Chapter 12, Problem 64P

A smaller disk of radius r and mass m is attached rigidly to the face of a second larger disk of radius R and mass M as shown in Figure P12.64. The center of the small disk is located at the edge of the large disk. The large disk is mounted at its center on a frictionless axle. The assembly is rotated through a small angle θ from its equilibrium position and released. (a) Show that the speed of the center of the small disk as it passes through the equilibrium position is

$v=2{\left[\frac{Rg(1-\cos \theta )}{(M/m)+{(r/R)}^2+2}\right]}^{1/2}$

(b) Show that the period of the motion is

$T=2\pi {\left[\frac{(M+2m)R^2+m{r}^2}{2mgR}\right]}^{1/2}$

Figure P12.64