Question

A man is running on a circular path of radius 20 m with the speed of 20π m/s. What will be the angular displacement in 1 s?

• A. $2\pi$
• B. $\pi$
• C. 0
• D. $\frac{\pi }{2}$

Answer 1

The correct option is B $\pi$

Radius of the circular path, r = 20 m
Linear speed of the man, v = 20π m/s
Let the angular speed be ω.
Now, v = rω
$\Rightarrow \omega =\frac{v}{r}$
$\Rightarrow \omega =\frac{20\pi }{20}=\pi rad/s$
Angular speed, $\omega =\frac{\text{Angular displacement}}{Time}=\frac{1}{t}$
$\Rightarrow \theta =\omega t$
$\Rightarrow \theta =\pi \times 1=\pi$ $(\because t=1s)$
Hence, the correct answer is option (b).