I'm tasked with the design of a variable inertia flywheel. I've concentrated on the change in location of mass about an axis and varying 'r'. I'm trying to analyze what happens without any change in torque (I.E. the flywheel free spins). My HS physics tells me that the angular momentum must remain constant- Lo=Le. But also, kinetic energy must be conserved - Eko=Eke. As I run trials with re=ro/2, the results substantiate what I would expect, since L is a function of w and Ek is a function of w2 (I can calculate a new w to conserve one (e.g. L) but not both). I know that I can adjust r without adding torque to the axis of rotation and it seems that the work required should not enter into the conservation question (if I increase r, centrifugal force would make work a negative value). Where am I missing the conservation question? Can it be both angular momentum and kinetic energy and if not, which is conserved? And what happened to the other? I've searched this forum as well as other internet sites and have found references to this dichotomy, but each leaves the fundamental question unanswered.