I never really thought about it but it seems arbitrary in which way we calculate friction in terms of problems involving rolling without slipping. That is you will get the same results whether you say the friction helps your rotational acceleration or your translational acceleration. For instance consider a cylinder rolling without friction due to some force being applied at R: It is not hard to see you get the following equations for a (where f is the force due to friction): F-f = ½ma F+f = ma Or if you chose the direction of the friction to be in the other direction: F+f = ½ma F-f = ma It's not hard to see that these equations will give the same acceleration. Physically however I don't understand this. I would argue that because the "mass" is less in the equation with ½m it is beneficial to have the frictional force "help" you here rather than help the translational motion where the mass is bigger. What is wrong with my thinking??