Momentum

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 translation?s. 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.