# Rest, Mass, and Kinetic Energy

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1. Oct 4, 2016

1. The problem statement, all variables and given/known data
I really don't have a homework question just a thought. Is rest energy "maximum energy" for a particle? As to say a particle at rest has a given energy, so when it is in motion it transfers some mass energy to kinetic energy, where both the mass and kinetic energy together equal the rest energy?

2. Relevant equations
E=mc^2
E= T+ mc^2

3. The attempt at a solution
I know that E=mc^2 is supposed to include both the mass energy and kinetic energy. But what about the second equation. To me, that suggests that the rest energy is actually the total energy, as to say it is equal to the kinetic energy plus the rest energy. Can you guys help me straighten this out in head?

2. Oct 4, 2016

### PeroK

You've got this wrong. Rest energy and mass energy are the same thing and do not include any kinetic energy. The total energy of a particle is given by

$E = \gamma mc^2 = T + mc^2$

Sometimes the rest energy is given as

$E_0 = mc^2$

3. Oct 4, 2016

### Staff: Mentor

Actually, the rest energy is the minimum energy. If it is moving then it's total energy will be greater than its rest energy.

4. Oct 4, 2016

### Staff: Mentor

You need to keep in mind that there are two basic ways of thinking about mass in relativity, which makes equations come out differently depending on which way a book's or website's author chooses.

The older way, which you find in old textbooks and (still) in most pop-science treatments of relativity, is to think in terms of "rest mass" $m_0$ and "relativistic mass" $m.$ In this case the total energy is $$E = mc^2 = \gamma m_0 c^2 = m_0 c^2 + T$$ (where $\gamma = 1 / \sqrt{1-v^2/c^2}$ and $T$ is kinetic energy) and the rest energy is $$E_0 = m_0 c^2.$$

The newer way, which you find in modern textbooks but not so much in pop-science treatments, is to think only in terms of what used to be called "rest mass" but is now just called "mass", and label it as $m.$ In this case the total energy is $$E = \gamma mc^2 = mc^2 + T$$ and the rest energy is $$E_0 = mc^2.$$

When you're reading any book or website or whatever, you need to be sure which way they're doing this.