Chapter 16.2, Problem 16.112P

A hemisphere of weight W and radius r is released from rest in the position shown. Determine (a) the minimum value of μ_s for which the hemisphere starts to roll without sliding, (b) the corresponding acceleration of point B. (Hint: Note that $OG=\frac{3}{8}r$ and that, by the parallel-axis theorem, $\bar{I}=\frac{2}{5}m{r}^2-m{(OG)}^2$.)

Fig. P16.111

16.112    Solve Prob. 16.111, considering a half cylinder instead of a hemisphere. (Hint: Note that OG = 4r/3π and that, by the parallel-axis theorem, $\bar{I}=\frac{1}{2}m{r}^2=m{(OG)}^2$.)