What is law of conservation of momentum ?

Explanation

According to law of conservation of linear momentum, if no external force acts on an isolated system then net linear momentum of system remains conserved.
According to Newton.s second law of motion `vecF= (dvecp)/(dt)` . If `vecF = 0`, then `(dvecp)/( dt) =0` or `vecp`= constant This is the law of conservation of momentum.
For system of n-particles, `vecF_(ex)=(d)/(dt)(vecp_(1)+vecp_(2) + -----+ vecp_(n)) = 0`
or `vecp_(1)+ vecp_(2)+ ........+ vecp_(n) = "constant"`.
Example: Recoil of gun: Let M be the mass of gun and m be the mass of bullet. Before firing, the gun and bullet are at rest.
`:.` Linear momentum of the system (gun+bullet) before firing, `vecp_(i) = 0`.
After firing, let bullet moves with a velocity v and gun with a velocity V. Therefore, momentum of the system after firing is given by
`vecp_(f)= mvecv+ MvecV`
By law of conservation of linear momentum
`vecp_(i)= vecp_(f)` or `0= mvecv+ MvecV` or `vecV= -(mvecv)/(M)`
Negative sign shows that and are in opposite directions i.e. as bullet moves forward, the gun will move in backward direction. This backward motion of gun is called recoil of the gun.