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yoyo question!

1. The problem statement, all variables and given/known data

similar to the situation in b. except the string and force P act from the edge of the yoyo rather than from an inner spool

A force (P) is applied to the string horizontally which is attached to the yoyo directly below its center of mass, where the yoyo is sitting stationary on a horizontal table with friction coefficient (u). What will happen?

2. Relevant equations
Just F=ma and moments

3. The attempt at a solution

So F(maximum friction) = uR where R = mg
F=umg in the opposite direction to P.
So if P > umg then the yoyo will start to slide to the right.
However if P > umg and assuming P acts from the edge of the yoyo, then taking moments about the center of mass Pr > umgr so there will be a moment anticlockwise and the yoyo will spin anticlockwise.
But what I am thinking is that the torque will still be greater than the frictional force so it wont grip and it will still slide to the right but while spinning anticlockwise...or will it? surely it must spin, but whether that will cause it to roll i dont know?!

Also i was thinking, if P acts at a distance which is less than r, so r-x, then could a situation arise where the moments will be such that while P>umg, P(r-x) = umgr so the yoyo will slide to the right but wont spin at all. Also then could the situation arise where P(r-x) < umgr so the yoyo will slide to the right and start to roll to the right?

Please help (at least with the basic problem where P acts at a distance r from COM) as there is a high chance that this will come up in a uni interview on tuesday!