. The London, Edinburgh and Dublin philosophical magazine and journal of science. lem of Uniform Rotation treated on the Principleof Relativity. By G. Stead, , and H. Donaldson,, Cavendish Laboratory, Cambridge*. EHRENFEST (Phys. Zeit. Nov. 1909, Science Abstracts,•Tan. 1910) advances the problem of the rotation ofa solid cylinder about its axis, in connexion with the Prin-ciple of Relativity. He suggests that a contradiction isinvolved from the facts that any element of circumference,which must be moving in the direction of its length, tends to contract in the usual ratio a /l— -2- :
. The London, Edinburgh and Dublin philosophical magazine and journal of science. lem of Uniform Rotation treated on the Principleof Relativity. By G. Stead, , and H. Donaldson,, Cavendish Laboratory, Cambridge*. EHRENFEST (Phys. Zeit. Nov. 1909, Science Abstracts,•Tan. 1910) advances the problem of the rotation ofa solid cylinder about its axis, in connexion with the Prin-ciple of Relativity. He suggests that a contradiction isinvolved from the facts that any element of circumference,which must be moving in the direction of its length, tends to contract in the usual ratio a /l— -2- : 1, where c is velocity of light and v the velocity of the element, whereasany radius tends to remain unaltered, because it moves in adirection perpendicular to its own length. A quantitativesolution of the problem in the simpler case in which therotating cylinder is reduced to a rotating disk has led torather interesting conclusions, and is here given. Consider the disk rotating about an axis through its centreperpendicular to its plane. In a small sector AOB of angle the. hB, any length ab, at a distance r from 0, will contract fromr . 80 to r . S6a / 1 2 wnen the disk is rotating, so that ab is moving with linear velocity v. As Ehrenfest pointed out, the Oa will have no tendencyto change, and if this condition is to be fulfilled it is im-possible for the disk to remain in the plane form. It mustassume a cup-like form, whose horizontal sections will, fromsymmetry, be circles, and whose shape is such that ab has / v2contracted to ab\/ 1 2, while Oa is unaltered. * Communicated by the Authors, Problem of Uniform Rotation. 93 If, therefore, AOA represent the vertical section of thefinal form of the disk containing the axis of rotation OX,
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Keywords: ., bookcentury1800, bookdecade1840, booksubjectscience, bookyear1840
