What are the units for the equation E=gamma*m?

[lavenderblue]

I'm using the equation: E=gamma*m

I want to know what the units of each of the quantities are. If I want to calculate the Lorentz factor, then do I need to make sure that both the Energy and mass have the same units?

I am also using the equation for length contraction: L=L0*gamma

Do I need to make sure that the length is in metres? And is L0 the length in the rest frame?

 

[Delphi51]

The formula relating E and m is E = mc². m in kg, E in Joules.
The gamma factor 1/sqrt(1-v²/c²) is dimensionless (no units).
It relates two times or lengths (moving to stationary measurements) as in length contraction and time dilation.

 

[Pengwuino]

You might want to take a look at this:

http://en.wikipedia.org/wiki/Natural_units

 

[Delphi51]

Oh, thank you! I haven't seen natural units for many years.
The article you linked answers your question: you must put the mass and energy in Planck units. The SI equivalents for the Planck units for mass and energy are listed in tables here:
http://en.wikipedia.org/wiki/Planck_units

 

[rwisz]

The units for the equation E=gamma*m are energy (E) in joules (J) and mass (m) in kilograms (kg). The Lorentz factor (gamma) is a dimensionless quantity and does not have any units. Therefore, in order to calculate the Lorentz factor, both energy and mass should have the same units.

For the equation L=L0*gamma, the units for length (L) and the rest length (L0) should be consistent, such as meters (m). L0 represents the length in the rest frame, while L represents the length in a moving frame. Both equations are part of the special theory of relativity and involve the concept of relativistic energy and length. It is important to use consistent units in order to accurately apply these equations.