Well, that's embarassing. That ends up being 0.45, which changes the final answer to 10.9 rad/s, corresponding with one of the multiple choice answers. Thanks.
[SIZE="4"]Homework Statement
[From Serway College Physics; Ch 8, problem 52] Use conversation of energy to determine the angular speed of the spool shown in the figure after the 3.00 kg bucket has fallen 4.00 m, starting from rest. The light string attached to the bucket is wrapped around the...