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Relativistic Energy

The equation of motion in relativistic mechanics is written as

The concepts of work done by a force, and of potential and kinetic energies remain valid in relativistic mechanics as well. Hence, work-energy theorem tells that if a particle, acted upon by a force F along X-axis, moves a distance dx, the change dE_k in its kinetic energy is given by

Or, dE_k = (dm) c²

Thus, increase in kinetic energy is equal to change in mass times c². If particle starts from rest (v = 0, m = m₀) and acquires speed v (hence mass the kinetic energy gained by the particle is,

The above equation gives the relativistic kinetic energy of the particle. The term m₀ c² is called rest mass energy – it is the energy of the particle stored in the form of mass when particle is at rest. When particle acquires velocity, it gains kinetic energy; the total energy of the particle in motion is,

E = E_k + m₀ c² = (mc² – m₀ c²) + m₀ c²