# What is the relationship between potential energy and inertia?

It seems to me that the two are very similar! Potential energy seems to either explain, or partially explain, directly or indirectly, the law of inertia. I already know that bodies do not move because of inertia, they move due to forces acting on them that change state of rest or constant motion, and i also know that inertia is the resistance of object to move.

Potential energy depends upon the presence of a force, and the actual configuration of objects. So a rock at the top of a cliff has potential energy $U=mgh$, due to $m$, the mass of the rock, $g$, the acceleration due to gravity, and $h$, the height of the cliff.
Inertia, as described by Newton's First Law of Motion, is that property of matter which, in the absence of external forces, keeps a body in motion travelling in a straight line at unchanging speed, which gives it a kinetic energy of $T=mv^2/2$, where $m$ is the mass, and $v$ is the velocity of the mass, with respect to a stationary observer. Of course, if the body was not already moving it would not start moving; this is also a part of the Law of Inertia.
Potential energy and inertia are related via Einstein's famous equation $E = mc^2$.
• Not quite. That equation is the special case of $v=0\Rightarrow\gamma=1$ for the more general equation for the total energy, rest+kinetic, of a moving particle of mass m: $E = \gamma mc^2$. – John McVirgo Apr 18 '16 at 20:51