Question

The torque transmitted by an engine to a rotor in $100 \text{ Nm}$. If the power of the engine is $15 \text{ kW}$, the angular speed of the engine is

• A. $100 \text{ rad s}^{-1}$
• B. $200 \text{ rad s}^{-1}$
• C. $125 \text{ rad s}^{-1}$
• D. $150 \text{ rad s}^{-1}$
• E. $15 \text{ rad s}^{-1}$

Hint:

Always convert 'kW' to 'W' (by multiplying by 1000) before starting calculations to ensure the resulting speed is in standard 'rad s$^{-1}$' units.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Power in rotational motion is defined as the product of torque and angular speed. This is analogous to linear power \( P = F \times v \).
Key Formula or Approach:
Power \( P = \tau \times \omega \)
Where \( \tau \) is torque and \( \omega \) is angular speed.

Step 2: Detailed Explanation:
Given values:
Torque \( \tau = 100 \text{ Nm} \)
Power \( P = 15 \text{ kW} = 15,000 \text{ W} \)
Rearranging the formula to find angular speed:
\[ \omega = \frac{P}{\tau} \]
\[ \omega = \frac{15000}{100} \]
\[ \omega = 150 \text{ rad s}^{-1} \]

Step 3: Final Answer:
The angular speed of the engine is $150 \text{ rad s}^{-1}$.