A rigid body of general shape has mass M and can rotate freely about a fixed horizontal axis. The centre of mass of the body is distance h from the rotation axis, and the moment of inertia of the body about the rotation axis is I.
Show that the period of small oscillations of the body about the downward equilibrium position is
2π(1/Mgh)1/2
Deduce the period of small oscillations of a uniform rod of length 2a, pivoted about a horizontal axis perpendicular to the rod and distance b from its centre.