Flywheel
It takes energy to get a wheel (any wheel) to rotate. If there is little friction (good bearings) then it will keep rotating a long time. When energy is needed, it can be taken from the wheel again. So it is a simple mechanical means of storing energy. The amount of energy stored is a function of the weight and the speed of rotation - making a heavier wheel rotate faster takes more energy. Another factor is the radius (size) because the farther from the axis a part of the wheel is, the more energy it takes to make is rotate. These three factors can be represented by M (mass),  (angular velocity), and R (radius). Combining the two equations below gives 2MR2/4. A fly-wheel is not just any wheel, but specifically designed to store energy. So it should be heavy and/or rotate fast. For example, some buses have a fly-wheel that is used for stopping and starting. When the bus stops (e.g. for a traffic light), the fly-wheel is connected to the wheels, so the rotational energy is transferred to it, so the bus will slow down while the fly-wheel speeds up. Then, when the bus has to start driving again, it is connected again and the energy is transferred back. Of course, you wouldn't want to lug a heavy wheel around on a bus, so it is made of a lighter material that can withstand extremely fast rotation.