544:
603:
repelled one another, twisting the fiber through a certain angle, which could be read from a scale on the instrument. By knowing how much force it took to twist the fiber through a given angle, Coulomb was able to calculate the force between the balls. Determining the force for different charges and different separations between the balls, he showed that it followed an inverse-square proportionality law, now known as
46:
38:
536:
1855:
2172:
In measuring instruments, such as the D'Arsonval ammeter movement, it is often desired that the oscillatory motion die out quickly so the steady state result can be read off. This is accomplished by adding damping to the system, often by attaching a vane that rotates in a fluid such as air or water
598:
The torsion balance consists of a bar suspended from its middle by a thin fiber. The fiber acts as a very weak torsion spring. If an unknown force is applied at right angles to the ends of the bar, the bar will rotate, twisting the fiber, until it reaches an equilibrium where the twisting force or
427:
is a thick, steel torsion-bar spring attached to the body of a vehicle at one end and to a lever arm which attaches to the axle of the wheel at the other. It absorbs road shocks as the wheel goes over bumps and rough road surfaces, cushioning the ride for the passengers. Torsion-bar suspensions
602:
In
Coulomb's experiment, the torsion balance was an insulating rod with a metal-coated ball attached to one end, suspended by a silk thread. The ball was charged with a known charge of static electricity, and a second charged ball of the same polarity was brought near it. The two charged balls
505:
used in mechanical pointer-type meters to measure electric current is a type of torsion balance (see below). A coil of wire attached to the pointer twists in a magnetic field against the resistance of a torsion spring. Hooke's law ensures that the angle of the pointer is proportional to the
164:(shear) stresses. A helical torsion spring actually works by torsion when it is bent (not twisted). We will use the word "torsion" in the following for a torsion spring according to the definition given above, whether the material it is made of actually works by torsion or by bending.
599:
torque of the fiber balances the applied force. Then the magnitude of the force is proportional to the angle of the bar. The sensitivity of the instrument comes from the weak spring constant of the fiber, so a very weak force causes a large rotation of the bar.
650:
The most important advance in experiments on gravitation and other delicate measurements was the introduction of the torsion balance by
Michell and its use by Cavendish. It has been the basis of all the most significant experiments on gravitation ever
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58:
1489:
1358:
1842:
320:
may be calculated from the geometry and various material properties. It is analogous to the spring constant of a linear spring. The negative sign indicates that the direction of the torque is opposite to the direction of twist.
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1240:
Torsion balances, torsion pendulums and balance wheels are examples of torsional harmonic oscillators that can oscillate with a rotational motion about the axis of the torsion spring, clockwise and counterclockwise, in
1859:
645:
of light. In the early 1900s gravitational torsion balances were used in petroleum prospecting. Today torsion balances are still used in physics experiments. In 1987, gravity researcher A. H. Cook wrote:
1691:
2110:. If the damping is low, this can be obtained by measuring the natural resonant frequency of the balance, since the moment of inertia of the balance can usually be calculated from its geometry, so:
156:
Torsion bars and torsion fibers do work by torsion. However, the terminology can be confusing because in helical torsion spring (including clock spring), the forces acting on the wire are actually
614:
of the torsion fiber must first be known. This is difficult to measure directly because of the smallness of the force. Cavendish accomplished this by a method widely used since: measuring the
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139:
Clocks use a spiral wound torsion spring (a form of helical torsion spring where the coils are around each other instead of piled up) sometimes called a "clock spring" or colloquially called a
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59:
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61:
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is a wheel-shaped weight suspended from its center by a wire torsion spring. The weight rotates about the axis of the spring, twisting it, instead of swinging like an ordinary
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964:
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back toward its center position as it rotates back and forth. The balance wheel and spring function similarly to the torsion pendulum above in keeping time for the watch.
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2173:(this is why magnetic compasses are filled with fluid). The value of damping that causes the oscillatory motion to settle quickest is called the critical damping
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1983:
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521:. It uses hundreds of thousands of tiny mirrors on tiny torsion springs fabricated on a silicon surface to reflect light onto the screen, forming the image.
