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

2

INTRODUCTORY CHAPTER

us some faint idea of how what appears to be solid may in
reality be made up of minute loose particles revolving round
each other at an enormous rate: and it is interesting to think
that nearly 2,000 years before this theory was formally stated,
the Roman poet Lucretius should have written six books of
majestic verse, one entirely, and the others partly, in support
of a theory extremely similar to this, propounded by the Greek
philosopher Democritus 400 years previously.
Let us consider for a few minutes the behaviour of an ordinary
spinning top. It is full of surprising contradictions. In the
first place, to take the most obvious of all, we cannot balance it
on its peg; but give it a spin and it will stay balanced for a
long time. We have known this all our lives; but few people
can explain the reason, except to say " because it's spinning "which begs the question. Again, supposing we spin it with
its axis vertical and then give it a knock, it will go round
the table in a slanting position; but if we spin it slanting to
begin with, it will almost immediately stand upright. And
once again, although it is the friction of the table and the
resistance of the air which eventually bring a spinning top to
rest, yet if we take a very smooth surface, such as a glass plate,
we find that many tops will not spin on it at all.
The childish delight which we felt in watching our tops
spinning remains with many of us a vivid recollection to this
day. Some tops would buzz about busily before settling down
to a regular motion; others would be steady and stately from
the first. Some would " go to sleep" almost at once, and, if
disturbed, would only show signs of life for a short time before
going to sleep again: these when they "died" would die very
suddenly. Others when disturbed would spin about in a
slanting position for a long time, particularly those with rather
a long "leg"; these took a long time to "die."
It is within everybody's experience that if a top is spun so
that the foot traces out (approximately) a circle on the table,
this circle will be described in the direction of rotation of the
chain we see that it is acted on (in addition to its weight) by two tensions, each
of very great magnitude, since they act at a very small angle to each other and
yet supply the normal force necessary for the circular motion. Hence any force
which deflects A B from its circular position will have to be extremely large to
A B
T3 T?~
overcome the resolutes of these tensions which would be immediately called into
play. Similarly in the case of the disc, any small elemental area is under the
action of two very large tensions, resolutes of which are immediately called into
play when a lateral blow is given to the disc.