The net moment of the body is zero that means the distance between the force and the rotational axis is zero.

The net moment of the body is zero that doesn’t mean that the distance between the force and the rotational axis is zero. This means moments caused by different forces cancels out. If this happens there is no motion of the body along with any direction and hence the body is said to be in equilibrium.

Suppose a gymnast is sitting on a rotating chair and his arms are outstretched. If he suddenly shortens his arms, what will happen?

For the conditions of the equilibrium of the body, i.e. the rigid body only the external forces defines the equilibrium. Because the internal forces cancels out so not to be considered.

The application of the internal forces does affect the conditions of the equilibrium of the body. Not only the external but the internal forces that are developed by the sake of external forces does develop a tending effect on the equilibrium of the body. Thus the internal forces doesn’t cancels out.

A particle is in UCM (uniform circular motion). Its angular momentum remains intact about:

A closed vessel of cylindrical shape is partly filled with water. If the vessel rotates along a horizontal plane around the perpendicular bisector, the moment of inertia ________