The Flying to Pieces of a Whirling Ring


DR. LODGE having set the ball of paradox rolling, perhaps I may be allowed to point out some of the paradoxes of his critics on the subject of revolving disks, of the well-known “grindstone problem.” Prof. Ewing refers to two treatments of this problem, which, however, stand upon quite different footings. Prof. Grossmann's discussion reduces the problem to one in two-dimensions, and leaves an unequilibrated surface stress over both faces of the disk. Even if the disk be moderately thin, the solution cannot be considered satisfactory till the degree of approximation has been measured by comparison with the accurate solution of the problem. But Grossmann's method is precisely that of Hopkinson (Messenger of Mathematics, vol. ii., 1873, p. 53), except that the latter has dropped by mischance an r in his equation (1) [or Grossmann's (6)]. This slip I pointed out in 1886; and Grossmann's results, such as they are, flow at once from Hopkinson's corrected equations. Between Hopkinson and Grossmann this theory has several times been reproduced in technical books and newspapers without comment on its want of correctness. Such first-class technical authorities as Ritter and Winkler have also given quite erroneous solutions of the “grindstone problem.”

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PEARSON, K. The Flying to Pieces of a Whirling Ring. Nature 43, 488 (1891) doi:10.1038/043488a0

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