# Bicycle Wheel

 The angulur momentum of the turning bicycle wheels makes them act like gyroscopes to help stabilize the bicycle. This gyroscopic action also helps to turn the bicycle. Having pointed to the gyroscopic nature of the bicycle wheel, it should be pointed out that experiments indicate that the gyroscopic stability arising from the wheels is not a significant part of the stability of a bicycle. The moments of inertia and the speeds are not large enough. The experiments and review of Lowell and McKell indicate that the stability of the bicycle can be described in terms of centrifugal force. A rider who feels an unbalance to the left will turn the handlebars left, producing a segment of a circular path with resulting centrifugal force which pushes the top of the bicycle back toward vertical and a balanced condition. Presumably the larger masses and speeds of motorcycle wheels do make the gyroscopic torques a much larger factor with motorcycles.
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Reference
Lowell and McKell

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# Turning a Bicycle

 A bicycle held straight up will tend to go straight. It is tempting to say that it stabilized by the gyroscopic action of the bicycle wheels, but the gyroscopic action is quite small. If the rider leans left, a torque will be produced which causes a counterclockwise precession of the bicycle wheel, tending to turn the bicycle to the left.

This is a good visual example of the directions of the angular momenta and torques, but the gyroscopic torques of bicycle wheels are apparently quite small (see Lowell and McKell). The gyroscopically motivated descriptions like "leaning left turns it left" are more appropriate to motorcycles.

 Another illustration of turning a bicycle
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# If you lean left, you turn left

 A rider leaning left will produce a torque which will cause the bicycle wheel to precess counterclockwise as seen from above, turning the bicycle left. The angulur momentum of the bicycle wheels is to the left. The torque produced by leaning is to the rear of the bicycle, as may be seen from the right-hand rule. This gives a rearward change in the angular momentum vector, turning the bicycle left.

This is a good visual example of the directions of the angular momenta and torques, but the gyroscopic torques of bicycle wheels are apparently quite small (see Lowell and McKell). The gyroscopically motivated descriptions like "leaning left turns it left" are more appropriate to motorcycles. With a bicycle at low speeds, the main turning influence comes from the turning of the handlebars.

In terms of the stability of the bicycle when riding, the association with leaning and turning does hold true. The construction of a bicycle is such that a left lean does cause the front wheel to turn left, contributing a kind of self-stability to the bicycle. If you feel youself unbalanced and leaning left, then turning left does help you correct the imbalance because the centrifugal force associated with the turn does tend to push the top of the bicycle back toward the vertical. Part of the process of learning to ride a bicyle would then seem to be the learning of how to turn the front wheel to produce the needed centrifugal balancing force to bring you back to an upright and balanced orientation. More drastic turns are needed at low speeds to get the necessary centrifugal force which depends upon the inverse of the radius of curvature. Much more gentle turns are sufficient at higher speeds since the centrifugal force depends upon the square of the velocity.

 Another illustration of turning a bicycle
Index

Vector rotation examples

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