The moment of inertia of a semicircular ring of mass M and radius R about an axis which is passing through its centre and at an angle $\mathrm{\theta }$ with the line joining its ends as shown in figure, is

If we complete the ring, its mass will become 2M

$\therefore I_{\text{whole ring }}=\frac{1}{2}\left(2M\right)\left(R^2\right)=M{R}^2$

(I_wholering = moment of inertia about any diameter)

$\therefore I_{\text{half ring }}=\frac{1}{2}M{R}^2$                          (About any radius)

This value is independent of angle $\mathrm{\theta }$.