# How to calculate moment of inertia of a disc about its one diameter if given mass per unit area is proportional to distance from centre?

##### 1 Answer

Jul 4, 2018

#### Explanation:

Let the radius of the disc be

Divide the disc into rings with inner and outer radii

- Area of a ring :
#2pi r\ dr# - mass of the ring :
# 2 pi mu r^2 dr#

Thus, net mass :

The moment of inertia of this ring about an axis passing through the center of the disc and normal to it is

A simple application of the perpendicular axis theorem then shows that the moment of inertia of the ring about a diameter is

Hence the moment of inertia of the disc is

Hence