Ok, I figured it out.
The problem was how friction accelerated a block (no slip) vs a rolling cylinder (no slip).
I was using f = ma for both (correct) and using it in the same reference plane for both (incorrect).
If I am standing on the slab, f = ma accelerates the cylinder and causes...
The problem is that they do not have the same acceleration (by observation).
However, if we take the scenario where their masses are the same, then their accelerations should also be the same...
UNLESS their forces of friction are different. This doesn't make sense though. Let's assume that...
Right, sorry. "m" instead of "M" was a typo in my sum of forces. However, I did say that "This is the linear acceleration an outside observer would see the cylinder moving at." The problem is still unresolved. How is this different than a block resting on the slab?
A uniform solid cylinder of mass M and radius R is at rest on a slab of mass m, which in turn rests on a horizontal, frictionless table. If a horizontal force F is applied to the slab, it accelerates and the cylinder rolls without slipping. Find the acceleration of the slab in terms of M, R, and...