A rotor rotating with an angular speed of `100rads^(-1)`. To make it rotate with same speed, an engine has to transmit a torque of 200 Nm. Calculate the power of engine.

Answer

To calculate the power of the engine, we can use the relationship between power (P), torque (τ), and angular velocity (ω). The formula is given by:

\[ P = τ \cdot ω \]

Where:
- \( P \) is the power in watts (W),
- \( τ \) is the torque in newton-meters (Nm),
- \( ω \) is the angular velocity in radians per second (rad/s).

### Step-by-Step Solution:

1. **Identify the given values:**
- Torque \( τ = 200 \, \text{Nm} \)
- Angular speed \( ω = 100 \, \text{rad/s} \)

2. **Substitute the values into the power formula:**
\[ P = τ \cdot ω = 200 \, \text{Nm} \cdot 100 \, \text{rad/s} \]

3. **Calculate the power:**
\[ P = 200 \times 100 = 20000 \, \text{W} \]

4. **Convert watts to kilowatts (if necessary):**
\[ P = 20000 \, \text{W} = 20 \, \text{kW} \]

Thus, the power of the engine is \( 20000 \, \text{W} \) or \( 20 \, \text{kW} \).

### Final Answer:
The power of the engine is \( 20000 \, \text{W} \) or \( 20 \, \text{kW} \).

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