Question

If a rigid rod of length $l$ is rotating about a fixed end with constant angular velocity of $2\omega \text{rad/s}$. The angular velocity of one particle w.r.t another particle (arbitrarily chosen on rod) is

• A. $\omega \text{rad/s}$
• B. $2\omega \text{rad/s}$
• C. $\frac{\omega }{2}\text{rad/s}$
• D. Zero

Answer 1

The correct option is B $2\omega \text{rad/s}$

Let us take a rigid rod and choose any two particles as shown in the below figure

So, let us find the angular velocity of $A$ w.r.t $B$

We have,
$v_B=2\omega x_1$ and $v_A=2\omega x_2$
$\Rightarrow {\omega }_{AB}=\frac{v_A-v_B}{x_2-x_1}=\frac{2\omega (x_2-x_1)}{(x_2-x_1)}=2\omega \text{rad/s}$