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