The Flying to Pieces of a Whirling Ring

Abstract

HAVING had occasion lately to devise a high-speed whirling-machine, I examined the speed at which it might be safe to work, and some of the results surprise me. For instance, it is easy to show (by equating the normal component of the tension to the centrifugal force of any element) that the critical velocity at which a circular ring or rim of any uniform section will fly, unless radially sustained, is given by T = v2p, where T is the tenacity, and p the density of its material. Thus a band of steel just able to bear a load of 30 tons to the square inch will fly to pieces at a peripheral speed of about 800 feet a second; and this without reference to its angular velocity, or radius of curvature. It may be objected that no such accident could occur with purely rectilinear motion, but such motion at the critical speed would be very unstable—the slightest shiver of a vibration running along it would precipitate a catastrophe.

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LODGE, O. The Flying to Pieces of a Whirling Ring. Nature 43, 439 (1891) doi:10.1038/043439b0

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