2. On the Whirling of Rotating Shaft at High Rotational Speed.

It is well known that the rotating shaft or bar often becomes unstable and finally bends double or breaks down at a rotational speed near its natural frequency of lateral vibration, on account of so called whirling phenomena. In our experiment, the magnetically freely suspended rod 1), 2.277 cm in length, 0.298 cm in diameter, bent double at the rotational frequency of 2.49 x 10 4 r. p. s. which is considerably lower than the expected value from ordinary calculations. Taking the shearing strain of the rod into consideration, which is ordinarily ignored, we tried to perform more accurate calculation, and obtained the following equation for an elastic lateral vibration of the bar rotating with angular velocity w, Ek2 04y+I/1k2p,o2 \02y(1E e4yk2(2,_112(_2Eeey- p ax4 AG)AG)8 x28t2 AG 814+^I4TG-- 0 x2Y)-0 (1) where E is Young's modulus, p the density, k the radius of gyration of cross-section about an axis perpendicular to the rod axis, G the rigidity, A the constant concerning the shape of cross-section. This can be solved easily so far as only the threshold 02v frequency of whirling is in question, i. e., the case812 =0. Then Eq. (1) is sim-plified to Ek2d4ynd 2y, ±,046,g‘ar•y =u,(2) pdxdx2AG Integrating Eq. (2) after the same method as in ordinary Eigen value problem, we obtain the value of co at which the bar becomes unstable. The result is to=e!E (3) /2 p Where