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60:
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of the beam and the elasticity of the fiber. Since the inertia of the beam can be found from its mass, the spring constant can be calculated.
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456:. The force of the spring reverses the direction of rotation, so the wheel oscillates back and forth, driven at the top by the clock's gears.
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to measure the gravitational force between two masses to calculate the density of the Earth, leading later to a value for the
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of the balance. If the free balance is twisted and released, it will oscillate slowly clockwise and counterclockwise as a
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2526:. Description of how torsion balances were used in petroleum prospecting, with pictures of a 1902 instrument.
2470:. Shows pictures of the Coulomb torsion balance, and describes Coulomb's contributions to torsion technology.
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631:
Recherches theoriques et experimentales sur la force de torsion et sur l'elasticite des fils de metal &c
161:
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Big G measurement, description of 1999 Cavendish experiment at Univ. of
Washington, showing torsion balance
409:. Small, coiled torsion springs are often used to operate pop-up doors found on small consumer goods like
2795:
2030:
2024:. When the oscillatory motion of the balance dies out, the deflection will be proportional to the force:
1242:
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1584:{\displaystyle T_{n}={\frac {1}{f_{n}}}={\frac {2\pi }{\omega _{n}}}=2\pi {\sqrt {\frac {I}{\kappa }}}\,}
1142:
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2644:
1401:, as is the case with torsion pendulums and balance wheels, the frequency of vibration is very near the
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661:
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in the opposite direction, proportional to the amount (angle) it is twisted. There are various types:
2674:
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2395:
Cavendish, H. (1798), "Experiments to determine the
Density of the Earth", in MacKenzie, A.S. (ed.),
1402:
588:
438:
83:
1704:
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2629:
1988:
1484:{\displaystyle f_{n}={\frac {\omega _{n}}{2\pi }}={\frac {1}{2\pi }}{\sqrt {\frac {\kappa }{I}}}\,}
1246:
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619:
576:
79:
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Coulomb first developed the theory of torsion fibers and the torsion balance in his 1785 memoir,
1943:
In a torsion balance the drive torque is constant and equal to the unknown force to be measured
2092:
1922:
1597:
1353:{\displaystyle I{\frac {d^{2}\theta }{dt^{2}}}+C{\frac {d\theta }{dt}}+\kappa \theta =\tau (t)}
1120:
1049:
782:
692:
278:
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and other devices that need near constant torque for large angles or even multiple revolutions.
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2297:
1837:{\displaystyle \omega ={\sqrt {\omega _{n}^{2}-\alpha ^{2}}}={\sqrt {\kappa /I-(C/2I)^{2}}}\,}
623:
87:
2176:
1919:
with weight screws set radially into the rim of the wheel, and then more finely by adjusting
1898:
sets the rate of the watch. The resonant frequency is regulated, first coarsely by adjusting
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397:. Other uses are in the large, coiled torsion springs used to counterbalance the weight of
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The balance wheel of a mechanical watch is a harmonic oscillator whose resonant frequency
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312:, equal to the change in torque required to twist the spring through an angle of 1 radian.
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Cook, A. H. (1987), "Experiments in
Gravitation", in Hawking, S.W.; Israel, W. (eds.),
484:
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133:
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The Theory and
Practice of Absolute Measurements in Electricity and Magnetism, Vol.1
389:
Some familiar examples of uses are the strong, helical torsion springs that operate
132:(coil) that is subjected to twisting about the axis of the coil by sideways forces (
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414:
118:
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is a constant with units of newton-meters / radian, variously called the spring's
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567:, is a scientific apparatus for measuring very weak forces, usually credited to
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17:
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Solved mechanics problems involving springs (springs in series and in parallel)
575:
sometime before 1783. Its most well-known uses were by
Coulomb to measure the
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390:
144:
140:
1245:. Their behavior is analogous to translational spring-mass oscillators (see
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615:
394:
50:
37:
2515:
2349:"Dynamics and Vibrations: Conservation Laws for Particles: Work and Energy"
665:- the idea that inertial mass and gravitational mass are one and the same.
143:. Those types of torsion springs are also used for attic stairs, clutches,
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468:
453:
433:
1940:
with a regulating lever that changes the length of the balance spring.
