A $56-kg$ dynamics instructor is demonstrating 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 $180$ with respect to its initial vertical position without changing

the $565-mm$ distance from the centerline of her body to the wheel center. The rim$-$weighted wheel has a mass of $14kg$ and a

centroidal radius of gyration of $325mm$ and is spinning at a fairly constant rate of $247re\frac{v}{m}in.$ The instructor has a mass

moment of inertia $I=3\mathrm{.}57kg*m^2$ about the vertical platform axis. What rotational speed do the students observe with the

wheel in this new position?