Mass - Summary of Mass Concepts and Formalisms

Summary of Mass Concepts and Formalisms

In classical mechanics, mass has a central role in determining the behavior of bodies. Newton's second law relates the force F exerted in a body of mass m to the body's acceleration a:

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Additionally, mass relates a body's momentum p to its linear velocity v:

,

and the body's kinetic energy K to its velocity:

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In special relativity, relativistic mass is a formalism which accounts for relativistic effects by having the mass increase with velocity.

Since energy is dependent on reference frame (upon the observer) it is convenient to formulate the equations of physics in a way such that mass values are invariant (do not change) between observers, and so the equations are independent of the observer. For a single particle, this quantity is the rest mass; for a system of bound or unbound particles, this quantity is the invariant mass. The invariant mass M of a body is related to its energy E and the magnitude of its momentum p by

where c is the speed of light.

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