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A particle moving on a circular path travels first one-third of the circumference in 2 s and the next one-third in 1 s. The average angular velocity of the particle is (in rad/s)

1. \(\frac{2\pi}{3}\)
2. \(\pi\)
3. \(\frac{4\pi}{9}\)
4. \(\frac{5\pi}{3}\)

Correct answer: \(\frac{4\pi}{9}\)

Solution

Average angular velocity is total angular displacement divided by total time. Here the particle covers \(\frac{2}{3}\times 2\pi = \frac{4\pi}{3}\) radians in \(2+1=3\) s. So \(\omega_{avg}=\frac{4\pi/3}{3}=\frac{4\pi}{9}\) rad/s.

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