A wooden plank OA rotates in vertical plane about horizontal axis through O with a constant angular velocity `omega = 3 `rad/s . As it passes the position `theta = 0 ` , a small mass m is placed upon it at a radial distance `r = 0*5` m . If the mass m starts sliding at ` theta = 37^(@)` , find the coefficient of friction between mass and the plane .

Explanation

To find the coefficient of friction between the mass \( m \) and the wooden plank as it rotates, we can follow these steps:

### Step 1: Understand the forces acting on the mass
When the mass \( m \) is placed on the rotating plank, it experiences gravitational force \( mg \) acting downwards, and a normal force \( N \) acting perpendicular to the surface of the plank. Additionally, there is a frictional force \( f \) acting along the surface of the plank.

### Step 2: Set up the equations of motion
At an angle \( \theta = 37^\circ \), the forces can be resolved into components:
- The gravitational force can be resolved into two components:
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