Question

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

• A. $2\text{rad/s}$
• B. $1\text{rad/s}$
• C. $0.5\text{rad/s}$
• D. $2.5\text{rad/s}$

Answer 1

The correct option is B $1\text{rad/s}$

It is given that position vector $\overrightarrow{r}=(3\hat{i}+4\hat{j})\text{m}$,
and the velocity vector
$\overrightarrow{v}=(4\hat{i}-3\hat{j})\text{m/s}$

Here $\overrightarrow{v}.\overrightarrow{r}=(4\hat{i}-3\hat{j}).(3\hat{i}+4\hat{j})=0$
$\Rightarrow \overrightarrow{v}\text{and}\overrightarrow{r}$ are perpendicular.

We know that,
$\Rightarrow \omega =\frac{v_{\perp }}{r}=\frac{\left|\overrightarrow{v}\right|}{\left|\overrightarrow{r}\right|}=\frac{5}{5}=1\text{rad/s}$

Hence option B is the correct answer