A bead of mass m can slide on a frictionless circular hoop in the vertical plane with radius R. When the hoop spins around the vertical axis with a rate of ω, the bead moves up the hoop by an angle θ which depends on the angular velocity of the hoop. (Pic attached) a) Find θ in terms of ω, R, m and g. b) If there is friction between the bead and hoop given by μ, within what range can ω change without changing θ? For part a what I have so far is that arad=R*ω2. The centripetal force (F) then is m*arad and the normal force is F/sinθ. The weight needs to cancel out the normal force then so the weight in the direction of the normal force is mg*cosθ = F/sinθ Am I anywhere close to being right?