Energy Confusion

[Mr. Astrophysicist]

is used to calculate the energy of moving objects; true or false?

E^2=(MC^2)^2+(PC)^2

is used to calculate the energy of objects that are not moving; true or false?

E=MC^2

So, or both formulas correct? I've been pondering over this...

[Klaynos]

Assuming "M" is rest mass your statement is true. The second equation is a simplification of the first when p=0

 

It's worth being careful with phrases such as moving and not moving as motion is relative.

[Sensei]

Yes,
when v=0 (object is in it's own frame of reference), then p=0, and longer formula version simplify to E=mc²

[ajb]

Both are true (mod your poor wording as Klaynos points out). Remember that energy is not a Lorentz invariant; meaning that it will depend on the inertial frames used to measure the energy.

 

Note that you can write the equation as

 

[math]E^{2}-p^{2}c^{2} = m^{2}c^{4}[/math],

 

and that this is independent of the inertial frame used. In short, although energy and momentum are dependent on the inertial frame you use, the combination "E^2 -p^2" does not depend on the frame and is essentially the mass.

Edited March 19, 2015 by ajb