# relativistic mass

relativistic mass
the mass of a body in motion relative to the observer: it is equal to the rest mass multiplied by a factor that is greater than 1 and that increases as the magnitude of the velocity increases.

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in the special theory of relativity, the mass that is assigned to a body in motion. In physical theories prior to special relativity, the momentum p and energy E assigned to a body of mass m and velocity v were given by the formulas p = mv and E = E0 + 1/2mv2, where the value of the “rest energy” E0 was undetermined. In special relativity the corresponding formulas for p and E, respectively, are p = mv/ √((1 - v2/c2)) and E = mc2/ √((1 - v2/c2)) , where c equals the speed of light (300,000 kilometres [186,000 miles] per second) and m is the “rest mass” of the body (i.e., its mass as determined when the body is at rest). It is convenient for certain purposes to define the relativistic mass mR of a body by the formula mR = m/ √((1 - v2/c2)) . Then, for all velocities we have the simple formulas p = mRv and E = mRc2 for the momentum and energy of a body. The relativistic mass mR becomes infinite as the velocity of the body approaches the speed of light, so, even if large momentum and energy are arbitrarily supplied to a body, its velocity always remains less than c.

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Universalium. 2010.

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