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On the terminal motion of sliding/spinning discs

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GFSW04 - Form in art, toys and games

We review the classic problem concerning the terminal motion of a slidingspinning disk on a horizontal surface which shows that sliding and spinningstop at the same time with terminal value ǫ0 = 0.653, where ǫ = v(t)/Rω(t)is the ratio of linear speed to tip speed of a disk of radius R.We then generalize to problem to find the terminal motion of annular disksand two-tier disks. For the annular disk the terminal speed ratio ǫ0 rangesfrom 0.653 to 1 as the radius ratio η = Rin/Rout varies from 0 to 1. Fortwo-tier disks composed of a lower disk of radius R1 and height H1 attachedto upper disk of radius R2 and height H2, one has a two parameter problemdefined by η = R1/R2 and λ = H1/H2. In addition to simultaneous terminalstopping motions, we find, for small regions in η − λ parameter space, thatthe two-tier disk can either stop spinning first and slide to rest, or stop slidingand spin to rest. An experiment is devised to capture these unique terminalmotions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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