Calculate the moment of inertia about the diameter if that of an axis

1.	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» 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 = \(\frac{I_z}{2}\) = \(\frac{MR^2}{4}\)

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»

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