539:
Drawing of
Coulomb's torsion balance. From Plate 13 of his 1785 memoir.
402:
157:
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428:
are used in many modern cars and trucks, as well as military vehicles.
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Shigley, Joseph E.; Mischke, Charles R.; Budynas, Richard G. (2003),
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is a straight bar of metal or rubber that is subjected to twisting (
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633:. This led to its use in other scientific instruments, such as
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in his measurements of the gravitational constant G at the U.S.
2590:
1686:{\displaystyle \theta =Ae^{-\alpha t}\cos {(\omega t+\phi )}\,}
467:
to power several types of ancient weapons; including the Greek
109:
A more delicate form used in sensitive instruments, called a
571:, who invented it in 1777, but independently invented by
492:
is a fine, spiral-shaped torsion spring that pushes the
401:, and a similar system is used to assist in opening the
268:
is the angle of twist from its equilibrium position in
2565:
How torsion balances were used in petroleum prospecting
2514:, Society of Exploration Geophysicists, archived from
2454:
Charles
Augustin de Coulomb biography, Chemistry Dept.
2401:, American Book Co. (published 1900), pp. 59–105
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when it is twisted. When it is twisted, it exerts a
2375:, American Philosophical Society, pp. 335–344,
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it is necessary to find the torsion spring constant
1594:
The general solution in the case of no drive force (
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2398:Scientific Memoirs, Vol.9: The Laws of Gravitation
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374:{\displaystyle U={\frac {1}{2}}\kappa \theta ^{2}}
373:
288:
260:
235:
208:
136:) applied to its ends, twisting the coil tighter.
459:Torsion springs consisting of twisted ropes or
441:systems also uses the torsion spring principle.
106:) about its axis by torque applied at its ends.
2573:. Web archive link, accessed December 8, 2016.
121:under tension, that is twisted about its axis.
2602:
1234:Distance from axis to where force is applied
172:As long as they are not twisted beyond their
66:Video of a model torsion pendulum oscillating
30:For torsion coefficients in mathematics, see
8:
2537:, vol. 6, Werner Co., 1907, p. 452
2448:. Detailed account of Coulomb's experiment.
934:Undamped (or natural) period of oscillation
82:its end along its axis; that is, a flexible
2457:, Hebrew Univ. of Jerusalem, archived from
2241:{\displaystyle C_{c}=2{\sqrt {\kappa I}}\,}
2162:{\displaystyle \kappa =(2\pi f_{n})^{2}I\,}
1964:, times the moment arm of the balance beam
128:, is a metal rod or wire in the shape of a
2754:
2609:
2595:
2587:
2511:Torsion balance, Virtual Geoscience Center
2416:, Cambridge University Press, p. 52,
659:, a torsion balance was used to prove the
176:, torsion springs obey an angular form of
2550:Torsion balance interactive java tutorial
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1866:Animation of a torsion spring oscillating
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1494:Therefore, the period is represented by:
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1419:
1413:
1394:{\displaystyle C\ll {\sqrt {\kappa I}}\,}
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897:Undamped (or natural) resonant frequency
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1104:{\displaystyle \mathrm {rad\,s^{-1}} \,}
1003:{\displaystyle \mathrm {rad\,s^{-1}} \,}
672:
611:
2274:
1012:Undamped resonant frequency in radians
715:Angle of deflection from rest position
393:and traditional spring-loaded-bar type
243:is the torque exerted by the spring in
209:{\displaystyle \tau =-\kappa \theta \,}
2474:Nichols, E.F.; Hull, G.F (June 1903),
2302:, New York: McGraw Hill, p. 542,
1621:), called the transient solution, is:
1247:Harmonic oscillator Equivalent systems
1113:Damped resonant frequency in radians
622:, at a frequency that depends on the
7:
2582:Milestones in the History of Springs
2505:. Describes the Nichols radiometer.
