The moment of inertia of a small mass
a distance y from an axis is
To find the moment of inertia of a uniform disc of constant mass per unit area
about an axis in the plane of the disc through the centre of the disc, construct the diagram below.
The mass of the small area of disc is
The moment of inertia of the small area
is
so the moment of inertia of the disc about the horizontal axis through the centre is
