Hi, I am trying to quickly resolve a fairly basic question that cropped when considering relativity. Classically, the total energy of a system is often described in term of 3 components:(adsbygoogle = window.adsbygoogle || []).push({});

Total Energy = Rest Mass + Kinetic + Potential

If I ignore potential energy, i.e. a particle moving in space far from any gravitational mass, then I assume the general form above can be reduced to:

[1] [tex]E_T = m_o c^2 + 1/2mv^2[/tex]

Now [tex]m_o[/tex] is the rest mass, while I assume [m] has to be described as the relative mass as a function of its velocity [v], i.e.

[2] [tex]m = \frac {m_o}{\sqrt{(1-v^2/c^2)}}[/tex]

However, relativity also introduces the idea of relativistic momentum:

[4] [tex] p = mv = \frac {m_o v}{\sqrt{(1-v^2/c^2)}}[/tex]

However, the following link show the definition of `Relativistic Energy in Terms of Momentumâ€™: http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html#c4 which I have expanded to the following form:

[5] [tex]E_X^2 = m_o^2 c^4 + p^2c^2 = m_o^2 c^4 + m^2v^2c^2[/tex]

Now my initial assumption was that [tex][E_X \equiv E_T][/tex], but examination of equations [1] and [5] suggests that this cannot be the case. Could somebody explain my error or the difference in the implied energy of these 2 equations?

As a side issue, energy is a scalar quantity, while momentum is a vector quantity. I see how multiplying [p] by [c] gets us back to the units of energy, but was slightly unsure about the maths of mixing these quantities. Would appreciate any clarification of the issues raised. Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Basic Energy-Momentum Issue

**Physics Forums | Science Articles, Homework Help, Discussion**