Flywheel

A flywheel stores kinetic energy in a rotating body. For fixed-axis rotation with moment of inertia $J$ and angular velocity $\omega$, its energy and axial angular momentum areAn applied torque changes the angular momentum; a drive can put energy into the flywheel, and a load can receive energy as it slows. Energy varies quadratically with speed, while angular momentum varies linearly.

For an original idealized calculation, take $J=0.20\mathrm{kg}{\mathrm{m}}^2$. Slowing from $300$ to $200\mathrm{rad}{\mathrm{s}}^{-1}$ releasesThe wheel still retains4000joules at the lower speed. Delivering the5000joule difference uniformly over10seconds would supply an average power of500watts before losses. This example distinguishes usable energy over a speed interval from the energy at the initial speed.

A NASA laboratory demonstration combined two flywheels to regulate electrical power while supplying a commanded torque. Its G2 and D1 units used magnetically levitated rotating wheels, were mounted on an air-bearing table, and operated between20000and60000revolutions per minute. A load cell measured table force so that output torque could be inferred. The apparatus connects energy exchange with the reaction torque exerted on the surrounding structure.^[ref]

A flywheel can also produce mechanical inertance through a rack and pinion. If relative terminal speed $v$ gives $\omega =v/r$, the ideal stored energy is $J{v}^2/(2r^2)$ and the equivalent inertance is $b=J/r^2$. Bearing losses, friction and material stresses constrain real devices; the ideal energy equation alone is not an operating-speed specification.