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, we can follow these steps:

### Step 1: Identify the Forces Acting on the Cylinder
When a solid cylinder of mass \( m \) and radius \( r \) rolls down an inclined plane with an angle \( \theta \), the forces acting on it are:
- Gravitational force \( mg \) acting downward.
- Normal force \( N \) acting perpendicular to the inclined plane.
- Frictional force \( f \) acting up the incline (to prevent slipping).

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