# Explain briefly how to find the moment of inertia of different bodies?

## Question:

Explain briefly how to find the moment of inertia of different bodies?

## Moment of inertia:

Moment of inertia is defined as the second moment of the mass or in other words, we can say that it shows the ability of solid to provide resistance to the change in the angular speed of the object.

As we know that the moment can be defined as the product of the mass and the perpendicular distance(i.e radius) from the rotational axis.

Therefore, the second moment can be defined as the product of the mass and the square of the distance from the rotational axis.

Since the mass is continuous in the body, therefore we have to consider an element of a body say of mass "dm" and the distance say "r" from the rotational axis, therefore the moment of inertia of the body would be

{eq}dI = dm\times r^{2} \\ \text {On intergration } \\ \int dI = \int r^{2}\times dm\\ I = \int r^{2} dm {/eq}