FORCES DEVELOPED IN A GYROSCOPE
We may conceive of a gyroscope as consisting of a stream of bullets all tied to a center, so that they fly around in a circle. Any effort to deflect the bullets out of their course will be resisted by each bullet as it comes to the deflector. Here each bullet acts individually, but in a gyroscope wheel the equivalent of the stream of bullets is a solid rim, each particle of which is rigidly connected to every other particle, and so the whole wheel immediately feels the deflecting force and resists it. As long as the wheel is maintained in its own plane of rotation, or moved into parallel planes, there is such a perfect balance of all forces that no more resistance is offered to the motion of the wheel as a whole than would be offered by any other object of equal mass. But when the wheel’s plane of rotation is moved angularly, a complicated series of forces is developed.
FIG. 77.—SOME OF THE FORCES DEVELOPED IN A GYROSCOPE WHEN ITS PLANE OF ROTATION IS SUBJECTED TO ANGULAR MOTION
Some idea of the nature of these forces and why they give rise to precession may be understood by reference to the diagram, Figure 77. Here we have a disk with a heavy rim turning on the axis X, X′. At A, B, C and D are four particles whose flights we are going to consider. Suppose the wheel to be at rest; then if X, X′ is tilted in the direction of the arrows x x′, the wheel will turn about the line Y Y′; D will move forward toward D′, and B backward toward B′, but A and C will remain where they are. Now, suppose, the wheel to be revolving clockwise, or in the direction A, B, C, D, then the particle A will pursue a spiral course that will bring it to B′, and C will pursue a spiral course that will bring it to D′. However, particle D will have an irregular course, as indicated by the dotted line, starting first to move forward and then curving back toward A. The same will be true of B, except in the reverse direction. The course of particles D and B is, therefore, materially different from that of A and C. Now, the particle D will resist being deflected from its course and will develop an opposing force represented by the arrow d. A moment later this is reversed as the particle bends back toward the axis Y Y′, and we may represent the new force by the arrow d′. It may be proved that the force d′ is more powerful than that of d. The particle A in the meantime exerts a force opposing its deflection, which is represented by the arrow a. On the other half of the wheel there are similar but opposite forces, b, b′ and c. The sum of these forces gives the wheel a tendency to turn about the axis Z Z′. To avoid complicating our diagram with too many arrows, we had better refer to a new diagram (Figure 78) which shows only the resultant of the forces developed. The application of the forces x x′, which would have turned the wheel on the axis Y Y′, had it been stationary, have resulted in the development of forces z z′ at right angles to x x′, tending to turn the wheel about the axis Z Z′. Now, if we go through the same processes of reasoning as before, it will be evident that the forces z z′ will result in a third set of forces y y′ at right angles to z z′ tending to turn the wheel about the axis Y Y′. The forces y y′ exactly balance the forces x x′, and hence the wheel does not turn about the axis Y Y′ in response to the original forces, but starts instead to revolve slowly about the axis Z Z. Because the forces x x′ and y y′ balance each other, there is no fourth couple developed and hence no opposition to the forces z z′.
FIG. 78.—DIAGRAM EXPLAINING PRECESSIONAL MOVEMENT OF A GYROSCOPE
The gyroscope was used as a toy ages ago. The top, which is one form of gyroscope, was a favorite plaything of ancient Egypt. But although known these many centuries, it is only in the past few years that any real effort has been made to set the top to work. Because it persists in maintaining its plane of rotation it has proved most useful on submarine torpedoes to control the rudder and hold the torpedo on a true course to its target.