All Problems Dynamics of a solid body
Problem 1.252
A uniform sphere of mass \(m\) and radius \(R\) rolls without slipping down an inclined plane set at an angle \(\alpha\) 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.
(a) \(k \geqslant 2 / 7 \tan \alpha\) (b) \(T=5 / 14 m g^{2} t^{2} \sin ^{2} \alpha\).