Voyenli and Eriksen [Am. J. Phys. 53, 1149–1153 (1985)] have derived some interesting and surprising results for a thin homogeneous disk (a hockey puck or a compact disk) and for a thin ring that is sliding and rotating over a flat but rough surface, assuming sliding friction with a constant coefficient. The properties that were observed and derived include the following: (a) When started with a pure translation, the disk will continue until it comes to rest in pure rectilinear translation without being set into rotation. (b) When started as a pure rotation around its center, the disk will continue to rotate while the center remains at rest until the disk stops. (c) In both cases the time it takes for the disk to come to rest increases with increasing values of the initial velocity. (d) When started with a combination of translation and rotation, the center will continue in a rectilinear motion until (e) the translation and rotation stop simultaneously, regardless of the initial velocity. The surprise is (e), which implies that there is a frictional coupling between the translation and rotation of the disk. This result was shown in Voyenli and Eriksen (1985) where it is established that for a thin ring of radius , the final stage of the motion is rolling-like, meaning that the disk slides with an angular speed proportional to its linear speed v, so that .
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For readers who are unfamiliar with this sport, we give the relevant details. An radially symmetric granite rock is projected down a sheet of ice. The rock is given an initial angular velocity as well as linear velocity by the curler, prior to its release. The underside of a curling rock resembles the underside of a teacup (there is a contact annulus of radius , which is much smaller than the rock radius of ). From Eq. (7) for curling rocks. The rock takes to slide 25 or down the ice, during which time it will veer a meter or so to the left or right (depending on the angular velocity direction).