A cord with negligible mass is wrapped around a pulley that is a uniform disk of mass 5.00 kg and radius 0.300 m and that can rotate without friction about its central axis. A 1.0 kg bucket is attached at the free end of the cord hanging down from the pulley and then released at time t = 0. The cord begins to unwrap from the pulley as the bucket descends. At t = 5.00 s, through how many rotations has the pulley turned (the bucket is still descending)?

Explanation

To solve the problem step by step, we will analyze the forces acting on the bucket and the resulting motion of the pulley.

### Step 1: Identify the forces acting on the bucket
The forces acting on the bucket (mass \( m = 1 \, \text{kg} \)) are:
- The gravitational force \( F_g = mg \) acting downward.
- The tension \( T \) in the cord acting upward.

Using \( g = 9.8 \, \text{m/s}^2 \), we can calculate the weight of the bucket:
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