A circular astroid belt of total mass, m, and average radial distance, R, rotates uniformly around a sun with angular speed, 9. After some time gravitational forces cause the astroid belt to condense into a spherical planet of radius r. If the planet orbits the sun at the same angular speed, 9, at what rate must the planet spin on its own axis, to, in order for the system to conserve total angular momentum? Take the moment of inertia of the astroid belt to be approximately that of a thin hoop about its central axis (I = M R2), and the planet to be that of a solid uniform sphere (I = ng2).