Momentum

In physics, momentum is a physical quantity related to the velocity and mass
of an object.

Momentum in classical mechanics

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.

     [I=\int F\,dt]

using the definition of force yields:

     [I=\int\frac{dp}{dt}\,dt]
     [I=\int dp]
     I = Δp

Momentum in relativistic mechanics

It is commonly believed that the physical laws should be invariant under
translations. Thus, the definition of momentum was changed when Einstein
formulated Special relativity so that its magnitude would remain invariant
under relativistic transformations. We now define a vector, called the
4-momentum thus:

     [E/c p]

where E is the total energy of the system, and p is called the "relativistic
momentum" defined thus:

     E = γmc2
     p = γmv

and

     [ \gamma = \frac{1}{\sqrt{1 - v^2/c^2}}].

The "length" of the vector that remains constant is defined thus:

     [p\cdot p-E^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.

Momentum in quantum mechanics

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.

Figurative use

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.

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