Question

A particle is moving along a circular path of radius 2m with constant angular velocity 3 rad/s. Determine the angular displacement and the distance traveled by the particle in 3s.

Answer 1

Step 1: Given data:
The radius of the circular path $\mathrm{r}=2\mathrm{m}$
Angular velocity $\omega =3rad/s$
Time taken $\mathrm{t}=3\mathrm{s}$

Step 2: To find the angular displacement:

The angular displacement of the particle is,
$\theta =\omega t$, where $\omega$ is the angular velocity and t is the time.
$\theta =3rad/s\times 3s$
$\theta =9rad$

The angular displacement of the particle in $3$ seconds is $9\mathrm{rad}$

Step 3: To find the distance traveled:

The distance traveled by the particle (s) is,
$s=r\theta$
$\mathrm{\theta }=2\mathrm{m}\times 9\mathrm{rad}$
$\mathrm{s}=18\mathrm{m}$
The distance traveled by the particle is 3 seconds is $18\mathrm{m}$.

The angular displacement and the distance traveled by the particle in 3 seconds is $9\mathrm{rad}$ and $18\mathrm{m}$.