The

law of conservation of linear momentumstates that if no external forces act on the system of two colliding objects, then the vector sum of the linear momentum of each body remains constant and is not affected by their mutual interaction.

^{nd}law of motion,

*Note: If the derivative of any quantity is zero, it must be a constant quantity.*)

**Deduction of Law of Conservation of linear momentum for two colliding bodies**

_{1}and m

_{2}moving in straight line in the same direction with initial velocities u

_{1}and u

_{2}. They collide for a short time ∆t. After collision, they move with velocities v

_{1}and v

_{2}.

^{nd}law of motion,

_{AB}= (m

_{2}v

_{2}-m

_{2}u

_{2})/∆t

_{BA}= (m

_{1}v

_{1}-m

_{1}u

_{1})/∆t

^{rd}law of motion,

_{AB}= -F

_{BA}

_{2}v

_{2}-m

_{2}u

_{2})/∆t = -(m

_{1}v

_{1}-m

_{1}u

_{1})/∆t

_{2}v

_{2}-m

_{2}u

_{2}= -m1v1+m1u1

Or, m

_{1}u_{1}+ m_{2}u_{2}= m_{1}v_{1}+ m_{2}v_{2}