Physics Rotational & Circular Motion UHS 2024
PMDC Verified Question 11 of 95
An air craft makes a turn in a horizontal circle of radius \( 100 \text{ m} \). It is travelling with a velocity of \( 250 \text{ m/s} \). The angular velocity of the air craft will be:
A
\( 1.5 \text{ rad/sec} \)
B
\( 2.5 \text{ rad/sec} \)
C
\( 3 \text{ rad/sec} \)
D
\( 3.5 \text{ rad/sec} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: \( 2.5 \text{ rad/sec} \)
Concept:

Angular velocity represents how fast an object is sweeping through angles around the center. It is a direct ratio of linear speed to the path's radius.

Formula:

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

Solution:

  • Given linear velocity \( v = 250 \text{ m/s} \).
  • Given radius \( r = 100 \text{ m} \).
  • Substitute into the formula: \( \omega = \frac{250}{100} \).
  • \( \omega = 2.5 \text{ rad/sec} \).


Why other options are incorrect:

  • Option A, Option C, Option D are mathematically incorrect calculations for the simple division of 250 by 100.

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