T1-T2=0
F1r1=F2r2
F1r1-F2r2=0
F1r1=F2r2
F1r1-F2r2=0
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The summation of torques will be equal to the product of the moment of inertia (a constant) and the angular acceleration. If there is no rotation the angular acceleration is zero & therefore the resultant torque is also zero.