Question

The end $A$ of a rod of length $l$ when it moves with a velocity ${\overrightarrow{v}}_A=v\hat{i}$ . If the rod rotates with an angular velocity $\overrightarrow{\omega }=-\frac{v}{2l}\hat{k}$ the instantaneous axis of rotation is located

• A. at a distance $l$ from $A$
• B. at a distance $1.5l$ from $A$
• C. at a distance $2.5l$ from $A$
• D. at a distance $2l$ from$A$

Answer 1

The correct option is D at a distance $2l$ from$A$

Draw a diagram of given problem.

Calculate distance of instantaneous axis of rotation.

Let us choose the point $P$ as $ICR$ in the extended rod.

$v_P=v_{PA}+v_A$
We have $v_p=0$
Hence, $v_{PA}+v_A=0$

Here, $v_A=v\hat{i},v_{PA}=-\omega r\hat{i}$

$\Rightarrow -\omega r\hat{i}+v\hat{i}=0$

$r=\frac{v}{\omega }=\frac{v}{\frac{v}{2l}}=2l$

Hence $lCR$ will be located at a distance $2l$ from $A$