momentum

Momentum is one of the three great conserved quantities of classical mechanics. For a point mass it is simply p = m·v — the product of mass and velocity, with a direction attached. In a closed system, the total vector sum of all the momenta stays constant through every internal interaction: collisions, explosions, chemical reactions, rocket burns. No internal force can change the total, because every internal force appears in equal-and-opposite pairs by Newton's third law, which cancel in the sum.

The idea was introduced by Descartes in 1644 as quantitas motus, but he used the magnitude |m·v| rather than the vector, and the quantity so defined is not conserved. Huygens (1669) and Wallis (1668) corrected the sign and established momentum as a genuine conservation law. Newton wrote it into the Principia as a cornerstone. In modern notation F = dp/dt — force is the rate of change of momentum — which is the most general form of Newton's second law and extends naturally to variable-mass systems like rockets.

Momentum conservation underlies every collision analysis in classical mechanics, every billiards problem, and every rocket trajectory. It also underlies the concept of the center of mass, whose motion is determined by the total momentum and cannot be altered by internal rearrangements. From it, Emmy Noether showed, momentum conservation is a consequence of the fact that physics is invariant under translations in space — a deeper reason why the law must hold.