Difference between revisions of "E^2=(mc^2)^2+(pc)^2"
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(username removed) (Added derivation) |
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− | '''<math> E^2=(m_0 c^2)^2+(pc)^2 </math>''' is a formula in [[relativity|special relativity]] that relates the relativistic energy, E, [[rest mass]], <math>m_0</math>, and [[momentum]], p, of a particle. From it the momentum of a [[photon]] can be derived | + | '''<math> E^2=(m_0 c^2)^2+(pc)^2 </math>''' is a formula in [[relativity|special relativity]] that relates the relativistic energy, E, [[rest mass]], <math>m_0</math>, and [[momentum]], p, of a particle. From it the momentum of a [[photon]] can be derived and so to the famous equation [[e=mc^2|E=mc<sup>2</sup>]]. |
== Derivation == | == Derivation == | ||
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Subtracting the momentum equation from the energy equation an rearranging gives: | Subtracting the momentum equation from the energy equation an rearranging gives: | ||
<math> E^2=(m_0 c^2)^2+(pc)^2 </math> | <math> E^2=(m_0 c^2)^2+(pc)^2 </math> | ||
+ | |||
+ | == Other Formulae == | ||
+ | |||
+ | The energy of a photon can be derived by setting the [[rest mass]], <math>m_0</math>, equal to zero, so: | ||
+ | <math>E=pc</math> | ||
+ | |||
+ | Mass energy equivalence can be derived by setting the momentum, <math>p</math>, to zero. This gives us one of the most famous equations in physics, <math>E=m_0 c^2</math> | ||
[[Category:Physics]] | [[Category:Physics]] | ||
[[Category:Relativity]] | [[Category:Relativity]] |
Revision as of 18:01, September 10, 2016
is a formula in special relativity that relates the relativistic energy, E, rest mass, , and momentum, p, of a particle. From it the momentum of a photon can be derived and so to the famous equation E=mc2.
Derivation
The relativistic equation for momentum is:
The equation for relativistic energy is:
These can be rearranged into the forms:
Subtracting the momentum equation from the energy equation an rearranging gives:
Other Formulae
The energy of a photon can be derived by setting the rest mass, , equal to zero, so:
Mass energy equivalence can be derived by setting the momentum, , to zero. This gives us one of the most famous equations in physics,