Solve Torque on Cylinder Homework Problem

[Xetricon]

Homework Statement

A cylinder having a mass of 5.0 kg can rotate about its central axis through point O. Forces are applied as shown in the figure: F₁ = 5.0 N, F₂ = 6.0 N, F₃ = 2.5 N, and F₄ = 5.5 N. Also, R₁ = 6.5 cm and R₂ = 12.0 cm. Find the magnitude and direction of the angular acceleration of the cylinder. (Take clockwise to be +.) (During the rotation, the forces maintain their same angles relative to the cylinder.)

Homework Equations

τ=I⋅α=r⋅F⋅sinΦ
I_cyl = ½MR²

The Attempt at a Solution

So I started with
τ_net=F₂⋅R₁ - F₁⋅R₂ + F₄⋅0
and τ=Iα , so F₂+R₁ - F₁⋅R₂=Iα.
Substituting in I:
F₂⋅R₁ - F₁⋅R₂=½MR²α
Solved for α to get
2[F₂⋅R₁ - F₁⋅R₂ ]/MR²=α
Plugging and chugging I got:
2[(6.0N-5.0N)(0.12m)+(2.5N)(0.065m)]/(5.0kg)(0.12m)²=α
α=0.94 rad/s²

But this isn't correct. Can you help me figure out what I'm doing wrong? Thanks!

 

[TomHart]

I didn't work all the way through your solution (I don't have much time right now), but your original τ_net equation has errors. You should carefully go through that.