The Moment of Inertia of a Thin Disc About Axis in Plane of Disc Through Centre

The moment of inertia of a small massa 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 areaisso the moment of inertia of the disc about the horizontal axis through the centre is

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