Rotational Inertia of a Pulley System

[Derpity Derp]

Homework Statement

Homework Equations

Kinetic Energy = 0.5 I w^2
v = r * w
torque = Inertia * angular acceleration

The Attempt at a Solution

That's the problem. I have no idea where to start. I assume that the end goal is to find the angular velocity, and convert to linear velocity, but I don't know how to go about doing that. Any hints are appreciated.

 

[haruspex]

I assume that the end goal is to find the angular velocity, and convert to linear velocity,

Not exactly. Both are unknown, but they are related by the equation you quote.
What will be the loss in PE as the pulley executes one revolution?
If the linear speed of the masses is v, what is the angular speed of the pulley?
In terms of v, what are the KEs of the masses and the pulley?