotational frequency
1096:, with respect to time,
732:Rotating reference frame
564:Hamilton–Jacobi equation
30:Not to be confused with
1843:"Rotational Quantities"
1464:{\displaystyle \omega }
1194:and it is analogous to
1186:Rotational acceleration
1116:). Similar to ordinary
673:Newton's laws of motion
533:Newton's laws of motion
1620:
1597:
1596:{\displaystyle \nu \,}
1573:
1505:
1485:
1465:
1445:
1423:
1341:
1271:
1248:
1224:
1054:revolutions per minute
700:Simple harmonic motion
613:Euler's laws of motion
407:D'Alembert's principle
290:
222:
103:
1621:
1598:
1574:
1511:is not valid for the
1506:
1486:
1466:
1446:
1424:
1342:
1272:
1249:
1225:
554:Hamiltonian mechanics
372:Statistical mechanics
291:
223:
104:
68:), by a factor of 2Ď€.
1863:Kinematic properties
1609:
1586:
1543:
1495:
1475:
1455:
1435:
1353:
1281:
1261:
1247:{\displaystyle \nu }
1238:
1214:
1191:angular acceleration
1042:units of measurement
998:Rotational frequency
777:Angular acceleration
769:Rotational frequency
549:Lagrangian mechanics
542:Analytical mechanics
298:Second law of motion
251:
198:
102:{\displaystyle \nu }
93:
40:Rotational frequency
1674:Rotational spectrum
1519:Regression analysis
1148:Rotational velocity
1090:number of rotations
629:Harmonic oscillator
607:Equations of motion
242:Classical mechanics
236:Part of a series on
1616:
1593:
1569:
1501:
1481:
1461:
1441:
1419:
1417:
1337:
1335:
1267:
1244:
1220:
1204:Related quantities
1126:period of rotation
1040:(s); other common
1038:reciprocal seconds
1012:, lowercase Greek
945:Physics portal
559:Routhian mechanics
434:Frame of reference
286:
218:
148:SI base units
99:
1801:978-92-822-2272-0
1763:(2008 ed.).
1537:radian per second
1529:angular frequency
1504:{\displaystyle r}
1484:{\displaystyle v}
1444:{\displaystyle r}
1270:{\displaystyle r}
1223:{\displaystyle v}
1062:angular frequency
1050:cycles per second
995:
994:
742:Centrifugal force
737:Centripetal force
693:Euler's equations
678:Relative velocity
454:Moment of inertia
284:
258:
231:
230:
16:(Redirected from
1880:
1847:
1846:
1839:
1833:
1829:
1827:
1826:
1811:
1805:
1804:
1793:
1783:
1777:
1774:
1772:
1771:
1756:
1750:
1749:
1729:
1712:
1709:
1703:
1695:
1659:Angular velocity
1647:tangential speed
1625:
1623:
1622:
1617:
1602:
1600:
1599:
1594:
1578:
1576:
1575:
1570:
1559:
1525:Rotational speed
1510:
1508:
1507:
1502:
1490:
1488:
1487:
1482:
1470:
1468:
1467:
1462:
1450:
1448:
1447:
1442:
1428:
1426:
1425:
1420:
1418:
1408:
1377:
1346:
1344:
1343:
1338:
1336:
1276:
1274:
1273:
1268:
1253:
1251:
1250:
1245:
1229:
1227:
1226:
1221:
1209:Tangential speed
1182:, respectively.
