A uniform rod of mass M and length a lies on a smooth table. A particle of mass m strikes it at distance a/4 from the centre and stops after the collision. Find the a) velocity of the centre of the rod and the b)angular velocity of the rod about its centre just after the collision. a) They have used linear momentum formula: mv=MV. where V is the velocity of the centre of the rod. How could they use it when the rod was undergoing rotational and not translational motion after collision? Shouldn't velocity of the centre of rod be 0 because its stationary? b) How do we find part b? Please explain the concept.

A uniform rod of mass M and length a lies on a smooth table. A particle of mass m strikes it at distance a/4 from the centre and stops after the collision. Find the a) velocity of the centre of the rod and the b)angular velocity of the rod about its centre just after the collision.

 

a) They have used linear momentum formula: mv=MV. where V is the velocity of the centre of the rod.

How could they use it when the rod was undergoing rotational and not translational motion after collision?

Shouldn't velocity of the centre of rod be 0 because its stationary?

 

b) How do we find part b? Please explain the concept.