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There is agreement that when starting a turn on a bicycle or motorcycle at
low speeds, the technique is to shift the body weight into the turn so that
the bike leans into the turn.
That is not the case with a bicycle. "Shift one's weight" is perhaps a
kinesthetically satisfactory process, but it is unphysical. In order to
produce any change in the motion of a body there must be a net external
force exerted on it. This force can be the reaction to some force
initiated by the body, but let us speak in terms of such forces. Mere
"shifting of the weight" is mystical; physics is not mystical.
There is agreement among those who have analyzed the problem correctly
that when starting to turn a bicycle from a straight course at any
speed whatsoever, the first thing that is done is to turn the front
wheel in the direction opposite the desired turn. This will result in
the bicycle being forced to that side, and the rider will continue in
the same direction as before. Thus he will start to fall over in the
direction of the desired turn.