Physics Rotational & Circular Motion NUMS 2022
PMDC Verified Question 68 of 95
A rotating wheel complete \( 12 \text{ rev} \) in \( 4 \text{s} \). Find the average angular velocity its rad/sec.
A
\( 24.6 \text{ rad/s} \)
B
\( 18.5 \text{ rad/s} \)
C
\( 18.8 \text{ rad/s} \)
D
\( 10.4 \text{ rad/s} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( 18.8 \text{ rad/s} \)
Concept:

Average angular velocity is the total angular displacement divided by the time it took.

Formula:

$$ \omega = \frac{\Delta \theta}{\Delta t} $$

Solution:

  • First, convert revolutions to radians: \( 12 \text{ rev} \times 2\pi = 24\pi \text{ radians} \).
  • Time taken is \( 4 \text{ s} \).
  • Divide: \( \omega = \frac{24\pi}{4} = 6\pi \text{ rad/s} \).
  • Multiply out \( \pi \approx 3.1416 \): \( 6 \times 3.1416 = 18.849 \text{ rad/s} \).
  • Rounding off yields roughly \( 18.8 \text{ rad/s} \).


Why other options are incorrect:

  • Option A, Option B, Option D are mathematically incorrect calculation results.

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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