Question

For a particle performing circular motion, the relation For a between it's linear and angular velocities is

• A. $\overrightarrow{v}=\overrightarrow{r}\times \overrightarrow{\omega }$
• B. $\overrightarrow{v}=r\overrightarrow{\omega }$
• C. $\overrightarrow{v}=\omega \overrightarrow{r}$
• D. $\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r^2}$

Answer 1

The correct option is A $\overrightarrow{v}=\overrightarrow{r}\times \overrightarrow{\omega }$

$ds=vdt$

$\therefore d\theta =\frac{vdt}{r}$

$or,\frac{d\theta }{dt}=\frac{v}{r}$

$i.e.,$ Angular velocity $w=\frac{v}{r}orv=wr$

In vector notation $\overrightarrow{v}=\overrightarrow{w}\times \overrightarrow{r}$

Hence,

option $\left(A\right)$ is correct answer.