Physics Rotational & Circular Motion SZABMU 2022
PMDC Verified Question 54 of 95
The centripetal force in terms of angular velocity is given by
A
\( F_c = mr\omega \)
B
\( F_c = mr\omega^2 \)
C
\( F_c = mr\alpha^2 \)
D
\( F_c = mr\alpha \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( F_c = mr\omega^2 \)
Concept:

Centripetal force is classically defined using linear velocity. Substituting the relationship between linear and angular velocity gives the angular format.

Formula:

$$ F_c = \frac{mv^2}{r} $$

Solution:

  • We know that linear velocity \( v = r\omega \).
  • Substitute \( (r\omega) \) in place of \( v \) in the force formula: \( F_c = \frac{m(r\omega)^2}{r} \).
  • Square the terms inside the parenthesis: \( F_c = \frac{mr^2\omega^2}{r} \).
  • One \( r \) cancels out, leaving: \( F_c = mr\omega^2 \).


Why other options are incorrect:

  • Option A is missing the square on the angular velocity.
  • Option C and Option D mistakenly use angular acceleration \( \alpha \) instead of angular velocity \( \omega \).

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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