Momentums

Momentum is a property of a moving object that combines its mass and velocity. In classical mechanics, it is a vector quantity, p = m v, meaning it has both magnitude and direction. Momentum characterizes motion and interacts with forces in predictable ways.

Linear momentum is defined as p = m v for a particle with constant mass. For a system of particles, the total momentum is the vector sum of the individual momenta. The unit is kilogram-meter per second (kg·m/s).

Impulse is the change in momentum caused by a force applied over time. If a force F acts for a time Δt, the impulse J = F Δt, and Δp = J. Newton's second law can be expressed as F = dp/dt.

Conservation of momentum states that in an isolated system, where no external forces act, the total momentum remains constant. This principle is central to analyzing collisions, rocket propulsion, and many problems in engineering and physics.

Relativistic momentum generalizes p = m v for high speeds, with p = γ m v, where γ = 1/√(1 − v^2/c^2). The energy–momentum relationship becomes E^2 = (p c)^2 + (m c^2)^2; massless particles carry momentum equal to E/c, such as photons.

Regarding terminology, the standard plural of momentum is momenta; momentums is used in some contexts but is generally considered nonstandard. The term momentum also appears in other domains, such as wave momentum and canonical momentum in Lagrangian mechanics.