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. 旋转的自行车轮的角动量使它们像陀螺一样作用，帮助稳定自行车。这种陀螺效应也帮助自行车转弯。 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. 在指出自行车轮的陀螺特性之后，应指出实验表明，来自轮子的陀螺稳定性并不是自行车稳定性的主要部分。角动量和速度并不足够大。Lowell和McKell的实验和综述表明，自行车的稳定性可以利用离心力来描述。当骑手感到向左不平衡时，会向左转动把手，产生一段圆周路径，从而产生一个向自行车顶部施加的离心力，使自行车顶部向垂直方向回正，达到平衡状态。 Presumably the larger masses and speeds of motorcycle wheels do make the gyroscopic torques a much larger factor with motorcycles. 显然，摩托车轮子较大的质量和速度使陀螺力矩成为摩托车中一个更重要的因素。

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. 当自行车直立时，它倾向于保持直立。人们有理由认为这是由于自行车轮的陀螺效应，但这种陀螺效应实际上非常微小。	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. 如果骑手向左倾斜，会产生一个力矩，导致自行车轮产生逆时针方向的进动，使自行车向左偏转。

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.

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. 一个骑手向左倾斜会产生一个力矩，这将导致自行车轮在上方观察时逆时针预旋，使自行车向左转动。自行车轮的角动量方向是向左的。由倾斜产生的力矩位于自行车的后方，如右手定则所示。这导致角动量矢量向后变化，使自行车向左转动。

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.