Others find in its going so fast the reason why the bicycle does not fall—referring, of course, in a blind way to that principle embodied by Newton in his first law: "A body in motion, if left to itself, will continue to move in a straight line forever." A brief examination will, I think, convince you that this, too, fails to account for the effect which we know is somehow produced.
It is another principle in physics that two forces acting at right angles to each other do not interfere. Each produces its own effect as fully as if the other did not act. For example, if a certain force sends a body (D, Fig. 5) north at the rate of ten feet in a second, and another force sends it east at the same rate, at the end of one second it will have gone ten feet north and ten feet east, exactly as if each force D had acted alone. Going toward A B does not in the least hinder its going toward B C Now, in case of a bicyclist, his forward motion, whether fast or slow, is at right angles to gravity, hence does not in any way resist it; and, therefore, as it is gravity that causes him to tilt over, the forward motion will not prevent his falling.
But it may be said that the force of gravity when the 'cycle leans, say to the right, is in fact resolved into two components, one vertical and the other lateral, and it is the latter only that causes the bicyclist to fall. This does not help the matter, for both components are perpendicular to the course of the bicycle, and hence its forward motion can in no way counteract either of them. Unless some other force comes into play, the bicyclist must fall toward whichever side he happens to begin to lean.
Many think they find this counteracting influence in "centrifugal force." You all are familiar with the effects of this "force." You feel them every time you turn a corner quickly, whether on foot or in a wagon, or on horseback. The bare-back riders in the circus lean well toward the center of the ring, to escape being thrown outward. We see its effect when the bicyclist spins around a corner. In such cases "centrifugal force" plays an important part, and is the real upholding force.
But centrifugal force is impossible so long as the body moves in the same direction—i. e., in a straight line. There must be change of direction, and, other things being equal, this force is greater in proportion to the abruptness of that change; or, as mathematicians say, the velocity being constant, it varies inversely as the radius of the curve in which the body moves. The