Torsion Coefficient
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, 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.
The energy U, in joules, stored in a torsion spring is:
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