Momenta

Momentum, in physics, is a quantity associated with motion that exists in several forms. The most familiar is linear momentum, defined for a particle of mass m moving with velocity v as p = m v. It is a vector, pointing in the direction of motion, and for a system it is the vector sum of its constituents’ momenta. Linear momentum reflects both the motion and the inertia of objects, and in an isolated system the total linear momentum is conserved.

The rate of change of momentum equals the net external force: F = dp/dt. The impulse delivered to an object, J = ∫ F dt, equals the change in its momentum, Δp. In collisions, if external forces are negligible during the interaction, the total momentum before and after remains the same (conservation of momentum).

Momentum has the same units as mass times velocity, kilogram meter per second (kg·m/s). In continuous media, momentum density is ρ v, and the total momentum is the integral over volume. The center of mass moves with velocity equal to the total momentum divided by the total mass.

In special relativity, momentum generalizes to p = γ m v, where γ is the Lorentz factor; at low speeds this reduces to m v. Rotational motion has angular momentum L = r × p, and in the absence of external torque, angular momentum is conserved (τ = dL/dt).

In quantum mechanics, momentum becomes an operator p̂ = −i ħ ∇, with eigenstates of definite momentum and the de Broglie relation p = h/λ. The momentum uncertainty plays a central role in the Heisenberg uncertainty principle.

The plural form momenta is the standard English plural of momentum; momentum is used for both a single quantity and multiple vectors in a system.