Weight attached to a bicycle Wheel - physics problem, please help!?

Consider a bicycle wheel that initially is not rotating. A block of mass, m, is attached to the wheel and is allowed to fall a distance, h. Assume that the wheel has a moment of inertia, I, about its rotation axis.

PART A:
Consider the case that the string tied to the block is attached to the outside of the wheel, at a radius r_A
Find omega_A, the angular speed of the wheel after the block has fallen a distance, h, for this case.
Express omega_A in terms of m, g, h, r_A, and I.
(PLEASE REFER TO IMAGE LINK BELOW)

PART B:
Now consider the case that the string tied to the block is wrapped around a smaller inside axle of the wheel of radius r_B. Find omega_B, the angular speed of the wheel after the block has fallen a distance h, for this case.
Express omega_B in terms of m, g, h, r_B, and I.
(PLEASE REFER TO 2ND IMAGE LINK)

http://www.imagehosting.com/show.php/170...
http://www.imagehosting.com/show.php/170...

part a:
-initial energy of system= potential energy= mgh
-energy of block= 0.5*r squared* omega squared *m
-energy of wheel= 0.5*I*omega squared

-conservation of energy
block + wheel= mgh

answer
omega=square root of the whole thing [(2mgh)/(m*r squared +I)]

part b
same ****, but r subscript B instead of A

part c
B>A