Torsion pendulum

A torsion spring is a spring that works by torsion or twisting; that is, a flexible elastic object that stores mechanical energy when it is twisted. When it is twisted, it exerts a force (actually torque) in the opposite direction, proportional to the amount (angle) it is twisted. There are two types. A torsion bar is a straight bar of metal or rubber that is subjected to twisting (shear stress) about its axis by torque applied at its ends. A more delicate form used in sensitive instruments, called a torsion fiber consists of a fiber of silk, glass, or quartz under tension, that is twisted about its axis. The other type, a helical torsion spring, is a metal rod or wire in the shape of a helix (coil) that is subjected to twisting about the axis of the coil by sideways forces (bending moments) applied to its ends, twisting the coil tighter. This terminology can be confusing because in a helical torsion spring the forces acting on the wire are actually bending stresses, not torsional (shear) stresses.

As long as they are not twisted beyond their elastic limit, torsion springs obey an angular form of Hooke's law:

where ${\displaystyle \tau \,}$ is the torque exerted by the spring in newton-meters, and ${\displaystyle \theta \,}$ is the angle of twist from its equilibrium position in radians. ${\displaystyle \kappa \,}$ is a constant with units of newton-meters / radian, variously called the spring's torsion coefficient, torsion elastic modulus, rate, or just spring constant, equal to the change in torque required to twist the spring through an angle of 1 radian. 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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