Does inertia have anything to do with conservation of energy?

Question

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.

Answer 1

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:

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