Here are several numerical problems related to rotational motion, ranging from basic to advanced levels. Each problem is followed by its solution for clarity.
### Problem 1: Moment of Inertia
**Problem:**
A solid cylinder of radius \( R = 0.5 \, \text{m} \) and mass \( M = 10 \, \text{kg} \) is rotating about its central axis. Calculate the moment of inertia \( I \) of the cylinder.
**Solution:**
The moment of inertia \( I \) of a solid


