A bucket is being lowered down into a well through a rope passing over a fixed pulley of radius 10 cm. Assume that the rope does not slip on the pulley. Find the angular velocity and angular acceleration of the pulley at an instant when the bucket is going down at at speed of 20 cm/s and has an acceleration of `4.0 m/s^2`.

Explanation

To solve the problem, we need to find the angular velocity and angular acceleration of the pulley when the bucket is being lowered.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Radius of the pulley, \( R = 10 \, \text{cm} = 0.1 \, \text{m} \)
- Linear speed of the bucket, \( v = 20 \, \text{cm/s} = 0.2 \, \text{m/s} \)
- Linear acceleration of the bucket, \( a = 4 \, \text{m/s}^2 \)
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