Let me explain myself. Imagine a massless rope over a pulley, two weights m1 and m2 attached to the ends of the rope. M1's weightforce (m1xg) exerts a force on the rope, call it T1. On the other end of the rope m2 exerts the force T2. If we assume that the rope is massless, the sum of T2 and T1 has to be zero, so we conclude that T1 = -T2 = T. I dont understand how two different tension forces on both ends of the rope lead to a uniform tension force throughout the rope, even if the math suggests it. Please help :(
This might be helpful to you! It goes over conservation of string with different pulley configurations which is what I figure you’re confused about and not a generic Atwood machine. Let me know if this helps! Start on the bottom of page 87 till page 94.