Question

A particle revolving in a circular path completes first one third of the circumference in $2s$, while next on third in $1s$. Calculate its average velocity.

Answer 1

We know,

${\overrightarrow{\omega }}_{av=\frac{Totalagulardisplacement}{Totaltime}}$

For first one third part of circle, Angular displacement

${\theta }_1=\frac{s_1}{r}=\frac{\frac{2\pi r}{3}}{r}$

For second one third part of the circle

${\theta }_2=\frac{\frac{2\pi r}{3}}{r}=\frac{2\pi }{3}rad$

Now total angular displacement

$\theta ={\theta }_1+{\theta }_2=\frac{4\pi }{3}rad$

And, total time $=2+1=3\sec$

So,

${\omega }_{av}$ = $\frac{\frac{4\pi }{3}}{3}$ rad/s }

$\frac{4\pi }{9}$