Question

The moment of inertia of a body is independent of:

Answer 1

Hint:In physics, moment of inertia of a body is a physical quantity which shows the tendency to oppose the angular acceleration of the body and mathematically it’s calculated as product of mass of the body and square of distance from the axis of rotation.

Complete answer:
Let us first look at the following factors on which Moment of inertia of a body depends: moment of inertia depends upon the mass of the body and it’s directly proportional to the mass of the body. Moment of inertia of the body depends upon the distance from the axis of rotation and it’s directly proportional to the square of the distance from the axis of rotation.

So, mathematically the moment of inertia of a body of mass $$m$$ and distance from the axis of rotation $r$ is given as $I=m{r}^2$.Moment of inertia is a scalar quantity. Since the body is rotating, one may think the moment of inertia should be written in the form of angular velocity of the body but the moment of inertia is independent of the angular velocity.

Hence, moment of inertia of a body is independent of angular velocity of the body.

Note: As a moment of inertia depends upon mass and distance from the axis of rotation, other than this Moment of inertia also depends upon the distribution of mass on the body its shape and size. Force acting on the body and its density also don’t affect the moment of inertia.