When pure rolling fails: A cylinder on a circular track as a case study in engineering dynamics

The motion of bodies on curved surfaces is a classical topic in engineering dynamics because it often combines conservation of energy, rotational motion, contact forces and friction within a single problem. This paper presents the case of a solid cylinder rolling down a circular track as an instructional example suitable for introductory mechanical engineering courses. A theoretical analysis based solely on Newtonian mechanics is developed to determine both the angle at which pure rolling can no longer be maintained and the angle at which the cylinder loses contact with the surface. Unlike previous treatments that employ Lagrangian methods, the derivations are accessible to students with a first-year course in dynamics. The analysis shows that the commonly assumed condition of pure rolling becomes invalid before the cylinder reaches the theoretical release angle. Expressions are obtained for the onset of slipping and for the subsequent release angle when kinetic friction is taken into account. To examine the predictions, a low-cost experiment was conducted using a bicycle rim, a cylindrical body, a digital camera and the freely available Tracker Online software. Measurements of the cylinder moving down the circular track showed good agreement with the theoretical model and confirmed that slipping occurs before loss of contact. From an educational perspective, the problem provides a compact framework for discussing the validity of modelling assumptions, the role of friction in rolling motion and the transition from idealized to physically admissible behavior. The combination of accessible theory, simple experimentation and opportunities for critical model evaluation makes the rolling cylinder on a circular track a valuable teaching example for introductory courses in engineering mechanics and dynamics. A didactical approach and suggestions on how to introduce the topic in the classroom are included as well.