= 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> are
$$
I\ddot\theta+\kappa\theta=0,\qquad T=2\pi\sqrt{I/\kappa}.
$$
Here $\kappa$ 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>.
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