Gyroscopic Motion - II

It is assumed that top is symmetric i.e., I_x = I_y .

We neglect the small angular momentum component due to the precesion and consider angular momentum H equal to , the angular momentum about the axis of the top associated with the spin only.

The magnitude of moment about O is due to the weight of the top and is , where r is the distance from O to the mass center measured along the axis of spin.

Change in angular momentum in time is . This is clear from the following figure. In this figure OB represents intial angular momentum and OC is the momentum after the precession of the top by an amount . BC represents the change in angular momentum. The angle BAC is . The intial horizontal component of angular momentum is represented by AB and final horizontal component of angular velocity by AC. The vertical component remains fixed in magnitude and direction. The horizontal component changes only in direction. Its magnitude is always . For very small angle , BC will be approximately .