# Relativistic Mass

on . Posted in Classical Mechanics

Relativistic mass, abbreviated as $$m_r$$, refers to the mass of a body which changes with the speed of the body as this speed approaches close to the speed of light.  Relativistic mass is a concept in Albert Einstein's theory of special relativity, which describes how the mass of an object changes as it moves at velocities close to the speed of light.  It is a fundamental idea that replaces the classical notion of invariant mass from classical physics.

• Rest Mass  -  The rest mass of an object is the mass it possesses when it is at rest, as measured by an observer who is also at rest relative to the object.  It is an intrinsic property of the object and does not change with its motion.
• Relativistic Mass Increase  -  As the velocity of an object approaches the speed of light, the denominator in the formula approaches zero.  This leads to an increase in the relativistic mass of the object. In other words, the faster an object moves relative to an observer, the more massive it becomes.
• Invariance of Rest Mass  -  While the relativistic mass increases with velocity, the rest mass remains constant and is the same in all reference frames.  It is a fundamental property of the object itself and does not depend on its motion.
• Energy-Mass Equivalence  -  Special relativity also introduces the concept that mass and energy are interchangeable.  This is famously described by Einstein's mass-energy equivalence formula, E=mc2.  This relationship demonstrates that mass can be converted into energy and vice versa.

The concept of relativistic mass is used to explain various relativistic effects, such as the increase in an object's inertia as it approaches the speed of light and the need for ever-increasing amounts of energy to accelerate an object to such velocities.  However, it's important to note that in modern physics, the concept of relativistic mass has largely been replaced by the concept of invariant mass or "rest mass" as a more fundamental and less ambiguous quantity for describing particle properties in high energy physics.

### Relativistic Mass Formula

$$m_r = m \;/\; \sqrt { 1 - v^2 \;/\; c^2 }$$
Symbol English Metric
$$m_r$$ = relativistic mass $$lbm$$  $$kg$$
$$m$$ = rest mass $$lbm$$ $$kg$$
$$v$$ = velocity $$ft\;/\;sec$$ $$m\;/\;s$$
$$c$$ = speed of light $$ft\;/\;sec$$ $$m\;/\;s$$

Tags: Mass