Question

Two points of a rod move with velocities $30\text{m/s}$ and $10\text{m/s}$ perpendicular to the rod and in the same direction, seperated by a distance $5\text{m}$. Find the angular velocity of the rod.

• A. $6\text{rad/s}$
• B. $4\text{rad/s}$
• C. $2\text{rad/s}$
• D. $0\text{rad/s}$

Answer 1

The correct option is B $4\text{rad/s}$

Let $A$ and $B$ be the points on the rod moving with speeds $10\text{m/s}$ and $30\text{m/s}$.
Then, angular velocity of rod
$\omega =\frac{\text{Relative velocity of B w.r.t A}}{\text{AB}}$
$=\frac{30-10}{5}$
$=4\text{rad/s}$