The energy momentum equation in special relativity is: $$E^2=(pc)^2+(mc^2)^2.$$ and it holds for a moving but not accelerating object. One special case is the massless photon: $$E=pc.$$ And another one is a resting object: $$E=mc^2.$$ The first term in the energy momentum equation seems to be kinetic energy of the object as a whole? That should mean that the second term is all other forms of energy? This could include kinetic energy of the constituents of the object. So a full battery for instance has more energy than an empty battery and therefore has a larger mass? Likewise a hot kilogram prototype has more energy than a cold one and therefore has larger mass? This thermic energy is kinetic energy at constituent level but not for the object as a whole.
In classical mechanics mass is a property of an object that has to do with its inertia. We could define $m=\frac{F}{a}$. In classical mechanics an empty battery has the same mass as a full one and a cold kilogram prototype has the same mass as a hot one.
Does this not mean that the concept of mass has changed in special relativity and now is a measure of all energy except kinetic energy of an object?
If so $E=mc^2$ does not necessarily predict the atomic bomb?
Instead of it saying that all objects have some intrinsic energy due to their mass it could say that an absolutely cold still object has no mass since it has no energy. Which sounds absurd.
So I am guessing that the old concept of mass from classical mechanics is an approximation to the new concept of mass in special relativity?