In classical mechanics, momentum is the product of mass
and velocity
of a moving object. More precisely, the momentum of a particle or rigid body
with mass
and velocity
is defined as
For a collection of
The SI unit of momentum is kilogram metre per second (kg m/s).
Momentum plays an important role in Newton's second law, which in its most concise formulation reads
expressing that the total force exerted on an object equals the time derivative of its momentum. In the special case that there are no forces acting on the object, we get back Newton's first law:
This last observation leads to the idea of a conserved quantity. It turns out that the law of conservation of momentum is equivalent to the invariance of the physical laws under translations. This idea can be extended: Noether's theorem shows that every continuous symmetry of a physical law that can be formulated as an action principle leads to a conserved quantity. In this setting, momentum can be viewed as the conserved quantity corresponding to spatial translations. This notion of momentum can be generalised in such a way that it is also possible to speak of the momentum of, for example, electromagnetic waves.
Momentum plays an important role in the Hamiltonian formalism of classical mechanics, where mechanical systems are described in terms of generalised coordinates and generalised momenta. This, in turn, explains the appearance of the momentum operator in the Schrödinger equation in quantum mechanics.
A quantity related to momentum is impulse, which is defined as the force exerted on a moving object integrated over a time interval
:
By integrating the two sides of Newton's second law over time, we obtain the equation
In words: the impulse is equal to the change in momentum.
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