I am trying to solve a problem from the book "Introduction to mechanics, matter and waves" by Uno Ingard.
Its about a weightless piston that pushes with a horizontal force F a uniform rigid cylinder of mass M and radius R, it also says that there is friction between the piston and the cylinder, and the cylinder is rolling without slipping. I'm having trouble writing the equations of motion.
Given that the cylinder is rolling without slipping, there is a friction force between the cylinder and the horizontal plane, and because of the friction between the piston and the cylinder we have two frictions forces, a horizontal (horizontal plane) and a vertical one (piston).
My question is, does the friction between the piston and the cylinder affect the friction between the cylinder on the horizontal plane?
If I wanted to write the equations of motion from a frame of reference Q at the point of contact between the cylinder and the horizontal plane, which directions should the friction forces have and how many forces would I have?