A massless string is wound around a solid cylinder that has a radius of 0.18 m and a mass of 27.23 kg. The free end of the string is tied to a block of mass 3.06 kg which hangs straight down. At t=0, the cylinder is allowed to spin about an axis through its center and the block falls, unwinding the string. Assume that the cylinder spins without friction. What is the acceleration of the block? I'm struggling to find the right angular acceleration of the pulley. I'm using Newton's second law for rotation, but I think I'm missing something. The only torque I have acting on the pulley is from the tension, but I know that the tension must be less than mg because the block is accelerating downward. How do I find the tension force of the string in a dynamic pulley system? (I asked this question before, and the expert got confused about the no friction thing, but I'm pretty sure that just means that the pulley rotates around the pivot without friction. There is still friction between the pulley and the string.)

A massless string is wound around a solid cylinder that has a radius of 0.18 m and a mass of 27.23 kg. The free end of the string is tied to a block of mass 3.06 kg which hangs straight down. At t=0, the cylinder is allowed to spin about an axis through its center and the block falls, unwinding the string. Assume that the cylinder spins without friction.
What is the acceleration of the block?

I'm struggling to find the right angular acceleration of the pulley. I'm using Newton's second law for rotation, but I think I'm missing something. The only torque I have acting on the pulley is from the tension, but I know that the tension must be less than mg because the block is accelerating downward. How do I find the tension force of the string in a dynamic pulley system?

(I asked this question before, and the expert got confused about the no friction thing, but I'm pretty sure that just means that the pulley rotates around the pivot without friction. There is still friction between the pulley and the string.)