### Rigid Body

The equilibrium position is along the radius, when the center of mass moves on the circular orbit. The angular velocity

on the orbit is obtained from

, that is,

. Since the graviational force and the centrifugal force depend on the radius, different forces are applied to the two masses. The total force on a mass at the radius

, rotating with the rod, is

, so that the difference is

. If the rod rotates by a small angle

the resulting torque is

, so that one has

where

. Thus,