Nonlinear Dynamics of Magnetic Gears Using Two Fidget Spinners

Magnetic gears, massive in scale or largely simplified, exhibit highly nonlinear and chaotic behaviour. We investigate the underlying phenomenon of rotation of fidget spinners with Neodymium (Nd) magnets placed at their ends through a theoretical and experimental lens. A simplified model is proposed, combining both the mechanics (i.e. nonlinear vibration of rotary mass-spring-damper system) and electromagnetics (i.e. Bio-Savart law and Larentz force) of such gears. We derive a governing equation using Newton’s law and basic electromagnetic theories, solve it numerically via simulation, and explore rotation angle dissipation. Key parameters are then compared and matched across theory and experiment. This research has been motivated by one of the problems proposed for IYPT (International Young Physicists’ Tournament) 2024.