Bucket on a spool falls into a well (angular velocity)

[Number47]

Homework Statement

Use conservation of energy to determine the angular speed of the spool shown in the figure below after the 3.00 kg bucket has fallen 3.90 m, starting from rest. The light string attached to the bucket is wrapped around the spool and does not slip as it unwinds.

relevant img: http://www.webassign.net/sercp/p8-36.gif

The Attempt at a Solution

I used the conservation of energy equation:
1/2*m*Vo^2 + 1/2*I*Wo^2 + m*g*ho = 1/2*m*Vf^2 + 1/2*I*Wf^2 + m*g*hf

I zeroed out the Initial KE's as it starts from rest, and the final potential energy as it ends with the height=0. I solved for the final velocity of the bucket using a separate conservation of energy equation and got that to be 8.74m/s after 3.90m of fall time. I input all known quatities into the full conservation of energy equation, solved for Wf via Wf=sqrt((m*g*h-(1/2)m*Vf^2)/(1/2)*I) and came up with .295 rad/s which is way too low relative to how fast the bucket is falling.

 

[Matterwave]

Why would you use 2 equations? Just note that v=w*r and you will have 1 equation with 1 unknown.