# Rolling on a track in vertical plane

A sphere of mass m and radius r is released from rest at point A on a track in vertical plane. The track is rough enough to support rolling between A and B and from B onwards it is smooth.

My thinking: From A to B it will roll and friction will do no work so mechanical energy at A = mechanical energy at B. After B since no friction is present and it going on an incline it cannot roll. Hence the height reached after B is proportional to it's translational kinetic energy only.

My question: If it cannot roll after B what will happen to it's rotational kinetic energy?

Note: The above question is not a homework question, it is a doubt that I have while solving the homework question.

This is partially true,it can roll but cannot be in a state of pure rolling. Usually an object requires frictional force to attain angular velocity sufficient enough for the "pure rolling" state($$v_{com}=\omega*r$$),but here when the ball leaves point B it has a certain amount of angular velocity so it will rotate about the center of mass until an external torque is given to oppose this velocity.