Question: Discuss moment of inertia. How is it related to the torque of a rotating body?

ANSWER

Moment of Inertia

When a body is rotating it resists changing its state of uniform angular velocity. This property due to which the body resists to change its state of uniform circular motion is called moment of inertia. Equally stated, the property of a rotating body by which it maintains its state of uniform circular motion is called moment of inertia. So moment of inertia opposes to produce angular acceleration in a rotating body.

In SI, the unit of moment of inertia is kg m².

Relation between torque and moment of inertia:

Consider a body of mass m attached to a rod of negligible mass. The rod can be rotated around a point O in a horizontal circle of radius r. Further suppose, there is no friction involved in the motion.

Now apply a force F on the mass perpendicular to the rod. The torque produced is given by;

Similarly, by Newton’s Second Law,

Put the value of F from equation (ii) in equation (i).

The quantity mr² is called moment of inertia and is represented by I. Therefore,

This is the relation between torque and moment of inertia. It stated that the product of moment of inertia and the angular acceleration gives the torque acting on the body.