A flywheel energy storage device has a central shaft, a flywheel having a flywheel rotor supported by and mounted for rotation around said shaft, and a motor/generator having a stator and a rotor. The rotor is formed integrally with the flywheel rotor. The stator has an outer cylinder that is cooled by a liquid flowing in contact with its cylindrical surface. Preferably, the stator has (i) a cylindrical hub having an outer surface and longitudinal channels formed therein, (ii) a cylinder surrounding said cylindrical hub thereby providing passages through the channels, and (iii) end caps sealing the passages and providing a distribution channel for distributing fluid to said passages, thereby providing fluid cooling passages for said stator. A radial vibration dampener can be positioned at one or both ends of the shaft. The dampener has a plurality of spring members positioned between two cylindrical surfaces, one end of each spring member being attached to each cylindrical surface.