Question

A solid sphere of mass 3kg and radius rolls down an inclined plane of height 4m. Assumethe surfaces are smooth, find the

(a) angular velocity of the sphere at the bottom of the incline.

(b) total rotational kinetic energy of the sphere.

Answer 1

$$mgh=0.5mv^2+0.5I\omega^2\\mgh=0.5mv^2+0.5(0.4)mv^2\\ v=\sqrt{\frac{10}{7}gh}=\sqrt{\frac{10}{7}(9.8)(4)}=7.5\frac{m}{s}$$

$$K_{rot}=0.5(0.4)(3)(7.5)^2=34\ J$$