1179:revolution speed
1083:
1006:rate of rotation
1002:rotational speed
1000:, also known as
987:
980:
973:
960:
955:
954:
947:
943:
942:
848:Johann Bernoulli
843:Daniel Bernoulli
764:Tangential speed
668:
644:
619:Fictitious force
614:
466:Mechanical power
456:
397:Angular momentum
295:
293:
292:
287:
285:
283:
275:
274:
265:
260:
259:
233:
227:
225:
224:
219:
217:
216:
208:
207:
173:
163:other quantities
161:Derivations from
149:
108:
106:
105:
100:
49:
37:
21:
1888:
1887:
1883:
1882:
1881:
1879:
1878:
1877:
1853:
1852:
1851:
1850:
1841:
1840:
1836:
1824:
1822:
1813:
1812:
1808:
1802:
1791:
1785:
1784:
1780:
1769:
1767:
1758:
1757:
1753:
1746:
1731:
1730:
1726:
1721:
1716:
1715:
1710:
1706:
1696:
1692:
1687:
1669:Rotation period
1664:Radial velocity
1655:
1630:For example, a
1607:
1606:
1584:
1583:
1541:
1540:
1521:
1493:
1492:
1473:
1472:
1453:
1452:
1433:
1432:
1416:
1415:
1394:
1388:
1387:
1363:
1351:
1350:
1334:
1333:
1317:
1311:
1310:
1291:
1279:
1278:
1259:
1258:
1256:radial distance
1236:
1235:
1212:
1211:
1206:
1152:vector quantity
1122:rotation period
1081:
1065:, ω, by a full
991:
950:
937:
936:
929:
928:
927:
802:
794:
793:
773:
727:Circular motion
721:
711:
710:
709:
666:
636:
633:
612:
591:
583:
582:
579:
578:
536:
526:
518:
517:
516:
475:
471:Mechanical work
464:
448:
386:
378:
377:
376:
331:
323:
300:
276:
266:
249:
248:
201:
196:
195:
171:
164:
162:
147:
131:
91:
90:
87:
77:
70:
69:
35:
32:Circular motion
28:
23:
22:
15:
12:
11:
5:
1886:
1884:
1876:
1875:
1870:
1868:Temporal rates
1865:
1855:
1854:
1849:
1848:
1834:
1817:(2 ed.).
1806:
1800:
1778:
1751:
1744:
1723:
1722:
1720:
1717:
1714:
1713:
1704:
1689:
1688:
1686:
1683:
1682:
1681:
1676:
1671:
1666:
1661:
1654:
1651:
1628:
1627:
1614:
1604:
1591:
1568:
1565:
1562:
1558:
1554:
1551:
1548:
1520:
1517:
1500:
1480:
1460:
1440:
1414:
1411:
1407:
1403:
1400:
1397:
1395:
1393:
1390:
1389:
1386:
1383:
1380:
1376:
1372:
1369:
1366:
1364:
1362:
1359:
1358:
1332:
1329:
1326:
1323:
1320:
1318:
1316:
1313:
1312:
1309:
1306:
1303:
1300:
1297:
1294:
1292:
1290:
1287:
1286:
1266:
1243:
1230:(Latin letter
1219:
1205:
1202:
1030:around an axis
993:
992:
990:
989:
982:
975:
967:
964:
963:
962:
961:
948:
931:
930:
926:
925:
920:
915:
910:
905:
900:
895:
890:
885:
880:
875:
870:
865:
860:
855:
850:
845:
840:
835:
830:
825:
820:
815:
810:
804:
803:
800:
799:
796:
795:
792:
791:
772:
771:
766:
761:
756:
754:Coriolis force
751:
750:
749:
739:
734:
729:
723:
722:
717:
716:
713:
712:
708:
707:
702:
697:
696:
695:
690:
680:
675:
670:
663:
652:
651:
650:
645:
632:
631:
626:
621:
616:
609:
604:
599:
593:
592:
589:
588:
585:
584:
581:
580:
577:
576:
571:
566:
561:
556:
551:
545:
539:
537:
530:
527:
524:
523:
520:
519:
515:
514:
509:
504:
499:
494:
489:
484:
479:
473:
468:
462:
457:
446:
441:
436:
431:
426:
425:
424:
419:
409:
404:
399:
394:
388:
387:
384:
383:
380:
379:
375:
374:
369:
364:
359:
354:
349:
344:
339:
333:
332:
329:
328:
325:
324:
322:
321:
316:
311:
305:
302:
301:
296:
282:
279:
273:
269:
263:
245:
244:
238:
237:
229:
228:
215:
212:
206:
193:
187:
186:
165:
160:
157:
156:
151:
142:
141:
132:
129:
126:
125:
120:
114:
113:
98:
88:
86:Common symbols
85:
82:
81:
78:
75:
72:
71:
52:Angular speed
51:
50:
42:
41:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1885:
1874:
1871:
1869:
1866:
1864:
1861:
1860:
1858:
1844:
1838:
1835:
1831:
1820:
1816:
1810:
1807:
1803:
1797:
1790:
1789:
1782:
1779:
1776:
1766:
1762:
1755:
1752:
1747:
1745:9780199587438
1741:
1737:
1736:
1728:
1725:
1718:
1708:
1705:
1700:
1694:
