A torsion spring or torsion pendulum is an elastic material that reacts against torsion (twisting motion). In particular, the more one twists it, the more force it takes to twist it further. A torsion spring is often made from a wire, ribbon, bar, or coil.

• Torsion ribbons are used in torsion pendulum clocks, where a weight is spun, oscillating in its spinning direction at the bottom of the clock. As the resonant period is very long, this mechanism is used in spring wound clocks designed to operate for an entire month or even a year without rewinding. This type of suspension is also used in sensitive devices used to determine constants associated with the gravitational effects of mass.

• Torsion bars (or sway bars) are used to support automobile suspension components, allowing those components (which indirectly support the wheels) to move in response to rough roads while allowing a smooth ride in the vehicle. The DeLorean DMC-12 uses cryogenically tempered torsion bars to assist with the opening of its gull wing doors. See torsion beam suspension. Since sway bars 'tie' the left and right suspension together, some offroad enthusiasts install quick disconnect sway bar links to allow the sway bar to be disconnected for greater articulation when offroading.

• coiled torsion springs are coils that are twisted (rather than pulled) to store energy.

• Large coiled torsion springs are used to counter-balance the weight of garage doors. Great care must be exercised when adjusting these as they store a large amount of mechanical energy.

• Small coiled torsion springs are often used to operate small pop-up doors such as are found on small consumer goods such as digital cameras and compact disk players.

Oscillatory motion of torsion pendulums

Torsion pendulums undergo oscillatory motion similar to springs. It oscillates (twists and untwists) after being given an initial torque.

If I is the moment of inertia of a body with respect to its axis of oscillation, and if K is the torsion coefficient of the fiber (torque required to twist it through an angle of one radian), then the period of oscillation of a torsion pendulum is given by

$T\; =\; 2\; \backslash pi\; \backslash sqrt\{\backslash frac\{I\}\{K\}\}$

Both I and K may have to be determined by experiment. This can be done by measuring the period T and then adding to the suspended body another body of known moment of inertia I', giving a new period of oscillation T'

$T\text{'}\; =\; 2\backslash pi\; \backslash sqrt\{\backslash frac\{I+I\text{'}\}\{K\}\}$

and then solving the two equations to get

$K\; =\; \backslash frac\{4\backslash pi^2I\text{'}\}\{T\text{'}^2\; -\; T^2\}$

$I\; =\; \backslash frac\{T^2I\text{'}\}\{T\text{'}^2\; -\; T^2\}$

The oscillating balance wheel of a watch is in effect a torsion pendulum, with the suspending fiber replaced by hairspring and pivots. The watch is regulated, first roughly by adjusting I (the purpose of the screws set radially into the rim of the wheel) and then more accurately by changing the free length of the hairspring and hence the torsion coefficient K.

Damped pendulum

The pendulum equation does not take into account the effects of friction and dissipation. While these effects can be very complicated to model, a good approximation is to add a term proportional to the velocity:

$\backslash ell\; \backslash frac\{d^2\backslash theta\}\{dt^2\}=-g\; \backslash sin\backslash theta\; -\; \backslash gamma\; \backslash frac\{d\backslash theta\}\{dt\}$

The positive constant γ is the viscous damping parameter. A system described by this equation is called a damped pendulum.

The Torsion Balance

The torsion balance is a device created by Charles-Augustin de Coulomb in 1777, to measure very weak forces. Coulomb used it to measure the electrostatic force between two charges. It was based on the principle that the magnitude of the electrostatic force between two point charges is directly proportional to the magnitudes of each charge and inversely proportional to the square of the distance between the charges. This principle is called Coulomb's law.

The torsion balance consists of two metal balls attached to the ends of an insulating rod suspended from the middle by a thin fiber. To measure the electrostatic force we charge one of the two balls, and then place near it a third ball with a similar charge. The two charged balls repel each other, causing the fiber to twist to a certain angle. If we then measure how much force, in newtons, is required to twist the fiber to that same angle, we then know how much force was exerted upon the fiber by the two balls and therefore the force between the balls.

The unit Charles Augustine de Coulomb used to measure this electrostatic force was named after him: the coulomb. One coulomb is the amount of charge accumulated in one second by a current of one ampere. Therefore a coulomb is one ampere flowing multiplied by one second, and the formula for that is: C = A • s. One coulomb represents a charge of approximately 6.241506 x 10¹⁸ e, e being the amount of electric charge on one electron.

There are, at first glance, a few setbacks to this device, one of them being that you are finding the charge of two metal balls when you might actually want to find the charge of two pieces of wool, or two pieces of plastic. The solution to that, however, is simple: you simply replace the metal balls with equally sized spherical samples of the item you’d like to measure.

Another difficulty is that both charged balls must have the exact same amount of charge on them. Coulomb solved this by discovering that two objects of the same size and shape charged to the same potential will have the same charge; so if the two balls are touched together, they will divide the charge equally.

A torsion balance was used in the Cavendish experiment in 1798 to measure the force of gravity. Torsion balances are still used in physics experiments.

Media

See also

• Torque
• Slinky

External links

• How To Replace Garage Door Torsion Springs by Dan Musick
• Measuring Big G, J.H. Gundlach, Measurement Sci.& Tech. 10 454 (1999) (Recent physics experiment at the University of Washington using a torsion balance)

Springs (mechanical)

Торсион