For a solid cylinder it is 1 2 m r 2 {\textstyle {\frac {1}{2}}mr In the Industrial Revolution, James Watt contributed to the development of the flywheel in the steam engine, and his contemporary James Pickard used a flywheel combined with a crank to transform reciprocating motion into rotary motion. High energy density flywheels can be made of carbon fiber composites and employ magnetic bearings, enabling them to revolve at speeds up to 60,000RPM (1 kHz).

Common uses of a flywheel include smoothing a power output in reciprocating engines, energy storage, delivering energy at higher rates than the source, controlling the orientation of a mechanical system using gyroscope and reaction wheel, etc. As with other types of accumulators, a flywheel inherently smooths sufficiently small deviations in the power output of a system, thereby effectively playing the role of a low-pass filter with respect to the mechanical velocity (angular, or otherwise) of the system. is the angular velocity, and I {\displaystyle I} is the moment of inertia of the flywheel about its axis of symmetry.Once suitably abstracted, this shared principle of energy storage is described in the generalized concept of an accumulator. The principle of the flywheel is found in the Neolithic spindle and the potter's wheel, as well as circular sharpening stones in antiquity. The use of the flywheel as a general mechanical device to equalize the speed of rotation is, according to the American medievalist Lynn White, recorded in the De diversibus artibus (On various arts) of the German artisan Theophilus Presbyter (ca.