2058:{\displaystyle \theta =FL/\kappa \,}
1174:Reciprocal of damping time constant
417:players. Other more specific uses:
41:Garage Door Sectional Torsion Spring
1165:{\displaystyle \mathrm {s^{-1}} \,}
53:powered by a helical torsion spring
2414:Three Hundred Years of Gravitation
1148:
1087:
1082:
1079:
1076:
986:
981:
978:
975:
843:
839:
610:To measure the unknown force, the
25:
2328:, Tata McGraw-Hill, p. 429,
851:{\displaystyle \mathrm {N\,m} \,}
555:(now NIST) between 1930 and 1942.
332:, stored in a torsion spring is:
2535:Encyclopædia Britannica, 9th Ed.
2476:"The Pressure due to Radiation"
2146:
2126:
2001:
1995:
1822:
1804:
1732:{\displaystyle \alpha =C/2I\,}
1678:
1663:
1347:
1341:
669:Torsional harmonic oscillators
32:Torsion coefficient (topology)
1:
2531:"Charles Augustin de Coulomb"
2446:, Macmillan, pp. 254–260
2299:Mechanical Engineering Design
2017:{\displaystyle \tau (t)=FL\,}
959:{\displaystyle \omega _{n}\,}
579:between charges to establish
517:chip is at the heart of many
2650:Electronic Stability Control
2571:Mechanics of torsion springs
553:National Bureau of Standards
488:or hairspring in mechanical
1204:Phase angle of oscillation
569:Charles-Augustin de Coulomb
2906:
2325:Design of Machine Elements
1403:natural resonant frequency
1042:Damped resonant frequency
515:digital micromirror device
29:
2555:Torsion spring calculator
2480:The Astrophysical Journal
2103:{\displaystyle \kappa \,}
1933:{\displaystyle \kappa \,}
1614:{\displaystyle \tau =0\,}
1131:{\displaystyle \alpha \,}
1060:{\displaystyle \omega \,}
793:{\displaystyle \kappa \,}
775:Angular damping constant
703:{\displaystyle \theta \,}
616:resonant vibration period
289:{\displaystyle \kappa \,}
261:{\displaystyle \theta \,}
2283:"Typewriter Maintenance"
805:Torsion spring constant
547:Torsion balance used by
2322:Bandari, V. B. (2007),
2194:{\displaystyle C_{c}\,}
1891:{\displaystyle f_{n}\,}
1192:{\displaystyle \phi \,}
922:{\displaystyle T_{n}\,}
885:{\displaystyle f_{n}\,}
823:{\displaystyle \tau \,}
475:and catapults like the
450:torsion pendulum clocks
302:torsion elastic modulus
236:{\displaystyle \tau \,}
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424:torsion bar suspension
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126:helical torsion spring
67:
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2440:Gray, Andrew (1888),
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662:equivalence principle
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463:, were used to store
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2885:Springs (mechanical)
2265:, helical toy spring
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674:Definition of terms
589:Cavendish experiment
339:
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187:
2617:Automotive handling
2492:1903ApJ....17..315N
2082:{\displaystyle F\,}
1978:{\displaystyle L\,}
1957:{\displaystyle F\,}
1912:{\displaystyle I\,}
1769:
1222:{\displaystyle L\,}
1030:{\displaystyle f\,}
763:{\displaystyle C\,}
733:{\displaystyle I\,}
675:
641:which measured the
620:harmonic oscillator
577:electrostatic force
502:D'Arsonval movement
298:torsion coefficient
168:Torsion coefficient
117:of silk, glass, or
86:object that stores
2567:(web archive link)
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745:Moment of inertia
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643:radiation pressure
639:Nichols radiometer
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439:vehicle suspension
403:trunk (boot) cover
