A flywheel used for kinetic energy storage and the construction of the flywheel using composite materials. The present invention provides a rotor support for coupling an annular flywheel rotor to a shaft for rotation with the shaft, the support comprising a body having a longitudinal axis about which it rotates in the finished flywheel assembly, wherein the body comprises a stack of sheets of a composite material including fibers, the stack includes at least two unidirectional sheets, each having substantially all of their fibers extending in the same direction, and the fibers of one of the unidirectional sheets are orientated at a different angle to the longitudinal axis of the body to the fibers in another unidirectional sheet. The body includes at least one side layer of woven fabric provided over a side of the stack of sheets. The rotor support configuration of the present invention provides a stiff construction.