Physics Rotational & Circular Motion UHS 2024
PMDC Verified Question 10 of 95
The centripetal acceleration of an object moving along a circle of radius 'r' with an angular speed '\( \omega \)' is given by the formula:
A
\( a = r\omega^2 \)
B
\( a = r\omega \)
C
\( a = r^2\omega \)
D
\( a = r^2\omega^2 \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( a = r\omega^2 \)
Concept:

Centripetal acceleration is standardly derived by substituting the relationship between linear and angular speed into the primary kinematic formula.

Formula:

$$ a_c = \frac{v^2}{r} \quad \text{and} \quad v = r\omega $$

Solution:

  • Substitute \( (r\omega) \) into the acceleration formula: \( a_c = \frac{(r\omega)^2}{r} \).
  • Square the terms in the numerator: \( a_c = \frac{r^2\omega^2}{r} \).
  • Cancel one 'r': \( a_c = r\omega^2 \).


Why other options are incorrect:

  • Option B defines linear velocity, not acceleration.
  • Option C and Option D feature an incorrectly squared radius term.

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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