The acceleration A of AB is the same, which is equal to the tangential acceleration of C. Let the tension of the rope on the left side of A be f 1 and the tension of the rope above B be f2, then the moment of C is M=(f2-f 1)R=Ia/R, and I is the moment of inertia. Meanwhile, a=f 1/mA=(mB*g-f2)/mB. Two unknowns and two equations can solve f 1 and f2, and then get a.