A Wheel, with Rotational Inertia I, Mounted on a Vertical $\omega$

Multiple Choice

A wheel, with rotational inertia I, mounted on a vertical shaft with negligible rotational inertia, is rotating with angular speed $\omega$ _0. A nonrotating wheel with rotational inertia 2I is suddenly dropped onto the same shaft as shown. The resultant combination of the two wheels and shaft will rotate at:

A) $\omega$ ₀ /2
B) 2 $\omega$ ₀
C) $\omega$ ₀ /3
D) 3 $\omega$ ₀
E) $\omega$ ₀ /4