What I am asking is, for instance, when I throw a ball my muscles turn sugar into chemical energy, but when that becomes movement energy in the ball how is it stored? If the ball was frozen in time, could you measure it and know that it has movement energy?
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While the ball is in motion, that energy is called kinetic energy. It’s difficult to consider measuring kinetic energy with time paused, as you out it, since obviously that is not possible. However, it’s not all that different from taking a derivative at a specific moment in flight. The ball will still have a measurable amount of kinetic energy even if you could somehow pause time
Since the kinetic (motion) energy of an object depends on an object’s motion’s speed, you cannot measure the kinetic energy of an object that was forced to stop moving through time.
Kinetic energy is basically “stored” in the concept of inertia. Put in the simplest terms possible, inertia is the characteristic of an object to resist changes in its speed and direction, until acted upon by anything else at all. And when I mean anything, I mean anything, from electromagnetism (even non-magnetic stuff is affected by it to some degree) to gravity, and including “another object”.
In the case of an impact with another object, they both try to keep their direction and speed as best they could. If object A is less massive and slower than object B, odds are that object A will be changed a lot, and object B will be barely recording a blip (think a plastic cat toy ball with a bell as object A, moving at 3 yards per hour, versus a bowling ball moving at 15 miles per hour: Bowling ball wins, and might not even register the cat toy).
If the two objects are of closer mass and speed, the situation would be more different, with both of them trying to continue, and deflecting the other in a new direction depending on the angle of impact. That angle of impact also dictates how much energy they give the other, with a head-on collision at equal speed and mass bring both objects to a near stop, or at least losing a great amount of said kinetic energy. This is because inertia is directional, and energy of object A in one direction, is equal to negative energy of that object in the opposite direction.
If I move North at 30 miles per hour, and I hit another car moving North at 31 miles per hour, the exchange of energy is negligible, and the one going at 31 miles per hour won’t quite feel it. If I move North at 31 miles per hour, and I hit another car moving South at 3 miles per hour, suddenly, the exchange of energy is bigger, and there will be more of an effect on us both. You can test that by grabbing two golf balls, and rolling them to impact each other at different speeds and angles.
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