State the explain the law of conservation of momentum of the system of particle.

Explanation

Newton.s second law for the system of particle, `(dvecp)/(dt)=vecF_(ext)`
If the sum of external forces acting on the system of particles is zero then
`(dvecp)/(dt)=0`
`therefore dvecp=0, therefore vec(p_(1))=vecp_(2)`
Means the linear momentum remains constant. (`vecp` = constant)
Equation `vecp` = constant, it is equivalent to three scalar equation as following :
`p_(x)=C_(1),p_(y)=C_(2),p_(3)=C_(3)`
where `p_(x),p_(y),andp_(z)` are the components of linear momentum `vecp` for respective axis X, Y and Z-axis and `C_(1),C_(2)andC_(3)` are constant.
..When external total force acting on a system of particles is zero, then its total linear momentum remains constant... This is known as conservation of linear momentum.
From `MvecA=vecF`, here `vecF` is total external force.
If `vecF=0` then `MvecA=0`
`therefore vecA=0`
Means, ..when total external force on system is zero, the velocity of centre of mass remains constant...
More over `vecA=(dvecv)/(dt)` then
If `vecA=0` then `(dvecv)/(dt)=0`
`therefore vecv` is constant.
Means, total external force on the system is zero, the velocity of centre of mass remains constant.