First slide

Rotational motion

Question

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

Moderate

A

$\frac{v}{2 L}$
B

$\frac{v}{L}$
C

$\frac{v \sqrt{3}}{2 L}$
D

none of these

Solution

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

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