Search any question & find its solution
Question:
Answered & Verified by Expert
If the body is moving in a circle of radius $r$ with a constant speed $v$, its angular velocity is
Options:
Solution:
2847 Upvotes
Verified Answer
The correct answer is:
$v / r$
Velocity of the revolving body $\overrightarrow{\mathrm{v}}=\overrightarrow{\mathrm{w}} \times \overrightarrow{\mathrm{r}}$
$\Rightarrow|\overrightarrow{\mathrm{v}}|=|\overrightarrow{\mathrm{w}}||\overrightarrow{\mathrm{r}}| \sin \theta$ where $\theta$ is the angle between the $\overrightarrow{\mathrm{w}}$ and $\overrightarrow{\mathrm{r}}$
As $\theta=90^{\circ} \Rightarrow \mathrm{v}=$ wrsin $90^{\circ}$
$\mathrm{v}=\mathrm{wr} \times 1 \Rightarrow \mathrm{w}=\frac{\mathrm{v}}{\mathrm{r}}$
$\Rightarrow|\overrightarrow{\mathrm{v}}|=|\overrightarrow{\mathrm{w}}||\overrightarrow{\mathrm{r}}| \sin \theta$ where $\theta$ is the angle between the $\overrightarrow{\mathrm{w}}$ and $\overrightarrow{\mathrm{r}}$
As $\theta=90^{\circ} \Rightarrow \mathrm{v}=$ wrsin $90^{\circ}$
$\mathrm{v}=\mathrm{wr} \times 1 \Rightarrow \mathrm{w}=\frac{\mathrm{v}}{\mathrm{r}}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.