Compute all parts of given problem:

Problem: A stiff piece of wire is bent into a circle and mounted (vertically) to rotate as shown. A wooden bead with a hole through its center can slide frictionlessly on that wire. The radius of the wire hoop is 15.0 cm and it rotates steadily with a period of 0.450 s.

Part A: At what angle theta will the bead rotate, along with the hoop, without sliding (up or down)? Show that there are two possible angles (solutions) for this hoop size and rotational speed. Include a clear free body diagram of the bead as part of your solution.

Part B: At what period would the ball not leave the bottom position (theta =0)?

Part C: At what period would theta =90o? What would that angular speed then be?

Part D: If the hoop were twice the radius, what would be the non-zero angle (at which the bead would rotate)?

Please show step by step process to the answer, explanation, as well as formulas. Thanks.