Delaram

FR1-TR2=I*alfa / alfa=rotational acceleration) alfa=a/R2 so we can find T T=FR1/R2-Ia/(R2^2) then we use T=ma to find a: a=FR1R2/(mR2^2+I)

in other words we must use second law of newton to find acceleration, a=T/m but since we don't have tension we should utilise torque equation to find T, the point here is that we should notice angular acceleration=a/R2