1691:
1684:
1680:
1677:
1675:
1672:
1670:
1667:
1665:
1662:
1660:
1657:
1656:
1652:
1650:
1648:
1643:
1641:
1637:
1633:
1632:stepper motor
1612:
1605:
1589:
1582:
1581:
1580:
1566:
1563:
1560:
1556:
1552:
1549:
1546:
1538:
1534:
1530:
1526:
1518:
1516:
1514:
1498:
1478:
1458:
1438:
1429:
1412:
1409:
1405:
1401:
1398:
1396:
1391:
1384:
1381:
1378:
1374:
1370:
1367:
1365:
1360:
1347:
1330:
1327:
1324:
1321:
1319:
1314:
1307:
1304:
1301:
1298:
1295:
1293:
1288:
1264:
1257:
1241:
1233:
1217:
1210:
1203:
1201:
1199:
1198:
1193:
1192:
1187:
1183:
1181:
1180:
1175:
1174:
1169:
1168:
1163:
1162:
1157:
1153:
1149:
1145:
1143:
1139:
1135:
1131:
1127:
1123:
1119:
1115:
1111:
1107:
1103:
1099:
1095:
1091:
1087:
1079:
1075:
1072:
1068:
1064:
1063:
1057:
1055:
1051:
1047:
1043:
1039:
1035:
1031:
1028:of an object
1027:
1023:
1019:
1015:
1011:
1007:
1003:
999:
988:
983:
981:
976:
974:
969:
968:
966:
965:
959:
949:
946:
941:
935:
934:
933:
932:
924:
921:
919:
916:
914:
911:
909:
906:
904:
901:
899:
896:
894:
891:
889:
886:
884:
881:
879:
876:
874:
871:
869:
866:
864:
861:
859:
856:
854:
851:
849:
846:
844:
841:
839:
836:
834:
831:
829:
826:
824:
821:
819:
816:
814:
811:
809:
806:
805:
798:
797:
790:
786:
782:
778:
775:
774:
770:
767:
765:
762:
760:
757:
755:
752:
748:
745:
744:
743:
740:
738:
735:
733:
730:
728:
725:
724:
720:
715:
714:
706:
703:
701:
698:
694:
691:
689:
686:
685:
684:
681:
679:
676:
674:
671:
669:
664:
661:
657:
654:
653:
649:
646:
643:
639:
635:
634:
630:
627:
625:
622:
620:
617:
615:
610:
608:
605:
603:
600:
598:
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594:
587:
586:
575:
572:
570:
567:
565:
562:
560:
557:
555:
552:
550:
547:
546:
544:
543:
538:
535:
534:
529:
528:
522:
521:
513:
510:
508:
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503:
500:
498:
495:
493:
490:
488:
485:
483:
480:
478:
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472:
469:
467:
463:
461:
458:
455:
451:
447:
445:
442:
440:
437:
435:
432:
430:
427:
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1016:, and also
923:von Neumann
590:Core topics
130:Other units
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1857:Categories
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1825:2019-10-23
1770:2023-07-17
1719:References
1679:Tachometer
1197:chirpyness
1173:spin speed
1167:revolution
1020:), is the
858:d'Alembert
838:Maupertuis
801:Scientists
683:Rigid body
357:Kinematics
1613:ω
1590:ν
1564:π
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1459:ω
1392:ω
1382:π
1361:ν
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1022:frequency
1008:(symbols
903:Liouville
785:frequency
705:Vibration
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347:Continuum
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319:Textbooks
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958:Category
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863:Clairaut
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789:velocity
759:Pendulum
747:reactive
719:Rotation
688:dynamics
638:Inertial
624:Friction
507:Velocity
482:Momentum
362:Kinetics
352:Dynamics
330:Branches
314:Timeline
1640:radians
1636:degrees
1513:planets
1150:is the
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1036:is the
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1792:(PDF)
1685:Notes
1533:angle
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898:Routh
853:Euler
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487:Space
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