Finding Maximum θ for Apparatus Not to Roll Right

[usamo42j]

Homework Statement

The apparatus in the diagram consists of a solid cylinder of radius 1 cm attached at the center to two disks of radius 2 cm. It is placed on a surface where it can roll, but will not slip. A thread is wound around the central cylinder. When the thread is pulled at the angle θ = 90◦ to the horizontal (directly up), the apparatus rolls to the right. Which below is the largest value of θ for which it will not roll to the right when pulling on the thread?

The figure can be found at www.aapt.org/physicsteam/2012/upload/WebAssign-exam1-2011-1-4.pdf (Problem 13)

Homework Equations

τ=Fr sinθ
I'm not sure about others; maybe the ones relating angular/translational kinematics

The Attempt at a Solution

I'm confused. Isn't the only torque caused by the force on the thread, so wouldn't the discs always roll to the right?...

 

[tiny-tim]

hi usamo42!

Isn't the only torque caused by the force on the thread, so wouldn't the discs always roll to the right?...

what about the torque of the friction force?