The first response, by Unknown, is not too bad. It quickly dispenses with angular momentum as negligible, and then explains how counter steering can work just fine without angular momentum.
The second response, however, by Dr. Ken Mellendorf, is a muddled mess and should be deleted. He first perpetuates the misconception that the spinning wheels somehow resist leaning and steering, and he follows that immediately with the misconception that the frame itself resists steering simply by moving forward.
The wheels are spinning in a vertical orientation, aligned with the path of the bicycle. The faster they spin, the more difficult it is to change them. The bicycle is moving forward. The faster it moves, the harder it is to make the body of the bicycle change direction.
Spinning wheels have no resistance to roll moments if they are prevented from precessing about the yaw axis. Instead, a roll moment causes the front wheel to precess in the direction of the lean, and the rear wheel, which is prevented from precessing by the frame and friction in the two contact patches, leans exactly as it would if it were not spinning.
Linear momentum is a vector quantity and so the linear momentum in one direction, such as forward, has no effect on linear momentum in an orthogonal direction, such as to the side. Thus the increased linear momentum from going faster is not responsible for the smaller steering inputs required to maintain balance. Instead, it is simply the fact that a give steering input works faster, that is causes a larger lateral acceleration of the contact patches, if the wheels are rolling forward faster.
Then, Dr. Mellendorf tries to tackle counter steering, and things really get crazy.
Once turned, the front wheel moves to the side. The body of the bike, however, tries to keep going forward. The “natural” thing for the bike to do is fall down as the front wheel pulls out from under it. The rider has to lean toward the inside of the turn to prevent this from happening. If the bike “tries” to flip to the right, The rider leans to the left to counter the effect.
If by “the rider has to lean” he means “the rider has to lean along with the bike”, why would the rider have to do anything other than stay with the bike as it does its “natural” thing? Does he also mean to say that the rider cannot lean relative to the bike? Better not tell these guys:
If by “the rider has to lean” he means “the rider has to lean relative to the bike,” better not tell these guys:
The fact is that a rider can stay perfectly in line with the frame of his bike, or lean relative to the bike either into the turn or away from the turn. All that matters is where the combined center of mass is located with respect to the tire contact patches, and the only time a rider must lean to the left if the bike “tries” to flip to the right is when the bike is not moving forward at all.
No, Dr. Mellendorf’s description is most definitely not how a bicycle works.