momentumconserving

Momentum-conserving, in physics, describes a property of a system in which the total linear momentum remains constant in time when no external impulses act on the system. This principle follows from Newton's laws and translational symmetry, and it applies to both simple and complex assemblies of particles. In practice, momentum conservation holds for closed or isolated systems where internal forces do not change the combined momentum.

In collisions, the total momentum before equals the total momentum after, even when objects exchange energy or change form; kinetic energy may be transformed, but the vector sum of momenta is preserved. If external forces, such as friction or gravity with net impulse, are present, momentum is no longer conserved. The impulse-momentum theorem relates the change in momentum to the external impulse.

Common examples include billiard ball collisions, recoil of a gun, and rocket propulsion when exhaust momentum is accounted for within the system. In fluids, internal pressures and flows can rearrange momentum among parts of a system while conserving the total momentum overall; boundaries and external fields can alter effective momentum by transferring it to surroundings.

Beyond physics, momentum-conserving concepts guide numerical simulations. Momentum-conserving algorithms aim to prevent artificial drift in computational models, using conservative discretizations or symplectic integrators to maintain the total momentum over long runs. In relativity and quantum mechanics, the conservation of total four-momentum follows from spacetime symmetries (Noether's theorem).

Limitations include open systems where external forces or energy exchange occur, or systems with external fields that impart impulse. Momentum conservation is a powerful organizing principle across disciplines, but its applicability depends on isolating the system and accounting for all external interactions.