Calculate the moment of Inertia of a semicircular disc of mass M and radius R about an axis passing through its centre and perpendicular to its plane.

Explanation

To calculate the moment of inertia of a semicircular disc of mass \( M \) and radius \( R \) about an axis passing through its center and perpendicular to its plane, we will follow these steps:

### Step 1: Understand the Geometry
The semicircular disc can be thought of as half of a full circular disc. The moment of inertia of a full circular disc about an axis perpendicular to its plane and through its center is given by the formula:
\[ I_{\text{full}} = \frac{1}{2} M R^2 \]
where \( M \) is the mass of the disc and \( R \) is its radius.
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