I have solved problems like this before, but they have all been, well atwoods, and the disk in that case can't move translationally. So at the top of the cylinder the tension in the string is T, and so that exerts a torque of T*r on the cylinder. Now I call the tension at the string where the mass m is t, I know t=ma. Now I believe this doesn't exert a torque on the cylinder because it is an internal force, or something, or because the mass m is what allows the tension to be T at the other side of the rope (if there was no mass m, then there wouldn't be a T at the other side). so T*r=I[tex]\alpha[/tex]...I know I=0.5mr2, and that there is no slipping, so I think that since the cylinder also moves translationally, the equation is something like (astring-acylinder)=r*[tex]\alpha[/tex]...however this doesn't seem quite right to me because the string doesn't really move uniformly if the cylinder is moving, like the string near the mass m won't even move for a while if the cylinder moves a lot, but the string on the other side will... Anyway because of this I'm not exactly sure what to do. Can anyone help please?