Question

A particle revolving in a circular path travels the first half of the circumference in 4 s and the next half in 2 s. What is its average angular velocity?

• A. \( \frac{4\pi}{9} \, {rad/s} \)
• B. \( \frac{\pi}{6} \, {rad/s} \)
• C. \( \frac{2\pi}{3} \, {rad/s} \)
• D. \( \frac{\pi}{3} \, {rad/s} \)

Hint:

In circular motion, the total angular displacement for one complete revolution is always \( 2\pi \) radians, regardless of the path's speed or duration.

Answer 1

The Correct Option is D

To find the average angular velocity, we need to consider the total angular displacement over the total time taken. For a complete revolution in a circle, the total angular displacement is \( 2\pi \) radians. Given that the particle completes half the circumference in 4 seconds and the other half in 2 seconds, the total time for one complete revolution is: \[ t_{\text{total}} = 4 \, \text{s} + 2 \, \text{s} = 6 \, \text{s} \] Thus, the average angular velocity \( \omega \) is given by: \[ \omega = \frac{\text{Total Angular Displacement}}{\text{Total Time}} = \frac{2\pi \, \text{radians}}{6 \, \text{s}} = \frac{\pi}{3} \, \text{rad/s} \]