Physics Rotational & Circular Motion ETEA 2016
PMDC Verified Question 89 of 95
The angular velocity for daily rotation of the earth is:
A
\( \frac{\pi}{3} \text{ radian hr}^{-1} \)
B
\( \frac{\pi}{6} \text{ radian hr}^{-1} \)
C
\( \frac{\pi}{12} \text{ radian hr}^{-1} \)
D
\( 12\pi \text{ radian hr}^{-1} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: \( \frac{\pi}{12} \text{ radian hr}^{-1} \)
Concept:

Angular velocity represents the angle swept by an object per unit time. The Earth completes one full rotation on its axis every 24 hours.

Formula:

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

Solution:

  • One full rotation equals \( 2\pi \text{ radians} \).
  • The time period \( T \) is 24 hours.
  • Therefore, \( \omega = \frac{2\pi}{24 \text{ hr}} \).
  • Simplify the fraction: \( \omega = \frac{\pi}{12} \text{ rad hr}^{-1} \).


Why other options are incorrect:

  • Option B assumes a 12-hour day.
  • Option A assumes a 6-hour day.
  • Option D incorrectly multiplies instead of dividing.

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