Momentum
Momentum is the Noether charge of translational invariance. As such, even fields as well as other things can have momentum, not just particles. However, in curved spacetime which isn't asymptotically Minkowski, momentum isn't defined at all.
In physics, momentum is a physical quantity related to the velocity and mass of an object.
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2 Momentum in relativistic mechanics 3 Momentum in quantum mechanics 4 Figurative use |
In classical mechanics, momentum (traditionally written as p) is defined as the product of mass and velocity. It is thus a vector quantity.
The SI unit of momentum is newton-seconds, which can alternatively be expressed with the units kg.m/s.
An impulse changes the momentum of an object. An impulse is calculated as the integral of force with respect to duration.
Momentum in classical mechanics
using the definition of force yields:
See also angular momentum.
It is commonly believed that the physical laws should be invariant under translationss. Thus, the definition of momentum was changed when Einstein formulated Special relativity so that its magnitude would remain invariant under relativistic transformations. See physical conservation law. We now define a vector, called the 4-momentum thus:
The "length" of the vector that remains constant is defined thus:
Momentum in relativistic mechanics
where E is the total energy of the system, and p is called the "relativistic momentum" defined thus:
and
Setting velocity to zero, one derives the result that objects have a rest mass which is related by the experession E=mc^2
Massless objects such as photons also carry momentum; the formula is p=E/c, where E is the energy the photon carries and c is the speed of light.
In quantum mechanics momentum is defined as an operator on the wave function. The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once.
A process may be said to gain momentum. The terminology implies that it requires effort to start such a process, but that it is relatively easy to keep it going.
See also Slippery slope.Momentum in quantum mechanics
Figurative use
