Question

There is a block of mass 1 on a frictionless surface attached to a string. The string goes over a frictionless pulley. The pulley is a hoop with a rotational inertia of I=MR^2. The other end of the string is attached to a hanging block of mass 2. The hanging block is then released. To find the acceleration of the system, why could one not treat Mass 1 as a point particle on the hoop, and create a point particle moment of inertia for the Mass 1 block, and add then that "I" to that of the hoop? And then one could have the Fg of mass 2 as the only force causing a torque on the pulley.