A simple demonstration. Take a piece of string, tie a 1 ounce weight on one end, and a one pound weight on the other. Hold the large weight in your hand, and whirl the string. Now do the same holding the small weight. The overall weight is the same, but the difference is certainly noticeable.
The weight held in your hand is simulating the weight that is close to the hub on the flywheel, while the free end represents the mass at the edge.
Jeff