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From a long time, I have a question that bicycle is not stable at low speed or for that matter it's difficult to balance bicycle on its wheels in static position (with zero speed and no brakes). Can this be explained by physics

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Yes it can be explained by physics. The reason you can balance relatively easily on a moving bike is that if you start to topple to one side you can steer to that side, which has the effect of bringing your centre of gravity back under the side that is leaning. The castor angle of the front fork gives the wheel a tendency to move in the right way to counterbalance the leaning, which is why people can learn to stay upright even when riding with no hands. When you are stationary you can't combat a lean in that way, so you are likely to topple over. You can also see the effect if you lock the steering of a bicycle in the straight ahead position, in which case it becomes almost impossible to ride without toppling over.

It used to be thought that the gyroscopic effect of the rotating wheels was the factor that enabled people to keep upright easily, but that's been disproved by experiments that have cancelled out the gyroscopic effects with counter-rotating wheels.

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