Calculate the moment of inertia of a ring of mass 0.5 kg and radius 0.1 m rotating about a tangent (a) in its plane (b) perpendicular to its plane.

Explanation

To calculate the moment of inertia of a ring of mass 0.5 kg and radius 0.1 m rotating about a tangent, we will solve the problem in two parts: (a) when the tangent is in the plane of the ring, and (b) when the tangent is perpendicular to the plane of the ring.

### Part (a): Moment of Inertia about a Tangent in its Plane

1. **Identify the Moment of Inertia about the Center**:
The moment of inertia \( I_z \) of a ring about an axis perpendicular to its plane and passing through its center is given by:
\[
I_z = m r^2
...