I have a quick question regarding a system with a pulley, a cylinder on an incline, and a block hanging down vertically from the pulley, all connected with a tension cord. IF the pulley has mass, then we consider the torque about that pulley. Then the acceleration of the system would be the same, correct. For an example, in general if a question asks to find the acceleration of the block and the cylinder on the incline, then I can solve for that easily by writing down both the torque formulas and the force formulas while knowing that the acceleration is the same for both.
However, if I have a system with the same cylinder on an incline, and a MASSLESS pulley with no inertia, and a block which hung vertically from the incline, then the acceleration of the system wouldnt be the same, correct? For an example, if a question asks what is the acceleration of both the cylinder and the block, I would have to solve each acceleration seperately because they are NOT the same due to a MASSLESS pulley. Please let me know if I am correct or not. A picture of the system is provided below.