Rotation -- Anuglar speed A uniform ring 2.2 M in diameter is pivoted at one point on its perimeter so that it is free to rotate about a horizontal axis. Initially, the line joining the support point and center is horizontal. (a) If the ring is released from rest, what is its maximum angular velocity? rad/s (b) What minimum initial angular velocity must it be given if it is to rotate a full 360°? rad/s What I did: I used energy of conservation on this. The maximum velocity would be when the potential energy is at 0 since it is all converted into kinetic energy. R = 1.1m Moment of inertia for the ring is MR^2 Moment of the inertia of the pivot = 1/2 MR^2 + MR^2 = 3MR^2/2 Ui + Ki = Uf + Kf MgR + 0 = 0 + 1/2 (3MR^2/2)*omega ^2 MgR = 1/2 (3MR^2/2)*omega ^2 omega = square root of 2(g/3R) V = omega * R = square root of 2(gR/3R) It is at the bottom when it is 2R so V= omega * 2R = square root of 4(gR/3) What did I do wrong? For Part B: To find the minimum velocity to do a full 360, can I do this: Ui + Ki = Uf + kf MgR + 0 = 2MgR + 1/2 (3MR^2/2)*omega ^2 and solve for velocity as I did above?