Try this experiment- take a bicycle wheel, hold it where it would normally attach to the forks, and start it spinning .Once it's spinning, try turning the wheel so that it is spinning around a vertical axis, rather than a horozontal axis.If I've been clear in my directions, you will notice that it's a lot harder to change the axis of rotation of the spinning wheel, than it does to change the axis of rotation of a stationary wheel.That's why it's easier to balance on a moving bike- or, rather, on a bike with rotating wheels.
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