Question

When a person throws a meter stick, it is found that the centre of the stick is moving with a speed of $10\text{m/s}$ vertically upward & the left end of the stick with a speed $20\text{m/s}$ vertically upward. Then, the angular speed of the stick is

• A. $20\text{rad/sec}$
• B. $10\text{rad/sec}$
• C. $30\text{rad/sec}$
• D. None of the these

Answer 1

The correct option is A $20\text{rad/sec}$


Assume angular velocity of the stick is $\omega \text{rad/s}$ in clockwise direction.
For meter stick, $L=1\text{m}$
Speed of left end of the stick $V_A=20\text{m/s}$
As we know,
$\overrightarrow{V_A}=\overrightarrow{V_0}+\overrightarrow{\omega }\times \overrightarrow{r_{AO}}\{\overrightarrow{r_{AO}}=-\frac{1}{2}\hat{i}\}$
$\Rightarrow 20\hat{j}=10\hat{j}+\omega (-\hat{\hat{k}})\times \frac{1}{2}(-\hat{i})$
$\Rightarrow 10\hat{j}=\frac{\omega }{2}(\hat{k}\times \hat{i})[\because \hat{k}\times \hat{i}=\hat{j}]$
$\Rightarrow 10\hat{j}=\frac{\omega }{2}\hat{j}$
$\therefore \omega =20\text{rad/s}$
[$\omega$ is positive hence, assumed direction is correct.]