Question

Suppose the particle of the previous problem has a mass m and a speed v before the collision and it sticks to the rod after the collision. The rod has a mass M. (a) Find the velocity of the centre of mass C of the system constituting "the rod plus the particle". (b) Find the velocity of the particle with respect to C before the collision. (c) Find the velocity of the rod with respect to C before the collision. (d) Find the angular momentum of the particle and of the rod about the centre of mass C before the collision. (e) Find the moment of inertia of the system about the vertical axis through the centre of mass C after the collision. (f) Find the velocity of the centre of mass C and the angular velocity of the system about the centre of mass after the collision.

Answer 1

a) If we take the two bodies as a system therefore total external force = 0

c) If the body moves towards the rod with a velocity of v, i.e. the rod is moving with a velocity – v towards the particle.
Therefore the velocity of the rod w.r.t. the centre of mass = V^–

(Velocity of centre of mass of the system before the collision = Velocity of centre of mass of the system after the collision)
(Because External force = 0)
Angular velocity of the system about the centre of mass,