Introduction to Classical Mechanics · Problem 9.49
Angular momentum, Part II (General L) — Morin
Physics — Mechanics · flipping-a-coin
Problem
Imagine flipping an initially horizontal heads-up coin. If the initial angular velocity is horizontal, then the coin will rotate around this horizontal diameter the entire time in the air. The fraction of the flight time that the coin spends heads-up is therefore 1/2. In practice, however, it is impossible to make the initial ω be exactly horizontal, so assume that the initial components are ω⊥ and ω3, with ω3≪ω⊥. Show that in this limit, the fraction of the flight time that the coin spends heads-up is 1/2+(4ω32)/(πω⊥2).