**ERIC Number:**EJ896407

**Record Type:**Journal

**Publication Date:**2010-Jul

**Pages:**11

**Abstractor:**As Provided

**Reference Count:**11

**ISBN:**N/A

**ISSN:**ISSN-0143-0807

Mass, Momentum and Kinetic Energy of a Relativistic Particle

Zanchini, Enzo

European Journal of Physics, v31 n4 p763-773 Jul 2010

A rigorous definition of mass in special relativity, proposed in a recent paper, is recalled and employed to obtain simple and rigorous deductions of the expressions of momentum and kinetic energy for a relativistic particle. The whole logical framework appears as the natural extension of the classical one. Only the first, second and third laws of non-relativistic classical dynamics are postulated, in an axiomatic form which does not employ the concept of force. The axiomatic statements of the second and third laws of relativistic dynamics, which yield the relativistic definitions of mass and four-momentum and the conservation of four-momentum for an isolated pair of relativistic particles with a small relative velocity, are proved as simple consequences of the classical ones and of the Lorentz transformation of coordinates. Then, relativistic four-force and three-force are defined, and the expression of relativistic kinetic energy is deduced. Finally, a simple proof of the Lorentz invariance of the conservation of the sum of four-momenta for any set of particles, with arbitrary relative velocities, is presented.

Descriptors: Kinetics, Physics, Motion, Scientific Principles, Molecular Structure, Energy, Validity, Science Instruction, Equations (Mathematics)

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**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A