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. Find the angular velocity of rod.
(a.) 3v/r
(b.) 4v/r
(c.) 5v/r
(d.) 2v/r

Answer 1

$w=\frac{2v}{r}$

Explanation:

• It is given that a rod is being moved with two different velocities of 3v and v on both the ends in the same direction.
• Let  the centre of mass of the rod must be moving with a velocity of v1.

So assuming w to be the angular velocity and r as the radius of the rod ,we have the following relations,

Formula for relating velocity and angular velocity is ,

$v=wr$

By applying the conditions we get,

$v1+wr=3v\\ \\v1-wr=-v$

Adding the equations we would get ,

$2v1=2v\\\\v1=v\\\\v+wr=3v$

$w=\frac{2v}{r}$

Hence this the angular velocity of the rod with the given conditions.