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why can you NOT do this problem with newton's second law for rotational motion (sum of...

why can you NOT do this problem with newton's second law for rotational motion (sum of torques = I*alpha)? For the apparatus shown in the figure, there is no slipping between the cord and the surface of the pulley. The blocks have mass of 3.0 kg and 5.7 kg, and the pulley has a radius of 0.12 m and a mass of 10.3 kg. At the instant the 5.7 kg mass has fallen 1.5 m starting from rest, find the speed of each block. (Assume the pulley is in the shape of a uniform solid disk and has no friction in its axle.)  

Only the energy solution to the problem get the right answer. Why not Newton's second law for this problem? If you can use Newton's laws, please provide the answer doing so.

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