Question

A uniform sphere of mass m and radius R rolls without slipping down an inclined plane set at an angle α to the horizontal. Find:

(a) the magnitudes of the friction coefficient at which slipping is absent;

(b) the kinetic energy of the sphere t seconds after the beginning of motion.

Answer 1

(a) Let us indicate the forces acting on the sphere and their points of application. Choose positive direction of x and ϕ (rotation angle) along the incline in downward direction and in the sense of vector ω (undirectional rotation) respectively. Now from equations of dynamics o f rigid body i.e.