Calculate the moment of inertia of a thin ring of mass m and radius r

Given:

The moment of inertia about O is = MR<sup>2</sup>

By perpendicular axis theorem,

Ix+Iy=Iz

We know that Ix and Iy are along the diameter,

Ix=Iy

2Ix = Iz = MR<sup>2</sup>

I<sub>diameter</sub>=MR<sup>2</sup>/2

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