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

52

THE PHENOMENA

friction, together with the equal reaction at 0, forms a couple
about the horizontal OX, which lies in the vertical plane through
the spindle, and consequently the axle of the top tends to set
itself towards OX, i.e. towards the coil, downwards, but is prevented from doing so by the normal reaction S of the coil.*
The spindle, in consequence, pressing hard against the coil,
and thus increasing the friction, rolls or skids along until it
reaches the end, when, no longer meeting with any resistance
from the coil, it rushes rapidly round the corner. After this
it presses up against the coil, since friction now acts out of
the paper towards the reader, and the motion is continued on
the same principle as before.
(2) Normal reaction. The effect of the reaction S is to
accelerate the motion of the spindle along the coil. For, if we
again take the position of Fig. 25, it is evident that S creates
a torque about an axis drawn from 0 into the paper, towards
which axis the spindle sets itself by the laws of precession.
It should be noticed that if the centre of gravity of the top
is at the point of support, the top, when at rest, will balance
with its axle at any inclination to the vertical. In this case,
even though it is touching the coil, there is no reaction at
the point of contact; but the moment the top is spun, any
contact with the coil involves friction, and therefore a precessional tendency against the coil.
52. The motion of the toy gyroscope in Figs. xvI.-xxi. is
due to the action of the external torque which causes the axle
to precess, but there still remain one or two points worthy of
remark in connection with the scientific gyroscope of Fig. xxII.
It was mentioned that if, while the gyroscope is spinning with
the weight attached at X, the screw at Z be tightened, then
the gyroscope at once turns about Y'Y. It is interesting to
note that the direct cause of this turning is not the moment of
the weight about Y'Y. The moment of this weight tends to
set up precession about ZZ', but since the screw at Z is tight,
and consequently the frame containing Y'Y is fixed, the pivots
at Y and Y' meet with resistance forming a left-handed couple
about Z'Z, and, as in the case of the gyroscopic top, it is this
resisting couple about Z'Z which turns the gyroscope about Y' Y
in accordance with the law of precession. Similarly, referring
to Fig. xxIII., it is this resisting couple about a vertical axis
which causes the gyroscope to set itself with its axis vertical,
and this couple reversed which brings about the somersault.
53. An explanation of the oscillations mentioned in the
Introductory Chapter on page 10 will be found in Chapter IV.

* This normal reaction is of very considerable magnitude, for it is found that
the coil, unless strongly constructed, becomes bent out of shape.