טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentTomer Bar-on
SubjectEuler's Disk and its Finit-Time Singularity
DepartmentDepartment of Physics
Supervisor Professor Emeritus Avron Joseph


Abstract

In this research we investigated the final stage of motion Euler's Disk. Euler's Disk is a circular disk that spins, without slipping, on a surface. The canonical example is a coin spinning on a table. It is universally observed that a spinning Euler's disk ultimately comes to rest, and it does so quite abruptly. The final stage of motion being accompanied by a whirring sound of rapidly increasing frequency (precession rate). The precession rate diverges in finite time as disk loses energy (diverges as a power law in time). This speeding up is evident as the sound produced by the rolling motion becomes a whirring or chattering sound just before the disk comes to a stop. Of course, such singularity cannot be realized in practice. Nature abhors singularity, and some physical effect must intervene to prevent its occurrence: the normal reaction at point of  contact cannot be negative, this implies that theory breaks down at a time before the collapse. Theoretical, numerical and experimental study has been devoted to find major process leading to the stop of  the disk, and compare those results with results available in literature.