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The problem of pulley in college physics is urgent! Why can the tension in the rope produce torque on the pulley and the tension in the rope does not act on the pulley!
Suppose the rope tension on the left is T 1, the right is T2, the acceleration of m 1 and m2 is A, and the angular acceleration of the pulley is β.

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.