A $60$ kg dynamics instructor is demostrating the principles of angular momentum to her class. She stands on a freely rotating platform with her body aligned with the vertical platform axis. With the platform not rotating, she holds a modified bicycle wheel so that its axis is vertical. She then turns the wheel axis $180$ degrees with respect to its initial vertical position without changing the $575-$mm distance from the centerline of her body to the wheel center. The rim$-$weighted wheel has a mass of $11$ kg and a centroidal radius of gyration of $335$ mm and is spinning at a fairly constant rate of $217$ rev$/$min$.$ The instructor has a mass moment of inertia I $=3\mathrm{.}18$ kg m$^2$ about the vertical platform axis. What rotational speed do the students observe with the wheel in this new position?