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The Rattling of Euler's Disk

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image of Multidiscipline Modeling in Materials and Structures

The motion of a disk spinning on a horizontal surface has drawn a great deal of interest recently. The objectives of the researches are to find out what produces an increasing rattling sound and why the spinning ends so abruptly. In order to understand the behaviour of the spinning disk better, we derived a mathematical model of the rolling/sliding motion of a thin, rigid disk on a rigid, rough horizontal plane, and found the numerical solution of the related initial value problem. Then we studied the motion of the commercially available Tangent Toy disk [3]. The results show that the normal contact force becomes very large whenever the inclination of the disk becomes small. As the inclination of the disk oscillates with time, the time-graph of the normal contact force exhibits periodical peaks, which correlate well with the peaks in the recorded sound response. They could well be responsible for the rattling sound heard during the motion.


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