The difference between T 1 and T2 is actually the friction between the rope and the pulley, that is, the friction causes the difference between T 1 and T2!
Force analysis:
m 1g-T 1=m 1a
T2-m2g=m2a
Time:
(T 1-T2)*r-Mf=J*β
J=( 1/2)m3r^2
a=r*β
Substituting the data, we can get: T 1, T2.