Bicycle physics
A rider stays upright on a bicycle by steering the bicycle so that the point where the wheels touch the ground stays underneath the center of gravity. Once underway, this effort is largely replaced by physical forces generated by the rotation of the wheels which produce a remarkable "self-steering" effect.3 The angular momentum of the wheels and the torque applied to them by the ground generates a phenomenon called precession, by which the wheel turns, or trails, toward whichever side to which the bicycle tilts. Like the rider's steering adjustments, this motion automatically returns the contact point of the wheel directly under the center of gravity. These forces, perhaps aided at very high speeds by the gyroscopic effect of the spinning wheels,4 are sufficiently strong that a riderless bicycle going down a slope will stay upright by itself. Conversely, a bicycle whose steering fork is locked in a perfectly straight ahead position is virtually impossible to balance.
That gyroscopic effects are unimportant at normal cycling speeds was shown by physicist and researcher into bicycle stability David E. H. Jones, whose series of "URBs" ("unrideable bikes" with various modifications to the front end) included a bike which cancelled the gyroscopic effect of the front wheel by dint of attaching a second wheel to his front forks (alongside the regular wheel) whose lower edge was about an inch (25 mm) above the ground. By gearing this wheel to the regular front wheel so that it spun in the opposite direction at equal speed, the net angular momentum of both wheels together was close to zero. Jones found he could ride this bike with no difficulty, but did discover that without a rider the non-gyroscopic bike fell over much faster than a regular bike.
Stability is also influenced by a geometric factor called trail. This is the distance between the point of contact the front wheel makes with the ground and the place the steering axis makes contact with the ground. The greater the amount of trail, the greater the reaction. One can see the effect that trail has by simply holding a bicycle by the seat and leaning it. The moment due to trail and the weight of the bicycle will turn the front wheel in the direction of the turn. Negative trail (rolling a bicycle backwards) results in immediate steering problems. Zero trail (as in a unicycle) requires constant rider adjustment. Positive trail - found on typical bicycles - creates positive stability by steering the contact patch back under the CG of the bicycle and rider.