Gyroscopic Motion - I

The reaction R of the vertical post is R = mg.

However there is a torque . It acts in the vertical plane XZ and its magnitude is mgr. It can be represented by a vector in +ve Y direction.

Now, by Euler's law, the rate of change of angular momentum is torque. Assume that the precession velocity is very small in comparision to spin velocity of the disk. The spin velocity may be written as ., where I₀ is the polar moment of inertia of the disk about X axis. is a rotating unit vector in the direction of X.

Now,