A solid sphere is set into motion on a rough horizontal surface with a linear speed u in the forward direction and an angular speed u/R in the anticlockwise direction as shown in figure (10-E 16). Find the linear speed of the sphere (a) when it stops rotating and (b) when slipping finally ceases and pure rolling starts.



Given:


Radius of the sphere= R


Linear velocity = u


Angular speed = u/R


Let us consider the point A, where external torque is zero


Using law of conservation of angular momentum





(b) linear speed when it starts rolling




1