A cylinder of mass M and radius R has a string wrapped around it, with the string coming off the cylinder above the cylinder. If the string is pulled to the right with a force F, what is the acceleration of the cylinder if the cylinder rolls without slipping?
One key to the problem is realizing that there is a static friction force acting on the cylinder. Let's assume this force acts to the left.
Draw the free-body diagram. Take positive to the right, and clockwise.