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657:Eötvös experiment
624:moment of inertia
356:
88:mechanical energy
63:
16:(Redirected from
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2821:MacPherson strut
2806:
2779:Semi-independent
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2700:Vehicle dynamics
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1763:
1754:
1738:
1736:
1735:
1730:
1721:
1692:
1690:
1689:
1684:
1681:
1655:
1654:
1620:
1618:
1617:
1612:
1590:
1588:
1587:
1582:
1579:
1570:
1569:
1558:
1556:
1555:
1546:
1538:
1533:
1531:
1530:
1518:
1513:
1512:
1490:
1488:
1487:
1482:
1479:
1470:
1469:
1467:
1465:
1454:
1449:
1447:
1439:
1438:
1429:
1424:
1423:
1400:
1398:
1397:
1392:
1389:
1381:
1359:
1357:
1356:
1351:
1325:
1323:
1315:
1307:
1299:
1297:
1296:
1295:
1282:
1278:
1277:
1267:
1249:). The general
1228:
1226:
1225:
1220:
1198:
1196:
1195:
1190:
1171:
1169:
1168:
1163:
1160:
1159:
1158:
1137:
1135:
1134:
1129:
1110:
1108:
1107:
1102:
1099:
1098:
1097:
1066:
1064:
1063:
1058:
1036:
1034:
1033:
1028:
1009:
1007:
1006:
1001:
998:
997:
996:
965:
963:
962:
957:
954:
953:
928:
926:
925:
920:
917:
916:
891:
889:
888:
883:
880:
879:
857:
855:
854:
849:
846:
829:
827:
826:
821:
799:
797:
796:
791:
769:
767:
766:
761:
739:
737:
736:
731:
709:
707:
706:
701:
676:
565:torsion pendulum
519:video projectors
465:potential energy
446:torsion pendulum
380:
378:
377:
372:
370:
369:
357:
349:
318:torsion constant
295:
293:
292:
287:
267:
265:
264:
259:
242:
240:
239:
234:
215:
213:
212:
207:
152:Torsion, bending
64:
21:
18:Torsion pendulum
2905:
2904:
2900:
2899:
2898:
2896:
2895:
2894:
2870:
2869:
2868:
2859:
2804:Double wishbone
2790:
2774:
2743:
2709:
2705:Weight transfer
2618:
2615:
2546:
2541:
2529:
2521:
2519:
2508:
2473:
2464:
2462:
2451:
2439:
2435:
2430:
2424:
2411:
2410:
2406:
2394:
2393:
2389:
2383:
2361:
2360:
2356:
2347:
2346:
2342:
2336:
2321:
2320:
2316:
2310:
2295:
2294:
2290:
2281:
2280:
2276:
2272:
2254:
2211:
2206:
2205:
2180:
2175:
2174:
2145:
2135:
2115:
2114:
2091:
2090:
2070:
2069:
2029:
2028:
1987:
1986:
1966:
1965:
1945:
1944:
1921:
1920:
1900:
1899:
1877:
1872:
1871:
1854:
1852:
1821:
1773:
1742:
1741:
1703:
1702:
1640:
1626:
1625:
1596:
1595:
1547:
1539:
1522:
1504:
1499:
1498:
1458:
1440:
1430:
1415:
1410:
1409:
1405:of the system:
1369:
1368:
1316:
1308:
1287:
1283:
1269:
1268:
1258:
1257:
1243:harmonic motion
1210:
1209:
1180:
1179:
1147:
1141:
1140:
1119:
1118:
1086:
1070:
1069:
1048:
1047:
1018:
1017:
985:
969:
968:
945:
940:
939:
908:
903:
902:
871:
866:
865:
833:
832:
811:
810:
781:
780:
751:
750:
721:
720:
691:
690:
671:
612:spring constant
587:in 1798 in the
585:Henry Cavendish
561:torsion balance
533:
531:Torsion balance
411:digital cameras
387:
361:
337:
336:
310:spring constant
277:
276:
249:
248:
224:
223:
185:
184:
170:
154:
134:bending moments
57:
35:
28:
23:
22:
15:
12:
11:
5:
2903:
2901:
2893:
2892:
2887:
2882:
2872:
2871:
2865:
2864:
2861:
2860:
2858:
2857:
2845:
2840:
2838:Sliding pillar
2835:
2830:
2818:
2813:
2800:
2798:
2792:
2791:
2789:
2788:
2782:
2780:
2776:
2775:
2773:
2772:
2767:
2761:
2759:
2752:
2745:
2744:
2742:
2741:
2736:
2731:
2726:
2720:
2718:
2711:
2710:
2708:
2707:
2702:
2697:
2692:
2687:
2682:
2677:
2672:
2667:
2662:
2657:
2652:
2647:
2642:
2637:
2635:Center of mass
2632:
2626:
2624:
2620:
2619:
2616:
2614:
2613:
2606:
2599:
2591:
2585:
2584:
2579:
2574:
2568:
2562:
2557:
2552:
2545:
2544:External links
2542:
2540:
2539:
2527:
2506:
2501:10.1086/141035
2486:(5): 315–351,
2471:
2449:
2436:
2434:
2431:
2429:
2428:
2422:
2404:
2387:
2381:
2367:McCormmach, R.
