Question

Find the instantaneous axis of rotation of a rod of length $l$ when its end $A$ moves with a velocity ${\overrightarrow{v}}_A=v\hat{i}$ and the rod rotates with an angular velocity $\omega =-\frac{v}{2l}\hat{k}$

Answer 1

Let us choose the point $P$ as ICR in the extended rod. We can say ISR is point of zero velocity. So we can write
$v_P=v_{P.A}+v_A$ We have $v_P=0$
Hence, $v_{P.A}+v_A=0$
Here, $v_A=v\hat{i};v_{P.A}=-\omega r\hat{i}$
Hence $-\omega r\hat{i}+v\hat{i}=0$
$v=\omega rr=\frac{v}{\omega }=\frac{v}{\left(v/2l\right)}=2l$
Hence ICR will be located at a distance $2l$ from $A$