- #1

- 11

- 0

## Homework Statement

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

α=ω

*T*(1-√[2M/(2M+5m)])

## Homework Equations

## 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?