The rolling dynamics of a plastic cup on the floor

Abstract This study aims to evaluate the generalizability of the rolling motion model proposed by Wibowo et al (2025) by extending its application to a different class of rolling objects, namely plastic cups. The investigation focuses on comparing theoretical and experimental turning radii of circular trajectories formed by cups with distinct sizes and geometries. Four plastic cups—green, blue-patterned, yellow, and dark green—differing in size, shape, and mass were tested. Theoretical radii were calculated based on geometric parameters, while experimental radii were obtained by tracing the cups’ rolling paths. The theoretical values ( R t ) were 35.90 cm (green), 38.88 cm (blue-patterned), 23.69 cm (yellow), and 68.01 cm (dark green), compared with experimental results ( R e ) of 39.09 cm, 40.14 cm, 25.64 cm, and 63.04 cm, respectively. The relative errors ranged from 3.23% to 8.89%, indicating strong consistency and confirming the robustness of the geometric model. Nevertheless, the results also revealed systematic deviations, with larger cups producing tighter curves than predicted, largely due to asymmetric mass distribution and rotational inertia that are not accounted for in the geometric formulation. These findings highlight the limitations of a purely geometric approach while demonstrating that the model remains a reliable approximation for a broader class of rolling objects. In addition to its theoretical contribution, the study underscores the pedagogical value of the rolling cup experiment, offering students a low-cost and engaging activity to explore rotational dynamics, geometric modelling, and error analysis while reflecting on the interplay between idealized models and real-world observations.