Chapter 10, Problem 53P

(I) Use the parallel-axis theorem to show that the moment of inertia of a thin rod about an axis perpendicular to the rod at one end is $I=\frac{1}{3}M{\mathcal{l}}^2$, given that if the axis passes through the center, $I=\frac{1}{12}M{\mathcal{l}}^2$ (Fig. 10–20f and g).