Longitudinal and Transverse Mass

In Newtonian mechanics the mass of a particle is constant and can be expressed as the ratio of the force to the acceleration:The force can be written as the rate of change of momentum:so

In Newtonian mechanicsandis constant so

In special relativity, mass plays more of a resistance to acceleration role, and has a different value in the direction of acceleration than at right angles to it.

In special relativity the momentum of a particle of rest massiswhere

If the acceleration is perpendicular tothen and

If the acceleration is in the direction of

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