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How can momentum be conserved when two objects collide?

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A diagram with labeled vector illustrations. Panel A shows vector addition with two green arrows A and B forming a parallelogram, and their sum C as a red diagonal. Panel B shows vector subtraction, with A and negative B forming resultant D. Panel C demonstrates vector components using angles and projections. Panel D uses the right-hand rule with thumbs to show the direction of the cross product E = A x B and its opposite, -E = B x A. — mechanics Figure 1: (A) The vector sum C = A + B = B + A. (B) The vector difference A + (−B) = A − B = D. (C, left) A cos θ is the component of A along B and (right) B cos θ is the component of B along A. (D, left) The right-hand rule used to find the direction of E = A × B and (right) the right-hand rule used to find the direction of −E = B × A.

In physics, the law of conservation of momentum states that in an isolated system, the total momentum remains constant regardless of internal interactions. When two objects collide, the sum of their individual momenta before the impact is equal to the sum of their momenta after the impact.123

This conservation occurs because, according to Newton’s third law, the forces exerted by the objects on each other during a collision are equal in magnitude and opposite in direction. While these forces may change the individual momentum of each object, the momentum lost by one object is exactly gained by the other, ensuring the total momentum of the system remains unchanged.241

This principle is highly useful because it allows physicists to predict the outcomes of collisions without needing to know the specific, complex forces acting between the objects during contact. Whether a collision is elastic (where kinetic energy is conserved) or inelastic, the total momentum of the system is always conserved in the absence of external forces.43