2363:Jungnickel, C.
2354:
2340:
2334:
2314:
2308:
2288:
2273:
2271:
2268:
2267:
2266:
2260:
2253:
2250:
2249:
2248:
2234:
2231:
2226:
2223:
2218:
2214:
2187:
2183:
2170:
2169:
2157:
2152:
2148:
2142:
2138:
2134:
2131:
2128:
2125:
2122:
2098:
2077:
2066:
2065:
2053:
2049:
2045:
2042:
2039:
2036:
2012:
2009:
2006:
2003:
2000:
1997:
1994:
1973:
1952:
1928:
1907:
1884:
1880:
1851:
1848:
1847:
1846:
1845:
1844:
1828:
1824:
1820:
1817:
1813:
1809:
1806:
1803:
1800:
1796:
1792:
1787:
1780:
1776:
1772:
1767:
1762:
1758:
1752:
1749:
1739:
1727:
1724:
1720:
1716:
1713:
1710:
1694:
1693:
1680:
1677:
1674:
1671:
1668:
1665:
1661:
1658:
1653:
1650:
1647:
1643:
1639:
1636:
1633:
1609:
1606:
1603:
1592:
1591:
1576:
1573:
1567:
1564:
1561:
1554:
1550:
1545:
1542:
1536:
1529:
1525:
1521:
1516:
1511:
1507:
1492:
1491:
1476:
1473:
1464:
1461:
1457:
1452:
1446:
1443:
1437:
1433:
1427:
1422:
1418:
1387:
1384:
1379:
1376:
1361:
1360:
1349:
1346:
1343:
1340:
1337:
1334:
1331:
1328:
1322:
1319:
1314:
1311:
1305:
1302:
1294:
1290:
1286:
1281:
1276:
1272:
1265:
1253:of motion is:
1236:
1235:
1232:
1229:
1217:
1206:
1205:
1202:
1199:
1187:
1176:
1175:
1172:
1157:
1154:
1150:
1138:
1126:
1115:
1114:
1111:
1096:
1093:
1089:
1084:
1081:
1078:
1067:
1055:
1044:
1043:
1040:
1037:
1025:
1014:
1013:
1010:
995:
992:
988:
983:
980:
977:
966:
952:
948:
936:
935:
932:
929:
915:
911:
899:
898:
895:
892:
878:
874:
862:
861:
858:
845:
841:
830:
818:
807:
806:
803:
800:
788:
777:
776:
773:
770:
758:
747:
746:
743:
740:
728:
717:
716:
713:
710:
698:
687:
686:
683:
680:
670:
667:
563:, also called
532:
529:
528:
527:
522:
507:
497:
485:balance spring
480:
471:and the Roman
457:
442:
429:
386:
383:
382:
381:
368:
364:
360:
355:
352:
347:
344:
314:
313:
284:
273:
272:
256:
231:
217:
216:
204:
201:
198:
195:
192:
169:
166:
160:stresses, not
153:
150:
149:
148:
137:
122:
113:consists of a
107:
78:that works by
72:torsion spring
27:Type of spring
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2902:
2891:
2888:
2886:
2883:
2881:
2878:
2877:
2875:
2854:
2849:
2846:
2844:
2841:
2839:
2836:
2834:
2831:
2827:
2826:Chapman strut
2822:
2819:
2817:
2814:
2810:
2805:
2802:
2801:
2799:
2797:
2793:
2787:
2784:
2783:
2781:
2777:
2771:
2768:
2766:
2763:
2762:
2760:
2756:
2753:
2750:
2746:
2740:
2737:
2735:
2732:
2730:
2727:
2725:
2722:
2721:
2719:
2716:
2712:
2706:
2703:
2701:
2698:
2696:
2695:Unsprung mass
2693:
2691:
2688:
2686:
2683:
2681:
2678:
2676:
2673:
2671:
2668:
2666:
2663:
2661:
2660:Inboard brake
2658:
2656:
2653:
2651:
2648:
2646:
2643:
2641:
2638:
2636:
2633:
2631:
2628:
2627:
