Momentum

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Momentum is a mathematical quantity related to the velocity and mass of an object. In classical mechanics, momentum (traditionally written as p) is defined as the product of mass and velocity. It is thus a vector quantity with units kg.m/s (equivalently, N.s).

An impulse changes the momentum of an object. An impulse is calculated as the integral of force with respect to duration.

I = ∫Fdt

using the definition of force yields:

I = ∫(dp/dt)dt
I = ∫dp
I = Δp

It is commonly believed that the physical laws should be invariant under translations. Thus, the definition of momentum was changed when Einstien formulated 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:

[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

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

p·p - E2

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.