Round and round it goes

We discuss the coupling of a rotating flywheel with a nonrotating flywheel. We find an expression for the tangential force between the wheels and an expression for the change in angular momentum of the system. Then, we calculate the fraction of rotational kinetic energy which is transferred from the rotating flywheel to the nonrotating flywheel. The theoretical results are compared with the experimental results in the article Mário S M N F Gomes et al, The 'Spinning disk touches stationary disk' problem revisited: an experimental approach (2018 Eur. J. Phys. 39 045709). We then introduce a series of initially nonrotating flywheels between the two original flywheels which are coupled and decoupled, beginning with coupling between the original rotating flywheel and the first wheel in the series and finally coupling between the last flywheel in the series with the original nonrotating flywheel. The condition for maximum energy transfer from the original rotating flywheel to the original nonrotating flywheel for a given number of flywheels will be shown to be achieved when the masses of the flywheels constitute a geometric series if all the flywheels are of the same type. If the flywheels are not of the same type the maximum is achieved when the product of the K-factors of the inertial moments and the masses constitute a geometric series.