Suppose there is a pulley (a disc) of mass m1 and a string passes over the pulley with masses m2 and m3 hanging on both ends of the string with m3 > m2. I know that the acceleration should be (m3 - m2)g/(1/2m1 + m2 + m3) and I know how to get there. However, since the pulley rotates and has mass, the tensions are different on the two ends of the string. That would mean that the string is not massless because there would be an infinite acceleration if the string was massless. However, the mass of the string appears nowhere in the final answer. Why is this so?