Question

In the figure shown, the instantaneous speed of end A of the rod is $v$ to the left. The angular velocity of the rod of length $L$ must be:

• A. $\frac{v}{2L}$
• B. $\frac{v}{L}$
• C. $\frac{v\sqrt{3}}{2L}$
• D. none of these

Answer 1

Answer: (B)

$\frac{v}{L}$

The velocities of the ends A and B along the length of rod should be the same.
Hence,
$v_{A}cos{30}^o=v_{B}cos{30}^o\Rightarrow v_A=v_B=v$
Hence, the angular velocity of the rod is
$\omega =\frac{(v_{AB}{)}_{\perp }}{L}=\frac{2vsin{30}^o}{l}\Rightarrow \omega =\frac{v}{L}$