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( Torsion spring) 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. The amount of force (actually torque) it exerts is proportional to the amount it is twisted. A torsion spring is often made from a wire, ribbon, or bar of metal or rubber, while more delicate ones are made of silk, glass, or quartz fibers.

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

where is the torque exerted by the spring in newton-meters, and is the angle of twist from its equilibrium position in radians. is a constant with units of newton-meters / radian, variously called the spring's torsion coefficient, torsion elastic modulus, or just spring constant, equal to the torque required to twist the spring through an angle of 1 radian. It is analogous to the spring constant of a linear spring.

The energy U, in joules, stored in a torsion spring is

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