The uniform, slender rod AB has mass m and length L. It is pinned to a fork (at point O), with this fork attached to a vertical shaft. The masses of the fork and shaft may be neglected, as well as any friction in the pinned joint. The cord keeps the rod AB at a constant angle while the shaft is brought up to speed. Once the shaft sustains a constant angular speed, the cord is cut. Show that the equations governing the ensuing motion are given by:.