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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.

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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.

So the Law of Inertia is not directly connected to potential energy. You obtain potential energy by arranging things to resist a force; a roller coaster is a typical class room example, where the car is initially at rest at the top of the system, having used work to haul it up their: it has a certain amount of potential energy from its position and gravity -- just like the rock on the cliff -- and when it is kicked into motion, by application of a mechanical force, it rolls downhill, converting the potential energy of its position into kinetic energy of its motion.

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Potential energy and inertia are related via Einstein's famous equation $E = mc^2$.

A compressed spring has more potential energy and therefore more inertial mass compared to an uncompressed one, making it more difficult to accelerate because of its increased inertia.

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  • $\begingroup$ By the looks of it, Einstein's equation seems to be a modification of the equation of kinetic energy, or is it the other way around? $\endgroup$ – Abdul Moiz Qureshi Apr 18 '16 at 15:10
  • $\begingroup$ 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: $E = \gamma mc^2$. $\endgroup$ – John McVirgo Apr 18 '16 at 20:51

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