Question

A particle is located at $(3,4)m$ and moving with velocity $\overrightarrow{v}=(4\hat{i}-3\hat{j})m/s$ . Find the magnitude of angular velocity about origin at this instant.

• A. $2rad/s$
• B. $1rad/s$
• C. $0.5rad/s$
• D. $2.5rad/s$

Answer 1

The correct option is B $1rad/s$

From the question, $\overrightarrow{r}=3\hat{i}+4\hat{j}m$
$|\overrightarrow{r}|=\sqrt{3^2+4^2}=5m$
$\overrightarrow{v}=4\hat{i}-3\hat{j}m/s$
$|\overrightarrow{v}|=\sqrt{4^2+(-3{)}^2}=5m/s$
Here, $\overrightarrow{v}.\overrightarrow{r}=0\Rightarrow \overrightarrow{v}$ & $\overrightarrow{r}$ are perpendcular
$\Rightarrow \omega =\frac{|\overrightarrow{v}|}{|\overrightarrow{r}|}=\frac{5}{5}=1rad/s$