Torsional Pendulum Period Calculator

A torsional pendulum is a mass suspended on a wire or rod that twists back and forth. The restoring torque is proportional to the twist angle, so it undergoes simple harmonic angular motion. A balance wheel in a mechanical watch and a torsion balance are common examples.

The period of a torsional pendulum is 2 pi times the square root of the moment of inertia divided by the torsion constant: T = 2 pi sqrt(I / kappa). The torsion constant kappa is the restoring torque per radian of twist, in newton-metres per radian.

The torsion constant, kappa, is how much restoring torque the suspension produces per radian of angular displacement. A stiffer wire has a larger kappa and a shorter period. It depends on the wire's material, length, and cross-section, and is supplied here as an editable input.

No, not for small twists. As long as the restoring torque stays proportional to the angle, the motion is simple harmonic and the period is independent of amplitude. This is why torsional oscillators make good timekeepers and sensitive instruments.

A larger moment of inertia lengthens the period, because more rotational inertia is harder to accelerate. A stiffer suspension (larger torsion constant) shortens the period. The period scales with the square root of inertia over stiffness, so quadrupling the inertia doubles the period.