Text: It is one of those things you do without thinking too deeply about - unless you are a mathematician. Spin a penny on a table top and as it falls the coin will speed up before abruptly coming to a halt. Quite why it behaves in this way has had serious physicists scratching their heads. But now, Professor Keith Moffat believes he can explain precisely what is going on. Intriguingly, there is a link with black holes and the equations involved may lead to better aircraft design and weather forecasts. The Cambridge University mathematician has shown how a thin layer of air between the disc and the table plays a crucial role in the spinning coin phenomenon. Rolling speed When the penny is spun, friction from the air and table causes it to lose energy. As it begins to settle, it starts to roll on its edge. This produces a strange effect in which the disc's energy is lost but its rolling speed accelerates. Theoretically, the rolling speed should take off and go on getting faster and faster for ever. In mathematical terms, it would attain an infinite point known as a "singularity". Nature abhors singularities and never lets them happen, except in the case of a black hole where matter at the heart of an exploding star is compressed to an infinite density. The coin never quite reaches the singularity point because its spinning action is abruptly brought to a halt. "The key to it is internal friction in the air. We call it viscosity," said Professor Moffatt. "In that final stage as the disc is vibrating above the table, there is a thin cushion of air trapped in there. That's why there is a lot of dissipation of energy and it suddenly stops." The phenomenon is an example of a "finite-time singularity", he reports in the journal Nature. Dynamic systems The scientist has applied his work to a novelty toy called Euler's Disc , named after the 18th century mathematician Leonhard Euler, who also studied spinning discs. The toy consists of a 400-gram chrome-plated steel disc which is spun on top of a mirrored surface. "It goes faster and faster and starts to hum," Professor Moffat told BBC News Online. "The pitch goes up slowly and then bang! The disc stops just like that." Professor Moffat's equations predict well the time it takes for the disc to settle. This is typically about 100 seconds, even when the disc is spun at different speeds and angles by the fingers. The mathematician believes the research may have implications for the study of turbulence where it is believed "finite-time" singularities may also occur. "There is a lot of numerical evidence from very high-powered computation that certain quantities become infinite. This is why there is a great deal of interest in this phenomenon in the turbulence community. "Any fundamental new understanding of turbulence would help improve the predictability of systems. This applies not only to aerodynamics and aircraft design, but also to atmospheric dynamics and weather forecasting."

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