Physics Rotational & Circular Motion SZABMU 2023
PMDC Verified Question 33 of 95
The relation between linear and angular acceleration is:
A
\( a = r\alpha \)
B
\( a = \frac{r}{\alpha} \)
C
\( a = r^2\alpha \)
D
\( a = r\alpha^2 \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( a = r\alpha \)
Concept:

Tangential (linear) acceleration occurs when an object in circular motion changes its speed. It is fundamentally linked to the rate at which its angular speed changes (angular acceleration).

Formula:

$$ a_t = r\alpha $$

Solution:

  • We know the linear velocity relation: \( v = r\omega \).
  • Differentiating both sides with respect to time yields: \( \frac{dv}{dt} = r \frac{d\omega}{dt} \).
  • Since \( \frac{dv}{dt} \) is linear acceleration \( a \), and \( \frac{d\omega}{dt} \) is angular acceleration \( \alpha \), we get \( a = r\alpha \).


Why other options are incorrect:

  • Option B divides instead of multiplies.
  • Option C and Option D incorrectly introduce squares, which applies to centripetal acceleration (\( a_c = r\omega^2 \)), not tangential acceleration.

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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