Weidman P D, Malhotra C P
Department of Mechanical Engineering, University of Colorado, Boulder, 80390-0427, USA.
Phys Rev Lett. 2005 Dec 31;95(26):264303. doi: 10.1103/PhysRevLett.95.264303. Epub 2005 Dec 23.
Analysis of the frictional motion of a uniform circular disk of radius sliding and spinning on a horizontal table reported by Farkas et al. [Phys. Rev. Lett. 90, 248302 2003] shows that the disk always stops sliding and spinning at the same instant with a terminal speed ratio epsilon = v/Romega = 0.653. We show that different terminal behaviors can be found when one considers the motion of a two-tier disk with lower section thickness H(1) and radius R(1), and upper section thickness H(2) and radius H(3). The terminal motion may be analyzed in terms of the normalized radius of gyration k. It is found that while translation and rotation cease simultaneously, their terminal ratio epsilon(0) either vanishes when k > sq.root(2/3), is a nonzero constant when k < 1/2 < k < sq.rt (2/3), or diverges when k < 1/2. Experiments performed with plastic disks sliding on a nylon fabric stretched over a horizontal plate qualitatively corroborate the three different types of terminal motion.
法卡斯等人[《物理评论快报》90, 248302 (2003年)]报道了对一个半径为 的均匀圆盘在水平桌面上滑动和旋转时的摩擦运动分析，结果表明圆盘总是在同一时刻停止滑动和旋转，其终端速度比ε = v/Rω = 0.653。我们表明，当考虑一个双层圆盘的运动时，会发现不同的终端行为，该双层圆盘下层厚度为H(1)，半径为R(1)，上层厚度为H(2)，半径为H(3)。终端运动可以根据归一化回转半径k来分析。结果发现，虽然平移和旋转同时停止，但其终端比ε(0)在k > √(2/3)时消失，在1/2 < k < √(2/3)时为非零常数，在k < 1/2时发散。用塑料圆盘在水平板上拉伸的尼龙织物上滑动进行的实验定性地证实了这三种不同类型的终端运动。
