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The Connectin Between Kinetic Energy in Newtonian and Relativistic Mechanics

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 massin the Newtonian equation (actually the rest mass) has become the relativistic mass

The relativistic energy is given byThis 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