$($II$)$ Figure $12\mathrm{.}70$ shows a spool of mass $(M$ with ay axle of radius $r$ and endplates of $($radius $R.$ The moment of inertia$)$ about an axis through the center $1.$ The thread is pulled with a force as shown. If there is no slipping, find: $($a$)$ the acceleration of the center of mass; $($b$)$ the force of friction. $($c$)$ Discuss what happens to these quantities when $r$ is less than, equal to$,$ and greater than $\frac{\text{I}}{M}R.$

FIGURE $12\mathrm{.}70$ Problem $8.$