Question

A rod of mass M is lying on a smooth horizontal table. A small disc sliding at speed V₀ hits the rod at one end normal to its length. The disc comes to a stop just after the collision.

(a) Write the velocity of the centre of mass of the rod just after the collision.

(b) Write the angular velocity of the rod about its CM just after collision.

(c) How much distance does the rod move in one rotation about CM ?

Answer 1

Since there is no external force on the rod + disc system, momentum is conserved.Let V be the velocity of CM of the rod.

(a) Conserving momentum,

(b) Angular momentum conservation about a point of space initially coinciding with the centre of the rod:

(c) As there is no friction, the rod slides with constant velocity after the collision. Let it move by s in time t. In one rotation angle turned is 2ω.Hence