Playground Physics: What Happens When Trying a 360° Swing?

Abstract

This work is inspired by a recent article in a German newspaper about the question of whether a 360° turn on an ordinary swing, that is, a seat suspended by chains, is possible. Although the author correctly negates the question, his remarks about the trajectory of the rocking person remain imprecise. Thus, we direct our attention to cases where the angle ϕ, which describes the displacement of the swing from its equilibrium position, exceeds 90° but its maximum ϕmax with respect to a taut chain remains smaller than 180°. After ϕmax is reached, the motion of the swing’s seat is intuitively hard to predict due to the lack of experience. For the sake of simplicity, we model the swing by a simple pendulum, but allowing amplitudes beyond 90°. Consequently, the chain and the seat as the supposed center of mass (together with the rocking person) are regarded as a massless cord and a point-sized bob, respectively. To elucidate the entire trajectory of the seat, we apply computer simulations. Because the analysis of the simulation data reveals a surprising simple relation between the coordinates of the prominent points of the seat’s path, we looked for and found a useful theoretical treatment of the seat’s motion.This work is inspired by a recent article in a German newspaper about the question of whether a 360° turn on an ordinary swing, that is, a seat suspended by chains, is possible. Although the author correctly negates the question, his remarks about the trajectory of the rocking person remain imprecise. Thus, we direct our attention to cases where the angle ϕ, which describes the displacement of the swing from its equilibrium position, exceeds 90° but its maximum ϕmax with respect to a taut chain remains smaller than 180°. After ϕmax is reached, the motion of the swing’s seat is intuitively hard to predict due to the lack of experience. For the sake of simplicity, we model the swing by a simple pendulum, but allowing amplitudes beyond 90°. Consequently, the chain and the seat as the supposed center of mass (together with the rocking person) are regarded as a massless cord and a point-sized bob, respectively. To elucidate the entire trajectory of the seat, we apply computer simulations. Because the analysis ...