An elementary treatment of the theory of spinning tops and gyroscopic motion, by Harold Crabtree.

INERTIA

59

heavy particles (corresponding to the shot in the cells) kept
in proximity to one another by a massless framework similar
to the one above described.
Z
u llll 0 1 II~CB o~silll X
0 X
FIG. 28. FIG. 29.
We know that a rigid body resists force in every direction;
or, to follow out our analogy, in whatever direction our framework is pushed, a resistance will be experienced, since the
moment the frameworF moves, each shot begins t press
agasta si Let us suppose owever that we
cou l conceive an imaginary body which possessed inertia in
two directions, say OX and OZ, but not in the direction
OY, such a conception might be approximately illustrated by
considering the skeleton framework to be composed of long
tubular cells, running parallel to O Y: for in this case an
attempt to push the frcamework in the direction OY would
meet with no resistance. Again, if the tubes were circular
in shape as in Fig. 29, and endless, their centres lying on the
line OZ, then the body would offer no resistance to being
turned about OZ.
60. Start of precession. In Art. 34 we explained that the
equation K=-Iw2 applies only to the maintenance of existing
precession and not to the starting of precession. We have yet
to consider what happens when precession is first set up.
Let a weight be attached to the gyroscope as in Figs. 30
and 31. This will clearly introduce an external couple which
acts on the gyroscope, but it should be noticed that there is
one already, due to the weight of the wheel and frame. The
additional weight will, however, give a clearer illustration.
Suppose that the wheel is spun in the direction indicated
in Figs. 30 and 31 while its axle XO is held in a horizontal
position, and let it be then released so that the attached weight
and the weight of the frame and wheel begin to act. It will be
observed that the whole system "wobbles" and oscillates con-.siderably, and then finally settles down to a steady precession
about the vertical OZ.