Question

Shown in the figure is a rod which moves with $v=2m/\sec$ and rotates with $\omega =2\pi rad/\sec$. The instantaneous axis of rotation is

• A. $\frac{3}{\pi }m$ from center of rod
• B. $\frac{1}{\pi }m$ from center of rod
• C. $\frac{2}{3\pi }m$ from center of rod
• D. $\frac{3}{2\pi }m$ from center of rod

Answer 1

The correct option is B $\frac{1}{\pi }m$ from center of rod

Draw a diagram of given problem.

Calculate instantaneous axis of rotation.

Given,

Velocity, $v=2m/\sec$

Angular velocity, $\omega =2\pi rad/\sec$

According to diagram, $P$ be the point of instantaneous axis of rotation.
Therefore,
$v_p=0$

$|{\overrightarrow{v}}_{PO}+{\overrightarrow{v}}_O|=0$
$\Rightarrow v_{PO}-v_O=0\Rightarrow v_{PO}=v_O$

Hence,
$\left(OP\right)\omega =v$

$\Rightarrow OP=\frac{v}{\omega }$

$OP=\frac{2}{2\pi }=\frac{1}{\pi }m$