I need help with this gyroscope question.?

Question

A gyroscope consists of a M=1.8 kg disk with a radius R=2cm mounted at the end of a light axle r=7cm. The gyro spins at f=50 rev/s. It is held horizontal at one end of its axle and precesses about its stand.

Helpful info:
Angular momentum of the disk about it's axle .113 kg*m^2/s

Torque about the point of support due to the weight of the gyro =1.23 Nm

The Question is: How long does it take the gyroscope to precess once around?

I know the precession rate is the torque divided by the component of angular momentum that is precessing. I cannot get the right answer. Please help!

Answer 1

Moment of inertia MI = M*R^2 = 0.00072 kg-m^2 or n-m-s^2
w = 50 * pi = 157.08 rad/s
Angular momentum L = MI * w = 0.1131 kg-m^2/s or n-m-s
Torque T = M*r = 1.2356 n-m
Precession rate about the vertical Wv = T/L = 1.2356/0.1131 = 10.93 rad/s.
So the time for one rotation is 2*pi/10.93 = 0.5751 s.
This solution is borne out by the ref., equation 7. Note that Wv is independent of theta, the gyro axis angle from the horizontal (as long as it isn't vertical).