Serway & Jewett — Rotation of a Rigid Object about a Fixed Axis: Problem 32

This problem describes one experimental method for determining the moment of inertia of an irregularly shaped object such as the payload for a satellite. Figure P10.32 shows a counterweight of mass \(m\) suspended by a cord wound around a spool of radius \(r\), forming part of a turntable supporting the object. The turntable can rotate without friction. When the counterweight is released from rest, it descends through a distance \(h\), acquiring a speed \(v\). Show that the moment of inertia \(I\) of the rotating apparatus (including the turntable) is \(mr^2(2gh/v^2 - 1)\).