Bicycles are built with mechanisms that help keep them balanced.
It’s commonly said that bikes are stable because of a gyroscopic effect created by the spinning wheels, but this is only partially true.
Engineers have built examples of strange looking bikes with counter rotating wheels that don’t have a gyroscopic effect but are still stable.
The key point is that bikes don’t stay perfect upright, they also lean. You actually can’t turn without first turning in the opposite direction to cause the bike to lean. You probably aren’t even aware that you are doing this, but look a bike in slow motion and it’s very obvious that this is happening.
In those cases the weight distribution of the bike causes the steering to turn in the direction of a lean causing the bike to go back to being straight. So long as the bike is moving it will remain stable.
It’s also possible for a bike to roll down a hill without a rider and remain upright. In that case when the bike leans over the steering naturally turns in the direction of the lean and the angle of the steering causes the bike to go back to being upright. So long as the front wheel doesn’t exceed a certain angle of turn then the bike would just fall over.
So bikes are stable in part because of the gyroscopic effect of the wheels, but also because of their inherently stable design, and because of its human rider using their own sense of balance to constantly turn against any lean to make it stay upright.
a 2 wheeled vehicle will always want to stay upright above a given speed (based on weight). If you lack the muscle memory to steer opposite to your goal, it can be difficult to reach that speed. What this means is to go rught, you push the right handlebar (turning the wheel to the left), the bike falls into the turn, you then correct, and it stands up. Check out Flick of the Wrist by Keith Code.
track stands are different. You can get to a point where you use small back and forth motions to keep balanced while stopped, but this is skill Nd not physics.
Training wheels teach kids the wrong movements. Balance bikes are better and teach the inherent physics without the tip-over
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