Slide the cup with the glued strips onto the dowel. It should be able to wobble freely on the pivot. Use scotch tape to center the open end of the cup to the dowel.
Begin gluing the strips to the Styrofoam disk on the other cup. Make the strips taunt when you glue them, but don't pull to hard or you will cause the wobble cup to be off center.
Continue with all the strips.