Rolling and slipping motion of Euler's disk

Area of Science:

• Physics of rotational dynamics and friction.

Background:

• Understanding the complex motion of spinning objects is crucial in various physics disciplines.
• Previous studies have explored spinning disk dynamics, but experimental data on long-term evolution and energy dissipation is limited.

Purpose of the Study:

• To experimentally investigate the temporal evolution of a spinning disk's motion.
• To analyze the influence of mass and friction on the disk's inclination angle, angular velocity, and precession rate.
• To identify the primary mechanisms of energy dissipation during the spinning motion.

Main Methods:

• Utilizing a high-speed video system to record the motion of a circular disk spun on a table.
• Systematically varying disk mass and surface friction to observe their effects.
• Measuring key parameters: inclination angle (alpha), angular velocity (omega), and precession rate (Omega).

Main Results:

• Both inclination angle and angular velocity decrease over time following a power law.
• The precession rate was observed to diverge as the spinning motion approached its end (collapse).
• Energy dissipation is primarily attributed to the slipping friction between the disk and the supporting surface.

Conclusions:

• The study provides detailed experimental data on spinning disk dynamics, confirming power-law decay for key parameters.
• Slipping friction is identified as the dominant factor in energy loss, leading to the eventual cessation of motion.
• The findings contribute to a better understanding of rotational mechanics and energy dissipation in physical systems.