I have a question about this(I know you want to see my soultion, but I've done it ok except the 2 things I'm asking about) :
1. How can I undersdant that I should sum up the angular velocity(w) of both bodies into one w, so that the the disk itself has the total w? why the disk doesn't have just w2?
2. Why the solution for contains reference of Vc, but the addition of relative velocity is from E to D, and not from C to D?