EXPERIMENTAL STUDY OF THE TRAJECTORY OF THE TOUCH POINT OF A TIPPE TOP WITH A HORIZONTAL SURFACE DURING ITS MOVEMENT

UDC 531.382

 

Karlovich Tatyana Borisovna − PhD (Physics and Mathematics), Assistant Professor, the Department of Mechanics and Design. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: tbkar@mail.ru

Vasekha Anton Pavlovich – Аssistant, the Department of Mechanics and Desigh. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: anton.vaseha@mail.ru

Lasovsky Ruslan Nikolayevich − PhD (Physics and Mathematics), Assistant Professor, the Department of Mechanics and Design. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: lasovskyr@gmail.com

 

DOI: https://doi.org/ 10.52065/2520-6141-2024-284-3.

Key words: mechanical system, dynamically symmetrical body, momentum, kinetic moment.

For citation: Karlovich T. B., Vasekha A. P., Lasovsky R. N. Experimental study of the trajectory of the touch point of a tippe top with a horizontal surface during its movement. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2024, no. 2 (284), pp. 19–24 (In Russian). DOI: 10.52065/2520-6141-2024-284-3.

Abstract

A tippe top is an example of a mechanical system tat is spun by hand and can tip 180º when rotated, exhibited dynamically unstable behavior. A top is a symmetrical body of rotation with equal moments of inertia about the horizontal axes and a different moment of inertia about the vertical axes. At rest, the center of gravity of the top is located below the center of the sphere described around it, and when moving, it can rise above the center of the sphere. The turning of the top is due to the presence of sliding friction on the surface. In this work, models of two types of tops in the form of thin-walled spherical shells, cut above the equator, and legs in the form of truncated cones, screwed into a cylindrical holes at the bottom of the spherical shells, were developed for the experiment. Partitions were added inside of the spheres to contain air. The models were printed on a 3D-printer using PLA-plastic. Then the tops were launched repeatedly on a smooth horizontal surface and their movement was videotaped. It turned out that the trajectories of movement are converging spirals, and for a top without partitions maximum visible diameter of a spiralturn is greater than for a top with partitions. This corresponds to the predictions of the theory of evolution of a heavy dynamically symmetrical spherical body on a horizontal plane with low friction.

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10.07.2024