Question

Calculate the moment of inertia about the diameter if that of an axis perpendicular to the plane of disc and passing through its center is given by \(\frac{1}{2}MR^2\).

Answer 1

Using theorem of perpendicular axes

I_z = I_x + I_y

As I_x and I_y are along the two diameters of disc so using symmetery,

I_x = I_y

So I_z = 2I_x But I_z = \(\frac{MR^2}{2}\)

So I_x = \(\frac{I_z}{2}\) = \(\frac{MR^2}{4}\)