The Eccentric Disk and Its Eccentric Behavior

Providing example problems that stimulate curiosity and cultivate intuition among students is a prominent responsibility for physics educators. A concept that can be particularly challenging for students to grasp and educators to convey is the relationship between frictional and normal forces in rolling motion. A system that may be a useful tool to exhibit a rich interplay between these forces is a rolling eccentric disk. An eccentric disk has a non-constant normal force and therefore has four distinct phases of motion: oscillations about a stable equilibrium, roll without slip, roll with slip, and hop. Thus, this paper examines the eccentric disk rolling down an incline as a valuable teaching medium and explores its peculiar behavior. The rolling system is analytically modeled using an augmented Lagrangian formulation, solved with numerical integration, and experimentally realized. Then, the results are presented and discussed in detail.