Difference between revisions of "E^2=(mc^2)^2+(pc)^2"

From Conservapedia
Jump to: navigation, search
(username removed)
(Added derivation)
(Added some relations to other formulae)
Line 1: Line 1:
'''<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 as <math>E=pc</math> and so to the famous equation [[e=mc^2|E=mc<sup>2</sup>]].
+
'''<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 ==
Line 18: Line 18:
 
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,