A solid sphere of mass M and radius R rotates freely in space with an angular velocity ω about a fixed diameter. A particle of mass m, initially at one pole, moves with constant velocity v along a great circle of the sphere. Show that, when the particle has reached the other pole, the rotation of the sphere will have been retarded by an angle
The Attempt at a Solution
Apologies for the ugly formatting, can someone please link me an article on how to type equations?
For the problem, I can find the solution if I set the sphere's rotation about the z axis and I assume that angular momentum about the z axis is constant. My question lies with the assumption that angular momentum about the z axis is constant. Angular momentum is constant if there is no external torque. However, the particle's movement from the top pole to the bottom pole implies that there is a torque.
What am I missing?