We take two identical pulleys, both with string wrapped around them. On the one on the left we apply an 8 N force to the string. On the one on the right we hang an object with a weight of 8 N. Which pulley has the larger angular acceleration?
The one on the left, because the tension in the string is 8 N. The tension in the string on the right is less than 8 N, because it is given by:
mg - T = ma
T = mg - ma = 8 - ma