Any questions??
Four-step plan
Step 1: FBD
Draw a free-body diagram for the disk.
Step 2: Kinetics – Work/energy
Write down the kinetic energy and potential energy expressions for the disk, along with the work done on the disk by non-conservative forces. Note that point C is the instant center (zero velocity point) for the disk. Because of this, you are able to write down the KE for the disk as Tdisk = 0.5*ICω2, if you choose to do so. The work done by F is equal to U = FsA, where sA is the distance traveled by end A of the cable.
Step 3: Kinematics
Here you need to relate the distance traveled by point O to the distance traveled by end A of the cable (these are not the same). In doing this, recall that C is the instant center of the disk as it rolls without slipping.
Step 4: Solve
Solve your equations from Steps 2 and 3 for the speed of point O.