CHAPTER II
ELEMENTARY GYROSCOPIC PHENOMENA
Let a wheel A ([Fig. 1]) be mounted on an axle B C journalled within a horizontal ring D. Let this ring in turn be mounted on journals E F within a vertical ring G and, further, let this vertical ring be carried on journals H J within a vertical frame K. This arrangement constitutes a gyroscopic system having three degrees of freedom, because relatively to the frame K the wheel may turn about three axes B C, E F, and H J mutually at right angles to each other and because, if the wheel is set spinning on its axle, gyroscopic properties will be manifested.
Fig. 1. Model Gyroscope, with Three Degrees of Freedom.
The following is a brief statement of the gyroscopic properties manifested when the wheel is spun on its axle:
(a) Let the wheel be spinning in the direction of the arrow L and let a weight W be hung on the horizontal ring at the end B of the axle. The movement produced by this weight is not a rotation of the horizontal ring, and the wheel within it, about the axis E F. Instead, the horizontal ring remains horizontal and the whole system inside the square frame sets off rotating at a uniform speed about the axis H J in the direction of the arrow marked M on the horizontal ring. This rotation or precession, as it is called, will be maintained so long as the weight W remains in action. There is here no question of perpetual motion. The work expended in overcoming the friction at the vertical journals is derived from the energy of the spinning wheel, and when this energy is exhausted the phenomenon ceases. The phenomenon can, in fact, only be maintained indefinitely by expending power to drive the wheel against the leakage of energy through friction at the journals of the axle and the vertical axis H J. A closer examination of the phenomenon would show that there is a slight rocking motion of the horizontal ring on its axis E F, and therefore an additional leakage of energy at the journals of this axis. This rocking motion can be neglected for our present purposes. It is sufficiently accurate to say that the horizontal ring remains horizontal.
(b) The speed of the precession is proportional to the weight W and to the speed of rotation of the wheel on its axle. For instance, doubling the weight doubles the speed of precession.
(c) If the direction of spin of the wheel is reversed the direction of the precession is also reversed.
(d) If the spin of the wheel is in the direction L, and if instead of attaching a weight at the end B of the axle we exert an upward force at this point the precession developed will be opposed to the direction of the arrow M.
(e) If instead of trying to rotate the wheel about the axis E F by means of a weight or force applied at B we attempt to turn it about the vertical axis H J by applying a horizontal force V to the outer ring, the wheel will not turn about the vertical axis H J, but about the horizontal axis E F, the end B of the axle rising up towards H.