 Torsion pendulum

A torsion pendulum oscillates by twisting a suspension rather than by swinging its support. A horizontal bar suspended from a thin wire experiences an approximately linear restoring torque $-\kappa \theta$ for small angular twists. With moment of inertia $I$ about the wire and negligible damping, its equation of motion and period of an oscillation areHere $\kappa$ is the torsion constant, and the angle is measured from the untwisted equilibrium.

Twist the bar gently, release it, and time several complete cycles. Adding two equal masses at equal distances from the wire increases $I$ without moving the center of mass off the axis, so the period of an oscillation increases. This makes a torsion pendulum useful for measuring a moment of inertia or calibrating the suspension of a torsion balance.