First slide

Rotational motion

Question

Two points of a rod move with velocities 3v and v perpendicular to the rod and in the same direction separated by a distance 'r' . The angular velocity of the rod is

Easy

A

$\frac{3 v}{r}$
B

$\frac{4 v}{r}$
C

$\frac{5 v}{r}$
D

$\frac{2 v}{r}$

Solution

$ω_{rod} = \frac{{(v_{rel})}_{⊥}}{r}$
here ${(V_{rel})}_{⊥} is the velocity of one point w.r.t. other perpendicular to rod$
$\Rightarrow ω_{rod} = \frac{3 v - v}{r}, {and}^{'} r' being the distance between the points.$
$\Rightarrow ω_{rod} = \frac{2 v}{r}$

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