The moment of inertia (\(I\)) of a disc depends on its geometry and mass distribution. For a solid disc with uniform density, the moment of inertia is calculated using the formula:

\(I = \frac{1}{2} M R^2\)

Where:

• \(I\) is the moment of inertia of the disc.
• \(M\) is the mass of the disc.
• \(R\) is the radius of the disc.

This formula indicates that the moment of inertia of a solid disc depends on both its mass and the square of its radius. The moment of inertia measures an object’s resistance to changes in rotation.

For a hollow disc (ring) with inner radius \(R_1\) and outer radius \(R_2\), the moment of inertia is calculated as:

\(I = \frac{1}{2} M (R_1^2 + R_2^2)\)

Where \(M\) is the mass of the disc, and \(R_1\) and \(R_2\) are the inner and outer radii, respectively.

In summary, the moment of inertia of a disc depends on its mass distribution and geometry. The formulas for solid and hollow discs provide a way to calculate the moment of inertia for different disc configurations.