1. The problem statement, all variables and given/known data You hang a thin hoop with radius R over a nail at the rim of the hoop. You displace it to the side (within the plane of the hoop) through an angle β from its equilibrium position and let it go. What is its angular position when it returns to its equilibrium position (use the gravitational potential energy equation). 2. Relevant equations K(1) + U(1) = K(2) + U(2) U(1) = mgh h = R - Rcosβ K(2) = (1/2)mv^2 = (1/2)m(ω^2)R^2 3. The attempt at a solution 0 + U(1) = K(2) + 0 mgh = (1/2)m(ω^2)R^2 mg(R - Rcosβ) = (1/2)m(ω^2)R^2 ω = √((2g(1 - cosβ)/R) The answer in my textbook is exactly the same as my answer but without the 2. What could have happened to the 2?