A ball of mass `M` and radius R is released on a rough inclined plane of inclination `theta`. Friction is not sufficient to prevent slipping. The coefficient friction between the ball and the plane is `mu`. Find
(a). The linear acceleration of the ball down the plane.
(b). the angular acceleration of the ball about its centre of mass.

Explanation

(a). Maximum friction will act
`thereforea=(mgsintheta-mumgcostheta)/(m)`
`=gsintheta-mugcostheta`
(b). Only friction will provide the torque
`thereforealpha=(tau)/(I)((mumgcostheta)R)/((2)/(5)R^(2))`
`=(5mugcostheta)/(2R)`