State and explain the law of conservation of momentum for a system of particles.

(N/A) Newton's second law for a system of particles is given by $\frac{d \vec{p}}{dt} = \vec{F}_{ext}$.
If the sum of external forces acting on the system of particles is zero, then $\frac{d \vec{p}}{dt} = 0$.
This implies $d \vec{p} = 0$, which means $\vec{p} = \text{constant}$.
This is equivalent to three scalar equations: $p_x = C_1, p_y = C_2, p_z = C_3$, where $C_1, C_2, C_3$ are constants.
"When the total external force acting on a system of particles is zero, its total linear momentum remains constant." This is the law of conservation of linear momentum.
From $\vec{F}_{ext} = M\vec{A}_{cm}$, if $\vec{F}_{ext} = 0$, then $\vec{A}_{cm} = 0$.
Since $\vec{A}_{cm} = \frac{d\vec{v}_{cm}}{dt}$, if $\vec{A}_{cm} = 0$, then $\vec{v}_{cm}$ is constant.
Thus, when the total external force on a system is zero, the velocity of the centre of mass remains constant.