Special Relativity

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Composition law for velocities in relativity

 , where:

s = Final Relative Velocity (m/s)

u = Velocity of reference frame one (m/s)

v = Velocity of reference frame two (m/s)

c = Speed of Light (m/s)

Kinetic Energy in Relativity

, where:

E = Kinetic Energy (J)

m = Mass (kg)

c = Speed of Light (m/s)

 = Lorentz Factor

Lorentz Contraction

 , where:

L' = Observed Length (m)

L = Proper Length in Rest Frame (m)

 = Lorentz Factor

Lorentz Factor

The formula for the Lorentz factor is derived from the Lorentz transformations, used in special relativity.  It can be easily calculated when the velocity of an object is known.  

 , where:

 = Lorentz Factor

v = Observed Velocity (m/s)

c = Speed of Light (m/s)

Mass-Energy Equivalence

 , where:

E = Energy (J)

m = Mass (kg)

c = Speed of Light (m/s)

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