Physics Rotational & Circular Motion ETEA 2017
PMDC Verified Question 86 of 95
A fly wheels rotates at a constant speed of \( 3000 \text{ rpm (rev/min)} \). The angle described by the shaft in radian in one second is:
A
\( 2\pi \)
B
\( 30\pi \)
C
\( 100\pi \)
D
\( 300\pi \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( 100\pi \)
Concept:

RPM (revolutions per minute) needs to be converted into radians per second to determine the angular displacement in one second.

Formula:

$$ \omega = \frac{2\pi N}{60} $$

Solution:

  • Given \( N = 3000 \text{ rev/min} \).
  • Convert revolutions to radians: \( 3000 \text{ rev} \times 2\pi = 6000\pi \text{ radians} \).
  • Convert minutes to seconds by dividing by 60: \( \omega = \frac{6000\pi}{60} \).
  • \( \omega = 100\pi \text{ radians per second} \).
  • Since the time interval is 1 second, the angle described is \( 100\pi \text{ radians} \).


Why other options are incorrect:

  • Option A represents just one single revolution.
  • Option B and Option D result from incorrect division or omitting the \( 2\pi \) conversion factor.

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