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

46 GYROSCOPIC RESISTANCE
the turning circle is R ft. Find the torque exerted by the bearings of
the shaft.
5. In the preceding question, taking a=4 ins., M= 12 tons, V=35 knots,
(o= 50 revolutions per minute, R=605 yds., estimate the torque in ft.-lbs.
These values are taken from H.M. T.B.D. " Tartar."
6. A motor cycle has a heavy fly-wheel, in the form of a disc of radius
4 ins. and weight 32 lbs., which is making 1,600 revolutions a minute. The
machine and rider weigh 320 lbs. If the rider rounds a curve of 25 ft.
radius when travelling at 20 mi./hr., find approximately the horizontal
distance that he must move the centre of gravity of himself and his machine
owing to the rotation of the fly-wheel.
NOTE. If the fly-wheel were not spinning he would have to lean over a
certain amount in order to turn the corner; but when the fly-wheel is
spinning, he must increase the arm of the gravity couple by a small amount,
x, in order that the fly-wheel may precess. It may be assumed that the
gyroscopic couple is the same as if the fly-wheel were in a vertical plane.
7. In the previous question, just before the rider rounds the corner he
leans over to the right with an angular velocity of a radian a second.
(a) How is the torque supplied which causes the fly-wheel to have this
angular velocity? (b) About what axis was it, and in what direction?
(c) What is the effect on the back wheel of the reaction to this torque?
(d) Find its magnitude.