Imagine two concentric cylinders, centered on the vertical axis, with radii R± ε, where ε is very small. A small frictionless puck of thickness 2ε is inserted between the two cylinders, so that it can be considered a point mass that can move freely at a fixed distance from the vertical axis. If we use cylindrical polar coordinates (p, op, z) for its position (Problem 1.47), then p is fixed at p = R, while op and z can vary at will. Write down and solve Newton's second law for the general motion of the puck, including the effects of gravity. Describe the puck's motion.

Imagine two concentric cylinders, centered on the vertical axis, with radii R± ε, where ε is very small. A small frictionless puck of thickness 2ε is inserted between the two cylinders, so that it can be considered a point mass that can move freely at a fixed distance from the vertical axis. If we use cylindrical polar coordinates (p, op, z) for its position (Problem 1.47), then p is fixed at p = R, while op and z can vary at will. Write down and solve Newton's second law for the general motion of the puck, including the effects of gravity. Describe the puck's motion.