Find the moment of inertia, about a diameter, of a uniform ring of mass M = 8kg and radius a = 1m?

Explanation

We know that the moment of inertia, `I_(oz)`, of the ring about OZ is `Ma^2`. We also know that, from symmetry, the moment of inertia about any one diameter is the same as that about any other diameter, i.e., `I(OX) = I_(OY)` Using the perpendicular axes theorem gives `I_(OZ)=I_(OX)+I_(OY)rArrMa^2=21_(OX)=21_(OY)` The moment of inertia of the ring about any diameter `=1/2Ma^2=4kgm^2`.