A uniform thin circular disc of radius R has a concentric circular hole of radius 2R cut out of it, leaving a ring-shaped lamina of mass M. Consider the following:
(i) Treating the lamina as the difference of two full discs, obtain an expression for its moment of inertia about any diameter.
(ii) Hence find the moment of inertia of the lamina about a tangent to the outer edge that lies in the plane of the lamina.
(iii) Comment on how the removal of the central portion affects the value obtained in part (ii) as compared with a full disc of the same outer radius and total mass M.