Introduction to Classical Mechanics · Problem 3.65
Oscillations — Morin
Physics — Mechanics · circular-motion-hoop
Problem
Horizontal 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 horizontal? 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.