## What To Remember from Lesson 18

### A New Kind of Energy

Mass is a kind of energy. In an object's own rest frame, the value of that energy is:

$$
E_m = mc^2 \nonumber
$$

As viewed by an observer in a co-moving inertial frame, that energy would appear to be:

$$
E_T=m\gamma c^2 \nonumber
$$

This can be interpreted as observing that a moving object appears to have more mass than its value measured within its own rest frame:

$$
m_R = \gamma m \nonumber
$$

where "relativistic mass" is sometimes used to represent that quantity. In our terms, this might also be written:

$$
m_H = \gamma m_A \nonumber
$$

With some algebra, we can write the total energy of an object in another way:

$$
E_T =& E_m + K \\
K =& E_T - E_m \\
K =& m\gamma c^2 - mc^2 \\
K =& mc^2(\gamma -1)
$$

where $K$ is the relativistic kinetic energy.