Introduction to Classical Mechanics · Problem 3.21
Using F = ma — Morin
Physics — Mechanics · circular_motion_hoop
Problem
Vertical acceleration **
A bead rests at the top of a fixed frictionless hoop of radius R that lies in a vertical plane. The bead is given a tiny push so that it slides down and around the hoop. At what points on the hoop is the bead's acceleration vertical? What is this vertical acceleration? Note: We haven't studied conservation of energy yet, but use the fact that the bead's speed after it has fallen a height h is given by v=2gh.
One such point is the bottom of the hoop. Another point is technically the top, where a≈0. Find the other two more interesting points (one on each side).