A toy gyroscope has a ring of mass M and radius R attached to the axle by lightweight spokes. The end of the axle is distance R from the center of the ring. The gyroscope is spun at angular velocity Ω, then the end of the axle is placed on a support that allows the gyroscope to precess.
a. Find an expression for the precession frequency Ω in terms of M, R, ω, and g.
b. A 120 g, 8.0-cm-diameter gyroscope is spun at 1000 rpm and allowed to precess. What is the precession period?