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- Homework Statement
- A uniform rod of length 6 a and mass 8 m lies on a smooth horizontal table. Two particles of masses m and 2 m moving in the same horizontal plane with speed 2 v and v respectively, strike the rod and stick to the rod after collision as shown in the figure. The velocity of centre of mass and angular velocity about centre of mass just after collision are respectively. ( Diagram is provided)

- Relevant Equations
- Integration(F.rdt)= impulse

I1.W1 = I2W2 [ I = Moment of inertia , W = angular speed ]

M1V1 = M2V2

So i was able to solve the angular velocity part but i don't know how to find the velocity of centre of mass . For the first part i simply conserved momentum about COM because if i consider the particles as a part of the same system as rod the collision are internal forces . I am mainly confused as to how to solve it mathematically and properly . Thanks