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

40

PRECESSION

It follows that, if w is constant,
0= JIKdt,
or the precessional angle swept out during any time is a measure
of the time-integral of the applied couple.
41. Analogy in linear motion. The application of a torque
to maintain the steady rotation of the axle of a spinning body
about a perpendicular line has its analogy in linear motion,
where a force is needed to mainZ Z, tain the steady rotation of the
line of motion of a particle
Bry~- moving uniformly in a circle.
For let a particle P, of mass
y" \ 25, ^z WI, move with constant velocity
[ ~\N \I 2 v round a horizontal circle whose
0 p| centre is 0, towards which is a
2 constant force F.
f "3 A4 Let PAZ, P2Z2, P3Z3 (Fig. 21)
be successive positions of the
vertical through successive posi/ 3^ tions of P. Then the effect of
FIG. 21. applying the force F perpendicular to the line of the momentum
mv of the particle, is to turn the line of momentum at a
constant rate about an axis perpendicular to F and itself.
In this case, if the rate at which the line of momentum is
being turned be Q, then Q2 is equal to the angular velocity of
V
the particle about 0, i.e. 2=-, and we have
F=
= 1V. S2.
42. Diabolo. The rule given above (Art. 38) for the direction
of precession will at once explain the reason for the instructions
(variously worded) which are given to beginners learning to
spin a Diabolo spool.
Let us suppose that the Diabolo is being spun right-handed
as in the illustration (Fig. 22), when the end farther away from
the performer begins to dip down, and the nearer end to rise.
To get the spool again horizontal it is necessary for the
performer to pull back his right hand and (in imagination)
press down the rising end of the spool with what may be
called the "working" end of the string. It will thus be seen
that a torque is created about an axis perpendicular to the
axle of the spool, and since the axle tends to set itself towards
the torque-axis (both being drawn in the same sense), the