A 10 mg bead is free to slide on a frictionless wire loop. The loop rotates about a vertical axis with angular velocity ω. If ω is less than some critical value ωc, the bead sits at the bottom of the spinning loop. When ω>ωc, the bead moves out to some angle θ. Suppose R = 3.0 cm. What is ωc in rpm for the loop? At what value of ω , in rpm, is θ = 30∘?