Suppose the particle of the previous problem has a mass m and a speed u before the collision and it sticks to the rod after the collision. The rod has a mass M. (a) Find the velocity of the center 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 center of mass C before the collision. (e) Find the moment of inertia of the system about the vertical axis through the center of mass C after the collision. (f) Find the velocity of the center of mass C and the angular velocity of the system about the center of mass after the collision.
Given:
Mass of the rod= M
(a) We can take the two bodies as a single system
Hence, total external force = 0
Using law of conservation of linear momentum
(b) Consider the velocity of the particle with respect to the center of mass = 
(c) Suppose the body is moving towards the rod with the velocity v, then it means the rod is moving with a velocity -v towards the particle
Therefore, the velocity of the rod with respect to the center of mass = -v
(d) The distance between the particle and the center of the mass is given as
The angular momentum of the body before collision
= 
=
Angular momentum of rod about center of mass
=
(e) Moment of inertia of the system = Momentum of inertia due to rod + momentum of inertia due to particle
(f) The velocity of the center of mass
Also, angular momentum of center of mass
