How Does Pulley Torque Affect Wire Tension in a Frictionless System?

[mvpshaq32]

Homework Statement

A 12.0kg box resting on a horizontal, frictionless surface is attached to a 5.00kgweight by a thin, light wire that passes without slippage over a frictionless pulley (the figure ). The pulley has the shape of a uniform solid disk of mass 1.70kg and diameter 0.600 m.
After the system is released, find the horizontal tension in the wire.

http://session.masteringphysics.com/problemAsset/1037926/6/YF-10-44.jpg

Homework Equations

The Attempt at a Solution

I'm thinking of approaching it as I would if the pulley was massless by setting m₁a= T_horz and m₂a=m₂g-T_vert, but I don't know where the pulley would come in

 

[gneill]

There will be different tensions on either side of the pulley. The net torque on the pulley will be due to the actions of the two tensions. The angular acceleration of the pulley will be dictated by the net torque and its moment of inertia. The horizontal tension determines the acceleration of M1. The vertical tension, in concert with force due to gravity on M2, determines the acceleration of M2. The inextensible wire endures that all the accelerations are the same.

Relate the angular acceleration of the pulley to the acceleration of the wire in order to tie everything together.