Randall D. Knight — Rotation of a Rigid Body: Problem 48

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 \(\omega\), 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 \(\Omega\) in terms of \(M, R, \omega\), and \(g\). b. A \(120\text{ g}\), \(8.0\text{-cm}\)-diameter gyroscope is spun at \(1000\text{ rpm}\) and allowed to precess. What is the precession period?