Variables:

The masses of the blocks are

mA and mB, where mA < mB.

mA hangs on the left hand side, mB hangs on the right hand side.

The mass and radius of the pulley are

mC and rC, respectively

and thus its moment of inertia is I = (mC * rC^2)/2

The gravitational acceleration is

g

The outline of my solution goes like this:

Three separate forces contribute to the total force:

The weight of the pulley

The forces in the rope on both sides of the pulley, which I denote

TA and TB

I'm assuming that the rope doesn't slip, and thus the magnitude of the acceleration is the same on both sides, as well as tangentially along the pulley. I denote this acceleration

aY

I've chosen my coordinate axes to be positive to the right, up and out of the paper. Thus the block pulling in the counterclockwise direction should give a positive moment and vice versa, right?

Give the above, I want to pose the solution like this:

I*(aY / r) = TA*r - TB*r (Newton's second for rotational motion)

mA*aY = TA - mA*g (Newton's second for block A)

mB*aY = mB*g - TB (Newton's second for block B)

Three unknowns, three equations. Seems like smooth sailing, but I get the wrong answer. I suspect I'm simply doing a slip-up somewhere in the calculation, but if anyone can spot some misunderstanding in how I approach the problem, or maybe even confirm that I'm on the right track, I'd be very grateful!