A toy is made using a frictionless spherical shell with an inner radius of 35 cm and a tiny pearl of mass 8.0 g. The pearl lies on the inner shell, as shown in the figure. The shell can rotate about a fixed vertical axis at various angular speeds. When playing, a child remarks that the pearl moves from the bottom of the shell to a higher position only when the shell rotates at an angular speed greater than ω_a. The line that connects the center of the shell to the pearl forms an angle α with the vertical. Find ω_a in revolutions per minute.