Question
What is the moment of inertia of disc of mass m and radius r about its axis?
Solution
Consider, M is the mass of a uniform circular disc of radius R with centre O.
Let, O be the centre of the ring. And YY' is the length of the axis.
So the axis is represented by YOY'.
Now,
Surface area of the disc =
Consider a small element of the disc, which would be a circular strip of radius x and width dx, say.
Length of this element = 2
x Surface are of this element =
Therefore,
Therefore, the moment of inertia of disc about its axis is 1/2 mr2 .