2625:
2621:
2612:
2607:
2605:
2600:
2598:
2593:
2592:
2589:
2583:
2580:
2578:
2575:
2572:
2569:
2566:
2563:
2561:
2558:
2556:
2553:
2551:
2548:
2547:
2543:
2536:
2532:
2528:
2518:on 2007-08-18
2517:
2513:
2512:
2507:
2502:
2497:
2493:
2489:
2485:
2481:
2477:
2472:
2461:on 2009-08-06
2460:
2456:
2455:
2450:
2445:
2444:
2438:
2437:
2432:
2425:
2423:0-521-34312-7
2419:
2415:
2408:
2405:
2400:
2399:
2391:
2388:
2384:
2382:0-87169-220-1
2378:
2374:
2373:
2368:
2364:
2358:
2355:
2350:
2344:
2341:
2337:
2331:
2327:
2326:
2318:
2315:
2311:
2309:0-07-292193-5
2305:
2301:
2300:
2292:
2289:
2284:
2278:
2275:
2269:
2264:
2261:
2259:
2256:
2255:
2251:
2232:
2229:
2224:
2221:
2216:
2212:
2204:
2203:
2202:
2185:
2181:
2155:
2150:
2140:
2136:
2132:
2129:
2123:
2120:
2113:
2112:
2111:
2096:
2075:
2068:To determine
2051:
2047:
2043:
2040:
2037:
2034:
2027:
2026:
2025:
2010:
2007:
2004:
1998:
1992:
1971:
1950:
1941:
1926:
1905:
1882:
1878:
1849:
1826:
1818:
1815:
1811:
1807:
1801:
1798:
1794:
1790:
1785:
1778:
1774:
1770:
1765:
1760:
1756:
1750:
1747:
1740:
1725:
1722:
1718:
1714:
1711:
1708:
1701:
1700:
1699:
1698:
1697:
1675:
1672:
1669:
1666:
1659:
1656:
1651:
1648:
1645:
1641:
1637:
1634:
1631:
1624:
1623:
1622:
1607:
1604:
1601:
1574:
1571:
1565:
1562:
1559:
1552:
1548:
1543:
1540:
1534:
1527:
1523:
1519:
1514:
1509:
1505:
1497:
1496:
1495:
1474:
1471:
1462:
1459:
1455:
1450:
1444:
1441:
1435:
1431:
1425:
1420:
1416:
1408:
1407:
1406:
1404:
1385:
1382:
1377:
1374:
1366:
1344:
1338:
1335:
1332:
1329:
1326:
1320:
1317:
1312:
1309:
1303:
1300:
1292:
1288:
1284:
1279:
1274:
1270:
1263:
1256:
1255:
1254:
1252:
1248:
1244:
1233:
1230:
1215:
1208:
1207:
1203:
1200:
1185:
1178:
1177:
1173:
1155:
1152:
1139:
1124:
1117:
1116:
1112:
1094:
1091:
1068:
1053:
1046:
1045:
1041:
1038:
1023:
1016:
1015:
1011:
993:
990:
967:
950:
946:
938:
937:
933:
930:
913:
909:
901:
900:
896:
893:
876:
872:
864:
863:
860:Drive torque
859:
831:
816:
809:
808:
804:
801:
786:
779:
778:
774:
771:
756:
749:
748:
744:
741:
726:
719:
718:
714:
711:
696:
689:
688:
684:
681:
678:
677:
668:
666:
664:
663:
658:
652:
647:
644:
640:
636:
635:galvanometers
632:
627:
625:
621:
617:
613:
608:
606:
605:Coulomb's law
600:
596:
594:
590:
586:
582:
581:Coulomb's Law
578:
574:
570:
566:
562:
554:
550:
545:
537:
530:
526:
523:
520:
516:
512:
508:
504:
503:
498:
495:
494:balance wheel
491:
487:
486:
481:
478:
474:
470:
466:
462:
458:
455:
451:
447:
443:
440:
437:used in many
436:
435:
430:
426:
425:
420:
419:
418:
416:
412:
408:
404:
400:
396:
392:
384:
366:
362:
358:
353:
350:
345:
342:
335:
334:
333:
