Would someone check my thinking please.

Question

A solid sphere (mass, r, and moment of inertia given) is rotating at a given angular speed. Friction is constantly applied at the 'equator' of the sphere, and brings it to rest in 3s.

Find the force. I worked out the torque, and then rearranged: T=rxF to give the force. Will i be right if the maths is ok?

Then, if the same force is applied (same conditions) half way between equator and pole, will it take longer or shorter to stop?

Thanks.

Answer 1

yes on the first.

On the second, the torque needed is the same, however, it will need a larger force to make that same torque.

Answer 2

Thanks for that.

So it would take longer to stop then?