Looping pendulum: theoretical and experimental studies

This work focuses on exploring the phenomenon of looping pendulum proposed by 'International Young Physicists' Tournament in 2019, specifically, the various types of loops observed and the physical conditions for a loop to be successful. Firstly, we establish a theoretical model for three distinct stages of the motion observed in the phenomenon, i.e. slipping, non-slipping, and pulling phenomena. We then construct a numerical algorithm for simulation studies so as to predict the looping trajectory, which is significantly influenced by the mass ratio between the masses, the initial release angle of the small mass and the initial distance between the small mass and the tangential point on the rod. Phase plots, which illustrate how varying some of these parameters will affect the type of loop produced, are generated. The theoretical looping trajectories and phase plots are verified experimentally. A qualitative analysis of the common trajectories observed and the successful trends in the phase plots are presented to provide further insights on the physics of this phenomenon. The findings presented in this paper reveal some properties of the looping pendulum and help us to gain a better understanding of its physical behavior.