Q. A particle is moving in a circular path. It covers the first one-third part of circumference in $2s$ and next one-third in $1s$ . Find the average angular velocity of the particle ( in $rad/s$ ).
NTA AbhyasNTA Abhyas 2020
Solution:
Suppose angular displacement of the first one-third of the circumference is $\theta _{1}$ -and the Second one-third angular displacement is $\theta _{2}$ .
$AverageAngularVelocity\left(\left(\omega \right)_{avg}\right)=\frac{Total Angular Displacement}{Total time}$
$\omega _{avg}=\frac{\frac{2 \pi }{3} + \frac{2 \pi }{3}}{2 + 1}$
$\omega _{avg}=\frac{\frac{4 \pi }{3}}{3}=\frac{4 \pi }{9}rad./sec$
Suppose angular displacement of the first one-third of the circumference is $\theta _{1}$ -and the Second one-third angular displacement is $\theta _{2}$ .
$AverageAngularVelocity\left(\left(\omega \right)_{avg}\right)=\frac{Total Angular Displacement}{Total time}$
$\omega _{avg}=\frac{\frac{4 \pi }{3}}{3}=\frac{4 \pi }{9}rad./sec$