Theoretical and experimental study of the looping pendulum

Abstract

We investigate the looping pendulum phenomenon proposed by the International Young Physicists’ tournament (IYPT) in 2019 with experiments and theoretical model based on Newtonian mechanics. When using high-speed video to measure the motion of objects, the acceleration measurement error may worsen significantly at a high frame rate due to position uncertainty. This issue is emphasized and can be resolved by additionally using a wireless acceleration sensor. The falling acceleration curves of heavy-load given by our theoretical model are in good agreement with the experimental measurement data. The mass ratio-release angle parameter space for a successful demonstration is given by numerical simulation, showing that a large value of heavy-light mass ratio should be more likely to make a successful demonstration experiment. The experiments reported here are appropriate for junior undergraduates to carry out experimental research.

The looping pendulum: optimization with analytical and computational analysis

“…For D, we initially used a measuring tape to find the distance between M's release position and where it stopped. However, we saw that when M's ẏ becomes zero, it sometimes recoils, so we end up measuring a falling distance smaller than the actual value (see [4] for a detailed discussion on this recoil). Moreover, when there are inwards slips, M falls more, which yields a value of D greater than the true one.…”

“…We propose a numerical solution to relate the falling distance-which we considered the 'effectiveness' of the setup-with relevant parameters, such as ratio of masses, release angle, length of string, radius of rod, coefficient of friction, and air resistance, and hence predict the optimal initial conditions. Three quantitative studies of different aspects of this phenomenon were found [2][3][4]. [2] displays the effects of system parameters (length of string, mass ratio, rod radius, and coefficient of kinetic friction) mostly through superposed trajectory plots.…”

“…[3] goes further and not only explores all possible loops that can occur during the motion, but includes parameter space plots relating the initial angle to the length of string and mass ratio. [4] enhances the parameter spaces by [3] to show in an intuitive manner the different trajectories for each situation and contributes with interesting discussions on the underlying numerical analysis. Aiming at adding more to this rich and highly educational phenomenon, we:…”

An analysis of pendulum motion in the presence of quadratic and linear drag

“…A historical survey of different approaches used in the study of pendulums with air resistance was given in [10]. The analysis of damped pendulum motion in relation to undergraduate engineering and physics education was discussed from both theoretical and experimental points of view in [11][12][13][14][15]. Classical mechanics and physics textbooks such as [16][17][18] also address various aspects of pendulum motion.…”

Dynamics of the looping pendulum: theory, simulation, and experiment

“…A series of recent papers [10][11][12] use Newtonian mechanics to study the trajectories followed by the looping pendulum in various regions of the system's parameter space. Those papers tend to break the motion up into distinct phases, such as the string sliding across the rod, or else wrapping without sliding.…”