Question

The instantaneous velocity of point $B$ of the given rod of length $0.5 \, m$ is $3 \, m \, s^{- 1}$ in the represented direction. What is the angular velocity (in $rad \, s^{- 1}$ ) of the rod for the minimum possible magnitude of the velocity of the end $A$ ? (Take $\sqrt{3}=1.7$ )

Answer 1

If rod is rotated about end A, then vertical component of velocity, $v_{\bot}$ of end a will be zero.

$\therefore \omega =\frac{v sin 60^{o}}{l}=\frac{\sqrt{3} \, v}{2 l}$
$=\frac{\sqrt{3} \times 3}{2 \times 0.5}=5.2$ $rad \, s^{- 1}$