Advantage of using a bigger pulley in belt drive?

Hi :

lets examine the following scenario

1.

M --------- o where M is a mass, o is a pulley with it's outter radius r attached to a mass by the belt drive -------. frictionless.


2.

M ---------O same setup but the radius is now bigger, R.



I was reading somewhere saying, a smaller pulley can move things quicker, so i decided to derive this to see for myself.


the following is the result:


for case 1:

alpha = T/(J+Mr^2)

case 2:

alpha = T/(J+MR^2)


in other word, for the same torque generated from DC motor, alpha is higher for case 1.



also, in the case where the pulley rotates at a constant velocity, constant torque output, case 1 amplify the force on the mass M where as the force on the Mass M in case 2 would be lower.



so my question is, why would anyone choose case 2 at all? what advantage does it have on any applications?


thanks