How is momentum conserved?
Linear momentum is the product of mass and the velocity vector. A system's total momentum stays constant when its net external force is zero. Conservation concerns the vector sum for the whole system, rather than the speed of each individual object.
Collisions and impulse
During a collision, objects exert forces on one another, and these internal interactions cancel in the system's momentum balance. External force acting over time produces impulse, equal to the change in momentum. If objects stick together, momentum can remain conserved while some kinetic energy becomes heat, sound, and deformation. Conservation of momentum therefore does not automatically imply conservation of kinetic energy.
Choosing the system boundary
For a rocket, expelled gas must be included in the system; rockets do not need to push against air and can operate in a vacuum. Billiard collisions approximately conserve momentum when table friction has little effect during impact. Directions must be represented by signs or components, so equal opposite momenta can sum to zero. External forces, rotation, and measurement uncertainty must be considered when interpreting discrepancies.