Why flywheels store energy in a way batteries cannot

Power against capacity, and the jobs each of them suits.

A flywheel stores energy as motion rather than as chemistry, so it can give that energy back or take more of it in almost as fast as something can be connected to spin it up or slow it down, while a battery's chemical reaction has a natural pace it cannot easily be rushed past, which is why the two are suited to very different jobs despite both being ways of storing energy for later.

What is really going on

A battery stores energy in the arrangement of its chemicals, and getting that energy back out means letting a chemical reaction run, a process with its own natural speed that pushing harder can only rush so far before the battery heats up, degrades, or simply cannot keep up with the demand. A flywheel stores its energy as the literal motion of a spinning mass, and giving that energy back out means letting the spin slow down, which can happen as fast as whatever is connected to the flywheel is able to draw the motion away, limited mostly by how strong the mechanical connection is rather than by any chemical pace at all. The same is true in reverse: charging a battery quickly is limited by chemistry, while spinning a flywheel up quickly is limited mostly by how much force can be applied to it, which is usually a much less strict limit than any battery's chemistry allows. Neither storage method loses this trade cleanly either, since a battery pushed to give up its energy faster than its chemistry likes tends to lose some of that energy as wasted heat rather than delivering it usefully, while a flywheel spun down too abruptly can strain whatever mechanical coupling is trying to draw the motion off it, a different kind of limit but a real one all the same.

The roundabout comparison

A playground roundabout takes real, sustained effort to bring up to a good spinning speed, but once it is spinning, a single hard shove from someone running alongside can noticeably speed it up further in an instant, and grabbing the rail suddenly can slow it down again almost as quickly, transferring a burst of energy in or out over a couple of seconds rather than gradually. A battery has no equivalent to that sudden shove, since forcing more current in or out faster than its chemistry allows tends to waste energy as heat rather than actually storing or releasing it any faster, while a flywheel, like the roundabout, is happy to accept or give up a burst of energy almost as quickly as something can physically push or pull on it. Nobody grabbing the rail of a fast roundabout to stop it is drawing on some slow chemical process to do it, they are simply resisting motion directly, and that direct mechanical resistance is exactly what a flywheel offers whatever it is connected to as well.

One figure worth keeping in mind

A flywheel can typically release the majority of its stored energy within seconds if connected to something able to draw it away that fast, a rate a battery of a similar stored energy could rarely match without significant losses, which is exactly why flywheels are chosen for jobs needing a short, powerful burst rather than a long, steady trickle spread out over minutes. A flywheel of a given weight would need to be considerably larger and heavier to match a good battery's total stored energy, so the comparison only favours the flywheel where speed of delivery matters more than how much energy is available overall.

What this changes in practice

Because a flywheel's strength is speed of delivery rather than total capacity for its size, since spinning mass generally stores less energy per unit weight than a good battery's chemistry does, flywheels tend to be chosen for smoothing out sudden peaks in demand over a few seconds, while batteries are chosen for delivering steady power over minutes or hours. Neither is simply a better version of the other, they are suited to opposite ends of the same problem, and a design that tries to use one where the other is actually needed usually announces the mismatch quickly, either by running out of energy far sooner than expected or by being unable to deliver a burst fast enough when it is actually called for.