Question

$\begin{array}{c}\text{Write vector relation between angular velocity}\left(\overrightarrow{\omega }\right),\text{tangential velocity}\left(\overrightarrow{v}\right)\text{and position}\\ \text{vector}\left(\overrightarrow{r}\right).\end{array}$.

• A. vector $=\overrightarrow{v}=\overrightarrow{6w}\times \overrightarrow{r}$
• B. vector $=\overrightarrow{v}=\overrightarrow{w}\times \overrightarrow{r}$
• C. vector $=\overrightarrow{v}=\overrightarrow{2w}\times \overrightarrow{r}$
• D. vector $=\overrightarrow{v}=\overrightarrow{3w}\times \overrightarrow{r}$

Answer 1

The correct option is B vector $=\overrightarrow{v}=\overrightarrow{w}\times \overrightarrow{r}$

$2s=v^{2}t$

$2\theta =\frac{v^{2}t}{r}$
$\frac{2\theta }{2t}=\frac{v}{r}$
Angular velocity(w)$=\frac{v}{r}$
$\therefore v=rw$
vector $=\overrightarrow{v}=\overrightarrow{w}\times \overrightarrow{r}$