Gyroscopic rotation.

Question

I have never encountered a gyroscopic movement question so i am going to require some assistance.

At the end of a rod of length $l$ is a solid disk with radius $R$, spinning with angular velocity $\omega$, the other end of the rod is attached to a pivot. The gyro precesses at $\omega_p$.What is $l$ in terms of $\omega, \omega_p, g, R$?

Let $m$ be the mass of the disk, $\tau = mgl$ The momentum of the spinning disk is $L=I\omega $ where $I$ is the moment of inertia of the disk. I know the moment of inertia of a spinning disk is $I = 1/2mR^2$. What i would like to know, is how can i relate these? well first, how do i find $\omega_p$?

I have no experience with gyro's, as you can tell.

Answer 1

$\omega_p = \frac{mgl}{I\omega}$.

Rearranging;

$ \frac{\omega_pI\omega}{mg} = l$.