State the expression for the moment of inertia of a thin uniform disc about an axis perpendicular to its plane and through its centre. Hence deduce the expression for its moment of inertia about a tangential axis perpendicular to its plane.

Explanation

To find the moment of inertia of a thin uniform disc about an axis perpendicular to its plane and through its center, we start with the known formula for the moment of inertia of a disc.

### Step 1: Moment of Inertia of a Thin Uniform Disc
The moment of inertia \( I \) of a thin uniform disc about an axis perpendicular to its plane and through its center is given by the formula:
\[ I = \frac{1}{2} M R^2 \]
where:
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