The bike stays upright because of the gyroscopic effect of the wheels turning. The faster the wheels are rotating, the greater the gyroscopic effect. That's why it doesn't fall over when you're moving, but it does want to fall over when you stop. You can keep it upright when stationary using balance, but you only need to use balance when there is little or no gyroscopic effect.
I don't think that's quite right. There is
a gyroscopic component, and it does
increase with speed, but it's not the most important factor.
Depends on your view of most important?
Think about when we learn to ride a bike, or teach a child to ride a bike. One of the key things is them cycling at a good enough speed for the gyroscopic effect to make it all easy for them, rather than the whole struggling for balance and trying to correct with steering.
I think Anthony got it just about right in that paragraph, in terms of the reality
of cycling. Largely, the gyroscopic effect is the most important factor - since when we're teaching kids to cycle, or learning, it's the major thing we try to exploit to make it all simple and work.
A cyclist in motion is constantly falling to one side or the other, and steering to correct his fall. It's this steering that keeps the bike upright.
I'm not fully buying that.
Sure, as you say in the bits I've snipped, gyroscopic effect increases with speed, but when cycling at a normal pace, there's not normally a concept of falling to one side or t'other. I accept and recognise there maybe some steering correction, and still some balance input from the cyclist, but some of that is due to changing direction. True enough, at low enough speed, without much in the way of gyroscopic effect, bikes do feel like their constantly falling to one or the other side - but that's merely because there's little gyroscopic effect going on.
Once there is sufficient speed, and a fair degree of gyroscopice effect going on, I'd actually contend the bike really wants to stay upright, and in "perfect" conditions, like the world of physics normally suggests to initially understand something, a bike at a certain speed would keep itself upright, without rider to correct (assuming no friction, perfectly flat surface... etc...etc)
People can cycle at a reasonable pace with no hands on the handlebars - now sure, I get you can still correct steering by leaning, and at lower speeds you'd need to - but at normal pace, any steering correction would be minimal - perhaps similar to minor steering correction when you're driving.
Don't get me wrong - I recognise your point that there is still a balance thing going on, even at speed. But the gyroscopic effect is significant. At a certain speed, a bike rolling along without a rider to correct would probably largely stay upright (given a reasonably flat surface and no other significant affecting factors) and carry on in it's current trajectory, until it's speed dropped below a point where steering correction to balance becomes more significant that the gyroscopic effect of the bike / wheels at speed.
That whole rider-less bike thing, at speed, plus consideration of, say, the higher speeds of motorcycles, does show the significance of the gyroscopic effect.