Derive an expression for the acceleration of a solid cylinder rolling without slipping down an inclined plane. Also find the minimum coefficient of friction required for pure rolling

Explanation

To derive the expression for the acceleration of a solid cylinder rolling without slipping down an inclined plane and to find the minimum coefficient of friction required for pure rolling, we can follow these steps:

### Step 1: Identify the Forces Acting on the Cylinder
When a solid cylinder rolls down an inclined plane at an angle \( \theta \), the forces acting on it are:
- The gravitational force \( mg \) acting downward.
- The normal force \( N \) acting perpendicular to the inclined plane.
- The frictional force \( f \) acting up the incline.

...