A uniform disk of mass M and radius R is pivoted such that it can rotate freely about a horizontal axis through its center and perpendicular to the plane of the disk. A small particle of mass m is attached to the rim of the disk at the top, directly above the pivot. The system is given a gentle start, and the disk begins to rotate.

(a) What is the angular velocity of the disk when the particle is at its lowest point?

(b) At this point, what force must be exerted on the particle by the disk to keep it on the disk?