[UPSC CSE 2008] Rigid Body Dynamics (Q225, 30M)

Derive an expression for the moment of inertia of a rigid body about any axis. What is an "ellipsoid of inertia" ? Explain clearly what you mean by the terms "principal axes" and "principal moments of inertia" ? Find the moment of inertia of a thin rectangular lamin a about an axis passing through the centre of the lamina and perpendicular to its plane. Hence determine the moments of inertia about axes passing through the midpoints of its both sides and perpendicular to its plane.