Euler's equations

Putting these in the Euler's equation, we get

Thus, in this case the disc experiences a torque about x-axis, which is supplied by the bearing reactions.

Necessary and sufficient condition for equilibrium of a rigid body:

For equilibrium the acceleration of the center as well as . Hence from Newton's law and Euler's equation, we see that

F = M =0 are necessary conditions for equilibrium.

Conversely, if F = M = 0 then velocity of the mass center does not change. Moreover at time t, and M = 0 implies that . Thus, the angular velocity must remain zero. Thus, if a body is initially in equilibrium, the conditions and M = 0 are suffiecient for maintaining equilibrium.