Thanks for the explanation… It seemed with the order of your calculation you arrived at that sigma at the bottom. I understand now that it’s part of the calculation parameters.
Are you solving for omega to find some sort of limiting angular velocity that will keep you under the allowable stress for your material?
Dunno if this will show up in the link, but the rules of thumb book for Mechanical Engineers book from Google Books has some useful formulas for the disk calculation:
See page 311 (I think the link above brings you to it)