Problem 3P

Express Newton's second law of motion for rotating bodies. What can you say about the angular velocity and angular momentum of a rotating nonrigid body of constant mass if the net torque acting on it is zero?

Solution 3P

Newton's second law of motion for rotating bodies can be expressed as follows

The Newton’s second law for rotating rigid bodies is expressed as where, is the net moment or torque applied on the body, is the moment of inertia of the body about the axis of rotation, and is the angular acceleration.

It can also be expressed in terms of the rate of change of angular momentum as

= == = where is angular velocity

which is also called as angular momentum equation.

The angular momentum equation can be stated as the rate of change of the angular momentum of a body is equal to the net torque acting on it.

For a non-rigid body of constant mass with zero net torque, the angular momentum remains constant. But the angular velocity changes in accordance with Iω = constant.