A wheel with a rotational inertia of `0.50kg*m^(2)` about its central axis is initially rotating at an angular speed of 15 rad/s. At time t = 0, a man begins to slow it at a uniform rate until it stops at t = 5.0 s. (a) By time t = 3.0 s, how much work had the man done? (b) For the full 5.0 s, at what average rate did the man do work?

Explanation

To solve the problem step by step, we will break it down into two parts as per the question.

### Part (a): Work Done by the Man at t = 3.0 s

1. **Identify Initial Conditions**:
- Rotational inertia (I) = 0.50 kg·m²
- Initial angular speed (ω_initial) = 15 rad/s
- Final angular speed after 5 seconds (ω_final) = 0 rad/s (the wheel stops)
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