IT FAZED me the first time I saw one. I was in Wales, where they call it a
rebellious celt, but it鈥檚 also called a rattleback or just a celt. 鈥淚t鈥� is a
10-centimetre-long plastic toy with a base shaped like the hull of a boat. When
you spin it one way, it turns a few times before the ends start to rattle up and
down. The more it pitches, the slower it rotates until it stops spinning
altogether. Then the most intriguing thing happens: the celt starts to spin in
the opposite direction. It鈥檚 as if some unseen hand is playing a joke on the
laws of physics. What on Earth is driving it?
The first attempt to analyse celts was a century ago. But it took until the
mid-1980s for full mathematical descriptions to emerge, one by Hermann Bondi,
then Master of Churchill College, Cambridge, and the other by Mont Hubbard,
professor of mechanical engineering at the University of California, Davis.
Bondi and Hubbard agree that the celt鈥檚 astonishing trick needs three main
ingredients. First, the curved base must have two different radii鈥攐ne long
radius for the lengthwise curve and one shorter radius for the tighter curve
across its width. Next, the axes of symmetry of the celt must be skewed slightly
from its principal axes of inertia (see
top Diagram). Any rigid object has three
principal axes of inertia. They sit at right angles to each other and if you
spin the object about one of them, there is no tendency to rotate about the
other two. Finally, there must be a different distribution of mass about each of
the two horizontal axes of inertia鈥攁 long, thin shape, say.
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Failed intuition
Given these characteristics, the maths predicts how the celt should behave.
The trouble begins, however, when you try to translate the equations into a
physical explanation for what鈥檚 going on. 鈥淚t鈥檚 only clear through the
equations,鈥� says Hubbard. 鈥淚 don鈥檛 intuitively understand it.鈥�
But there are at least a few hints about what鈥檚 going on. Let鈥檚 start halfway
through the celt鈥檚 journey, while it is pitching up and down like a rocking
horse (see
lower Diagram). Friction acts horizontally鈥攁t the point of
contact between the celt and the surface鈥攖o prevent the celt from
slipping. One component of this frictional force creates a torque that tends to
rotate the celt about its vertical axis.
鈥淭o make it more complicated, the point of contact is moving all the time and
the torque changes,鈥� says Hubbard. If the inertial and symmetrical axes of the
celt coincided, the average torque over a single oscillation would be zero. But
for the celt, there is a net torque in one direction. And it is this that
reverses the angular momentum, says Bondi.
Another way to understand how the celt works is in terms of energy. It
emerges from the maths that each direction of spin is linked to a different mode
of oscillation: if clockwise rotation feeds the pitching oscillation, then
anticlockwise spin would feed a side-to-side, or rolling, oscillation. So, when
the celt spins clockwise, any tiny pitching oscillation grows exponentially. It
feeds off the rotational energy and so slows down the spin. 鈥淏ut even when there
is zero spin, the torque still acts,鈥� says Hubbard. So the direction of spin
changes. Some celts will reverse spin directions again by trading rotational
energy with the rolling oscillation.
It seems that we鈥檒l have to wait for a better physical description of how the
celt behaves. Still, after a hundred years of probing the toy, it鈥檚 unlikely
that scientists will stop now. 鈥淭he thing about scientists is that they really
like toys,鈥� says Brian Pippard of the University of Cambridge, who鈥檚 devised a
way to make a celt from part of a wine bottle. 鈥淭hey have an interest in
anything that looks odd. And they鈥檙e not happy until they can describe how it
丑补辫辫别苍蝉.鈥