A composite flywheel rotor includes a flywheel hub having tapered outer surface and an axis of rotation and a flywheel rim having an axis of rotation coinciding with the hub axis of rotation. The flywheel rim has multiple rings axially press-fit together to precompress the rings to form a composite flywheel rim. Each ring is made of approximately equal radial thickness and the entire non-dimensionalized radial thickness ratio of the assembled rim should be between approximately 0.38 to 0.48. The rim is optimally made up of four or five individual rings, each of which rings has tapered inner and outer diameters, preferably tapered at small angles to produce large radial forces when the rings are pressed onto each other and the hub by pressing axially, resulting in a high radial compressive preload in the assembled rim. A taper angle of 1-5° is suitable.