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

PRECESSION

43

A familiar illustration of this independence of translation
and rotation can be given by tilting back a chair and then
letting it fall forward again. The air no only swings forward
to'T r i g-niti itionbut also moves forward along the carpet:
for, as it swings forward, its centre of gravity has a forward
translational motion, and, before the chair can come to rest, this
motion has to be stopped (by the friction on the carpet), independently of the rotation. The rotation is, of course, stopped
by the moment of the vertical reaction of the floor on the
two front legs about the line joining the points of contact of
the two hind legs with the floor.
44. Further illustrations of precession.
Hoop. If a wheel, or an ordinary hoop, is rolling along the
ground it has an angular momentum about its central perpendicular axis or axle. If the hoop begins to move in the
slightest degree out of the vertical plane, the external forces
acting on it (i.e. the reaction of the ground and the weight
of the hoop) tend to tilt over the axle, with the result that it
"precesses" about an axis very nearly vertical, and its path
becomes a curve instead of a straight line.
Engine wheels. The tilting moment may be considerable
without the wheel leaning over at a large angle to the vertical,
as in the case of wheels of a railway engine where the reaction
of the rails on the wheels is very large. Let us suppose the
engine turning to the right, looking in the direction in which
the train is going. To make each wheel precess to the right,
a couple must be applied about a horizontal axis (through its
centre of gravity, say) parallel to the direction of motion of
the train; and this couple must, as we have seen, be in a
direction tending to lift up the left-hand end of the axle and
to depress the right-hand end. Therefore, owing to the rotation of the wheels (apart from any motion of translation), it is
necessary to raise the left rail slightly in rounding the curve.
If this were not raised the whole turning of the train would
be effected by the lateral pressure on the left-hand flanges,
which (in addition to considerable wear to rails and wheels)
would tend to make the wheels precess to the left, and would
increase the risk of their "jumping the metals."
Gyroscopic action in a bicycle. The wheels of an ordinary
bicycle have rims so light compared with the rest of the
machine that their angular momentum does not play a preponderating part in the motion of the whole machine. At times,
however, it is quite an appreciable quantity, as can be easily
realised by taking the front wheel out of its bearings, holding
the axle in the hands and attempting to turn the axle after
a considerable spin has been given to the wheel.
There is a certain amount of gyroscopic action brought into
play when the rider, finding himself falling over, say to the