In Newtonian mechanics, the momentum and kinetic energy are given by
and
The relationship between momentum p and kinetic energy is often written as
Many equations and concepts in Newtonian mechanics have close analogies in special relativity. For example the equation for momentum in Newtonian mechanics is
The equation for momentum in special relativity is
where
Notice that the mass
in the Newtonian equation (actually the rest mass
) has become the relativistic mass
The relativistic energy is given by
This is the total energy of the particle. The kinetic energy is found by subtracting the rest mass energy
The relationship between kinetic energy and momentum is found thus
Hence