We derive the moment of inertia for differently shaped objects. Please express your answers to (a) and (b) symbolically in terms of M, L and R.
(a) Consider a pendulum made from a uniform, solid rod of mass M and length L attached to a hoop of mass M and radius R. Find the moment of inertia I of the pendulum about the pivot depicted at the left end of the solid rod.
(b) Consider a wheel made from a hoop of mass M and radius R attached to three uniform solid rods, each of mass M and length 2R. Find the moment of inertia of the wheel about the pivot depicted at the center of the wheel.
(c) Compare the moment of inertia to that of part (a) if the pivot were at the right end of the solid rod. Justify your answer.