The law of conservation of momentum states that the total momentum of a closed system remains constant, regardless of the internal forces acting within the system. Mathematically, this can be expressed as:

$$\sum p_i = \sum p_f$$

where:

- \(p_i\) represents the initial momentum of the system

- \(p_f\) represents the final momentum of the system

This equation implies that the vector sum of the momenta of all objects within a closed system remains constant. In other words, if there are no external forces acting on the system, the total momentum before and after any interactions within the system will be the same.