1. The problem statement, all variables and given/known data You hang a thin hoop using radius R over a nail at the rim of a the hoop. You displace it to the side (within the plane of the hoop) through angle β from its equilibrium position and let it go. Using U = M*g*y(center of mass), what is the angular speed when it returns to its equilibrium position 2. Relevant equations ycm = R - R*cosβ K = U → 0.5*I*ω^2 = M*g*y(center of mass), where I = MR^2 for thin walled and hollow cylinders. 3. The attempt at a solution 0.5*I*ω^2 = M*g*ycm 0.5*M*R^2*ω^2 = M*g*(R - R*cosβ) ω = √((2*g*(1 - cosβ))/R) But my book, which seems to never be wrong, has everything but the 2, ω = √((g*(1 - cosβ))/R) I just can't see how I could be wrong.