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Q.
A particle revolving in circular path completes first one third of circumferences in $2\, sec$, while next one third 1s. Calculate the average angular velocity of particle?
Solution:
$\theta_{1}=\frac{2 \pi}{3}$ and $\theta_{2}=\frac{2 \pi}{3}$
Total time $T =2+1=3 s$
$\therefore < W_{a v} > =\frac{\theta_{1}+\theta_{2}}{T}$
$=\frac{\frac{2 \pi}{3}+\frac{2 \pi}{3}}{3}=\frac{3}{3}$
$=\frac{4 \pi}{9} rad / s $