Question

Why must momentum be conserved?

Answer 1

1. It's because of Newton's third law, in the end. Internal forces within a system, in other words, cannot influence the system's motion.
2. The vector sum of the momenta of each particle that make up the system is the total momentum of the system. This is referred to as the system's center of mass momentum. However, according to Newton's second equation of motion, the rate at which an object's momentum varies is equivalent to the combined vector force acting on that object.
3. As a result, the vector sum of all the forces acting on each particle or object in a system of entities equals the rate of change of total momentum. Because each object interacts with every other object, there can be a large number of separate forces to account for if the system has a lot of elements.
4. But here's the thing: within a system of objects or particles, every internal force is part of a Newton third law pair. If particle A applies a force on particle B, then B exerts the identical force in the opposite direction on A, resulting in the sum of the two forces being zero. That is, all internal forces operating between system components always cancel out... As a result, the vector sum of all forces acting on the overall system of particles is simply the external forces.