Kevin Zhou — Advanced Mechanics IV Problem 4 · Kevin Zhou #M8.4
Physics · mechanics
Problem
Problem 9 (KK 7.6, Morin 9.23). With the right initial conditions, a coin on a table can roll in a
circle.
As shown, the coin leans inward, with its axis tilted to the horizontal by an angle ϕ. The radius of
the coin is b, the radius of the circle it follows on the table is R, and its velocity is v.
(a) Assuming the coin rolls without slipping and b ≪ R, show tanϕ = 3v2/2gR.
(b) No longerassuming b ≪ R, show thatthe describedmotion is only possible ifR > (5/6)bsinϕ.