Rotational Motion Around Two Cylinders

[lila.haj]

Homework Statement

The ropes in the figure are each wrapped around a cylinder, and the two cylinders are fastened together. The smaller cylinder has a diameter of 10 cm and a mass of 5.0 kg; the larger cylinder has a diameter of 20 cm and a mass of 20 kg. What is the angular acceleration of the cylinders? Assume that the cylinders turn on a frictionless axle. I know the answer is 3.5 rad/s².

Figure: http://session.masteringphysics.com/problemAsset/1176936/5/P7-59.jpg

Homework Equations

[itex]\alpha[/itex]=τ/I
τ=rF
I=1/2*M*R²

The Attempt at a Solution

I tried calculating the net torque of the cylinders caused by the hanging masses. I then divided the net torque by the total inertia on the cylinders using the first equation listed above.

 

[jbsteele]

When I did this, however, I actually got a negative answer. Can someone please explain where I am going wrong or how I should approach this problem?