18.8. What To Remember from Lesson 18#
18.8.1. 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:
\[\begin{split}
E_T =& E_m + K \\
K =& E_T - E_m \\
K =& m\gamma c^2 - mc^2 \\
K =& mc^2(\gamma -1)
\end{split}\]
where \(K\) is the relativistic kinetic energy.