Chapter 17.1, Problem 17.30P

A half-cylinder with mass m and radius r is released from rest in the position shown. Knowing that the half-cylinder rolls without sliding, determine (a) its angular velocity after it has rolled through 90°, (b) the reaction at the horizontal surface at the same instant. (Hint: Note that GO = 4r/3π and that, by the parallel-axis theorem, $\bar{I}=\frac{1}{2}m{r}^2-m{(GO)}^2$.)

Fig. P17.30