Physics Rotational & Circular Motion NUMS 2024
PMDC Verified Question 20 of 95
A particle moves in a circle of radius \( 200 \text{ cm} \) with a linear speed of \( 20 \text{ m/s} \). Find the angular velocity:
A
\( 2 \text{ rad s}^{-1} \)
B
\( 200 \text{ rad s}^{-1} \)
C
\( 20 \text{ rad s}^{-1} \)
D
\( 10 \text{ rad s}^{-1} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: \( 10 \text{ rad s}^{-1} \)
Concept:

Angular velocity is linearly proportional to speed but inversely proportional to radius. Units must be carefully harmonized into standard SI (meters) before calculating.

Formula:

$$ \omega = \frac{v}{r} $$

Solution:

  • First, convert the radius into meters: \( 200 \text{ cm} = 2 \text{ meters} \).
  • Given linear speed \( v = 20 \text{ m/s} \).
  • Substitute into the formula: \( \omega = \frac{20}{2} \).
  • \( \omega = 10 \text{ rad s}^{-1} \).


Why other options are incorrect:

  • Option B occurs if you forget to convert centimeters to meters and perform \( \frac{20}{200} \) backward, or some other math error.
  • Option C just repeats the linear speed.
  • Option A just repeats the converted radius.

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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