A solid sphere of mass M and radius R rotates freely in space with an angular velocity w about a fixed diameter. A particle of mass m, initially at one pole, moves with a 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 angle

Where T is the total time required for the particle to move from one pole to the other.

2M a = wT 2M + 5m