Principle of conservation of linear momentum:

Explanation

(i) When two particles interact with each other, they exert equal and opposite forces on each other. The particle 1 exerts force `vec(F)_(21)` on particle 2 and particle 2 exerts an exactly equal and opposite force `vec(F)_(12)` on particle 1, according to Newton's third law.
`" "vec(F)_(21)=-vec(F)_(12)`
(ii) The force on each particle (Newton's second law) can be written as,
`vec(F)_(12)=(dvec(p)_(1))/(dt) " and " vec(F)_(21)=(dvec(p)_(2))/(dt)`
(iii) Here `vec(p)_(1)` is the momentum of particle 1 which changes due to the force `vec(F)_(12` exerted by particle 2. Further `vec(p)_(2)` is the momentum of particle 2. This changes due to `vec(F)_(21)` exerted by particle 1.
`(dvec(p)_(1))/(dt)=-(dvec(p)_(2))/(dt)`
`(dvec(p)_(1))/(dt)+(dvec(p)_(2))/(dt)=0`
`d/(dt)(vec(p)_(1)+vec(p)_(2))=0`
(iv) It implies that `vec(p)_(1)+vec(p)_(2)=` constant vector (always).
(v) `vec(p)_(1)+vec(p)_(2)` is the total linear momentum of the two particles `(vec(p)_("tot")=vec(p)_(1)+vec(p)_(2))`. It is also called as total linear momentum of the system. Here, the two particles constitute the system.
(vi) If there are no external forces acting on the system, then the total linear momentum of the system `(vec(p)_("tot"))` is always a constant vector.