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On the terminal motion of sliding/spinning discs

Presented by: 
Patrick Weidman University of Colorado
Thursday 30th November 2017 - 14:10 to 14:50
INI Seminar Room 1
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.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons