Gyroscopic Precession -- from Eric Weisstein's World of Physics

Precession of a gyroscope under the torque due to gravity. Let L be the angular momentum, be the torque, M be the mass of the gyroscope, g the gravitational acceleration, and r the torque arm. Then

so

But the torque is given by

Using

where dL is perpendicular to L because of the torque , it follows that

and, for all vertical inclinations, the angular frequency of precession is

Gyroscope, Precession, Precessional Torque