

[ 92 ] 



VI. The Problem of Uniform Rotation treated on the Principle 

 of Relativity. By G. Stead, B.A., and H. Donaldson, 

 J5.Sc, Cavendish Laboratory, Cambridge*. 



EHRENFEST (Phys. Zeit. Nov. 1909, Science Abstracts, 

 •Tan. 1910) advances the problem of the rotation of 

 a solid cylinder about its axis, in connexion with the Prin- 

 ciple of Relativity. He suggests that a contradiction is 

 involved 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, whereas 

 any radius tends to remain unaltered, because it moves in a 

 direction perpendicular to its own length. A quantitative 

 solution of the problem in the simpler case in which the 

 rotating cylinder is reduced to a rotating disk has led to 

 rather interesting conclusions, and is here given. 



Consider the disk rotating about an axis through its centre 

 perpendicular to its plane. In a small sector AOB of angle 



the 



hB, any length ab , at a d istance r from 0, will contract from 

 r . 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 tendency 

 to change, and if this condition is to be fulfilled it is im- 

 possible for the disk to remain in the plane form. It must 

 assume a cup-like form, whose horizontal sections will, from 

 symmetry, be circles, and whose shape is such that ab has 



/ v 2 

 contracted to ab\/ 1 2 , while Oa is unaltered. 



* Communicated by the Authors, 



