Friday, June 11, 2010

Rotating Elastic Rings, Disks and Hoops - Greg Egan

"In the history of special relativity, numerous thought experiments have involved rotating rings, disks and hoops. One striking feature of a uniformly rotating body in special relativity is that a family of observers who are tied to the body — and hence in a colloquial sense might seem to be “at rest” relative to each other — nonetheless can't synchronise their clocks, or agree on a shared definition of how spacetime should be split up into space and time. The reason, of course, is that the forces that maintain the body's shape are accelerating each point of the body, and the magnitude and direction of the acceleration varies from point to point. Unlike the situation where observers are tied to a body undergoing uniform linear motion, there is no way to slice up spacetime into hypersurfaces that are everywhere orthogonal to the observers' world lines.

The purpose of this web page is to give a very simple model for an annular ring of elastic material rotating with a constant angular velocity in the plane of the ring. If the inner radius of the annulus is zero, we have a disk; if the inner and outer radii are equal, we have a hoop. We will assume that the vertical thickness of the ring is zero, making the problem essentially one in two spatial dimensions, plus time."

5 out of 5

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