I remember with surprising clarity the day I was to learn to ride a bike the hard way. I'm not sure if that's how it was put exactly, but it probably involved something to the effect of learning to ride a bike "like a man" or somesuch, e.g. without training wheels.
This was in a part of Colorado where there are no flat roadways and, I'll admit, that makes the no-training-wheels strategy a bit more reasonable because you could just sit on the thing and be moving and upright with gravity and the bicycle physics doing all the work. I didn't know about bicycle physics, however, because physics of any kind weren't pushed very hard in preschool, I don't think. So, the whole thing mostly didn't make sense, and I also happened to be clumsiest four or five year old to ever grace a bicycle seat. It didn't work out, or, rather, it would work out so long as I didn't have to interact with the bike at all and could just sit there, terrified. After that, hello ground.
Thinking about this now, I'm surprised to note that I still don't really understand bicycle physics. Mostly, I just make the same assumptions you probably do about angular momentum or forward momentum or whatever. But it turns out that not only is that not the answer, even physicists are still a bit mystified by the whole bike thing. In any case: Minute Physics. Enjoy.