# Does inertia have anything to do with conservation of energy? [closed]

I have googled this and not found anything. It seems to me that if objects at rest did not resist being accelerated (which is what I once thought was the case in outside of gravity like in outer space) then the object once in motion would provide free energy. If this is correct, maybe I am not googling it right.

## closed as unclear what you're asking by CuriousOne, ACuriousMind♦, Danu, user36790, rob♦Mar 21 '16 at 19:06

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• Inertia has nothing to do with conservation of energy. $E_{kin}=mv^2/2$. If you lower the inertia of an object by making the mass smaller, the same kinetic energy will simply lead to a higher velocity. As $v$ approaches the speed of light, you would have to switch to the relativistic formula, and then even for $m=0$ you would simply get $E=pc$ for the case of the massless photons. – CuriousOne Mar 15 '16 at 23:26
• The force required to accelerate an object is related to the mass of the object -- is that not related to inertia? An object at rest remains at rest unless force is applied to it. – Jeff Mar 15 '16 at 23:31
• Yes, and the result of that is the (non-relativistic) kinetic energy formula $E_{kin}=mv^2/2$. It tells you the relationship between kinetic energy and velocity, so if you impart a certain amount of energy to a(n initially resting) mass, it will have a certain velocity. If the object has a large mass, it will be slower, if it has a low mass, it will be faster. Conservation of energy doesn't care about that. It only says that any energy that one part of the system loses can be found in some other part of the system. – CuriousOne Mar 15 '16 at 23:35
• It wouldn't violate any laws. It would simply not happen. – CuriousOne Mar 16 '16 at 0:03
• I would suggest you take a good look at the definition of science. It's not a belief system and it's not mathematics, either. – CuriousOne Mar 16 '16 at 4:59

## 1 Answer

Conservation of energy is the result of a symmetry of the universe called time shift symmetry. One result of this is that the kinetic energy of an object cannot change unless some work is done on it. So inertia isn't the cause of conservation of energy but rather the result.

The word inertia isn't precisely defined in physics, but I guess you mean that it means you have to apply a force to accelerate a mass. Assuming a constant force the change in energy is equal to the force times the distance the mass moves:

$$\Delta E = F\,\Delta x$$

You get a similar result from considering conservation of momentum, which is due to a fundamental symmetry called translational symmetry. The change of momentum is equal to the applied force multiplied by the time the force is applied:

$$\Delta p = F \, \Delta t$$

• Yes, inertia is the result of conservation of energy. In the original question, I was not explicit about what caused what but that is what I had in mind. – Jeff Mar 16 '16 at 10:36