Question:
A wheel rotates with an angular velocity of 420 revolutions/minute when power of 660 W is transferred to it. The torque acting on the wheel is:
A wheel rotates with an angular velocity of 420 revolutions/minute when power of 660 W is transferred to it. The torque acting on the wheel is:
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Power in rotational motion is related to torque and angular velocity: \(P = \tau \omega\). Always convert rev/min to rad/s.
Updated On: Jun 19, 2026
- 25 N m
- 18.5 N m
- 15 N m
- 12.5 N m
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The Correct Option is C
Solution and Explanation
Step 1: Convert angular velocity.
Given \(\omega = 420~\text{rev/min} = 420 \cdot \frac{2 \pi}{60}~\text{rad/s} = 44~\text{rad/s (approx.)}\)
Step 2: Relation between power and torque.
\[ P = \tau \omega \Rightarrow \tau = \frac{P}{\omega} \] Given \(P = 660~\text{W}\): \[ \tau = \frac{660}{44} \approx 15~\text{N m} \]
Step 3: Conclusion.
The torque acting on the wheel is 15 N m.
Given \(\omega = 420~\text{rev/min} = 420 \cdot \frac{2 \pi}{60}~\text{rad/s} = 44~\text{rad/s (approx.)}\)
Step 2: Relation between power and torque.
\[ P = \tau \omega \Rightarrow \tau = \frac{P}{\omega} \] Given \(P = 660~\text{W}\): \[ \tau = \frac{660}{44} \approx 15~\text{N m} \]
Step 3: Conclusion.
The torque acting on the wheel is 15 N m.
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