Question

In the figure shown, the instantaneous speed of end $A$ of the rod is $3\text{m/s}$ to the left. Find the angular velocity of the rod at the given instant.

• A. $1\text{rad/s}$
• B. $2\text{rad/s}$
• C. $0.5\text{rad/s}$
• D. $0\text{rad/s}$

Answer 1

The correct option is C $0.5\text{rad/s}$

Given that, speed of $A\left(V_A\right)$ is $3\text{m/s}$
The components of velocities of $A$ and $B$ along $AB$ should be same. (Because$AB$ is a rigid rod)


$V_A\cos {30}^0=V_B\cos {30}^0⟹V_A=V_B=3\text{m/s}$

Angular velocity of the rod
$\left(\omega \right)=\frac{\text{Relative velocity of AB}}{AB}$
= $\frac{V_A\sin {30}^0+V_B\sin {30}^0}{6}$
=$\frac{3}{6}=0.5\text{rad /s}$