A shaft rotating at N r.p.m. under a torque T transmits a power of:
Try it first: pick an option, then read the explanation.
Correct answer: A. TπN/30 N·m/s
Asked in SSC JE 23/01/2018 (Evening)
Detailed Explanation
Power = torque × angular speed, with ω in rad/s.
\[ \omega = \frac{2\pi N}{60}\ \text{rad/s} \qquad P = T\omega = \frac{2\pi NT}{60} = \frac{\pi NT}{30}\ \text{N·m/s (W)} \]
Why “TπN/30 N·m/s” Is Correct
The power is TπN/30 N·m/s (watts, with T in N·m).
Why the Other Options Are Wrong
- B. TπN/30 N·m/min: Right expression, wrong unit — 2πNT/60 is per second, not per minute.
- C. TπN/60 N·m/min: πNT/60 is half the correct value, and per minute is wrong.
- D. TπN/60 N·m/s: πNT/60 is half the correct value (2π dropped to π).
Key Point
P = 2πNT/60 = πNT/30 watts (T in N·m, N in rpm).
Key Concepts for Students
- 2πNT is the work per minute.
- Use mean torque for power; design for maximum torque.
- 1 kW = 1000 N·m/s.
Practice more: this is question 16 in Torsion MCQs – Part 2. Try the whole set and check every answer instantly.