Euler's Disc Visited Experimentally

By Kevin T. Kilty

This is a brief note to accompany my earlier web page on a theory of the Euler Disc. Here I present experimental data obtained by spinning a Sacajawea Dollar on my counter top, photographing the resulting motion from a position level with the disk, and then obtaining angle versus time data from analyzing the video frames with a comparator. There are the results of two different successful runs of this experiment displayed, and, as you may see, the results are similar.I performed the experiment on 05/28/00.

In the top graph I have plotted the time into the precessing spin against the cube of angle the coin makes with the counter-top. Moffatt has shown that when viscosity of air is the dominant braking effect of the disc, then this relationship should be a straight line declining to zero. The latter part of the experimental motion does adhere to this expectation, but during the early time the motion of the disc decays much faster than expected.

In the earlier note on my web page, I showed that rolling friction provides the same same finite-time sigularity, but that the decaying angle of the disc raised to the 3/2 power is proportional to time. You can see in the lower graph that the same data from the upper graph are not perfectly linear when plotted according to this expectation, but that this is a better fit to the early time motion, and a reasonable fit to the late time motion.