Rolling motion including torque and acceleration

[XxBollWeevilx]

Homework Statement

A constant horizontal force \vec{F} is applied to a lawn roller in the form of a uniform solid cylinder of radius R and mass M. If the roller rolls without slipping on the horizontal surface, show that (a) the acceleration of the center of mass is \frac{2\vec{F}}{3M} and (b) the minimum coefficient of friction necessary to prevent slipping is \frac{F}{3Mg}. (Hint: Take the torque with respect to the center of mass.

Homework Equations

Not quite sure.

The Attempt at a Solution

Well, this is my last problem of the night to finish. To be honest, i have no idea where to begin. I don't know how to examine the acceleration or how to use torque to find friction. Any step in a positive direction would be helpful. I appreciate it.

 

[XxBollWeevilx]

I was thinking maybe a force diagram...but I'm not sure how it would apply to the rolling motion.

 

[XxBollWeevilx]

Also, I'm not sure whether the applied force is causing any torque or not.