331:
327:
322:
319:
311:
307:
303:
299:
282:
275:
274:
271:
254:
247:-meters, and
246:
229:
222:
221:
220:
202:
199:
196:
193:
190:
183:
182:
181:
179:
175:
174:elastic limit
167:
165:
163:
159:
151:
146:
142:
138:
135:
131:
127:
123:
120:
116:
112:
111:torsion fiber
108:
105:
101:
97:
96:
95:
93:
89:
85:
81:
77:
73:
52:
47:
39:
33:
19:
2848:Trailing arm
2770:De Dion tube
2738:
2630:Car handling
2534:
2520:, retrieved
2516:the original
2510:
2483:
2479:
2463:, retrieved
2459:the original
2453:
2442:
2433:Bibliography
2413:
2407:
2397:
2390:
2371:
2357:
2343:
2324:
2317:
2298:
2291:
2277:
2171:
2067:
1942:
1869:
1850:Applications
1695:
1593:
1493:
1362:
1239:
772:joule s rad
660:
654:
649:
630:
628:
609:
601:
597:
573:John Michell
564:
560:
558:
549:Paul R. Heyl
525:Badge tether
510:
500:
483:
445:
432:
422:
415:compact disc
399:garage doors
388:
325:
323:
315:
309:
305:
301:
297:
218:
171:
155:
125:
110:
104:shear stress
99:
71:
69:
2796:Independent
2680:Tire / Tyre
2655:Fishtailing
2623:Main topics
685:Definition
391:clothespins
324:The energy
178:Hooke's law
145:typewriters
100:torsion bar
2874:Categories
2843:Swing axle
2833:Multi-link
2809:Jaguar IRS
2786:Twist beam
2749:Suspension
2690:Understeer
2675:Suspension
2522:2007-08-04
2270:References
1367:is small,
637:, and the
395:mousetraps
308:, or just
141:mainspring
2880:Pendulums
2765:Beam axle
2758:Dependent
2734:Pneumatic
2685:Transaxle
2665:Oversteer
2640:Downforce
2465:August 2,
2372:Cavendish
2230:κ
2133:π
2121:κ
2097:κ
2052:κ
2035:θ
1993:τ
1927:κ
1802:−
1791:κ
1775:α
1771:−
1757:ω
1748:ω
1709:α
1676:ϕ
1667:ω
1660:
1649:α
1646:−
1632:θ
1602:τ
1575:κ
1566:π
1549:ω
1544:π
1472:κ
1463:π
1445:π
1432:ω
1383:κ
1378:≪
1339:τ
1333:θ
1330:κ
1313:θ
1280:θ
1186:ϕ
1153:−
1125:α
1092:−
1054:ω
991:−
947:ω
817:τ
787:κ
697:θ
583:, and by
363:θ
359:κ
283:κ
255:θ
230:τ
203:θ
200:κ
197:−
191:τ
162:torsional
51:mousetrap
2816:Dubonnet
2670:Steering
2645:Drifting
2369:(1996),
2252:See also
802:N m rad
506:current.
469:ballista
454:pendulum
448:used in
434:sway bar
405:on some
80:twisting
2739:Torsion
2488:Bibcode
1696:where:
1365:damping
1363:If the
655:In the
490:watches
473:scorpio
270:radians
158:bending
84:elastic
2890:Torque
2715:Spring
2420:
2379:
2332:
2306:
2263:Slinky
651:since.
477:onager
407:sedans
330:joules
245:newton
219:where
119:quartz
92:torque
76:spring
2751:types
2717:types
1985:, so
742:kg m
682:Unit
679:Term
461:sinew
328:, in
130:helix
115:fiber
74:is a
2729:Leaf
2724:Coil
2467:2007
2418:ISBN
2377:ISBN
2330:ISBN
2304:ISBN
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