Exploring Friction & Acceleration in a Cylinder System

[aaaa202]

Consider the system on the attached file. I did an assignment with it, which made me think a lot.
So the spring like thing in the cylinder is a torsional spring, which when released produces a certain torque round the cylinder making it rotate. But that creates a friction and assuming a high enough coefficient of friction it will start to roll. One then had to assume that:
Ffriction * R = I * α (1)
To find the angular acceleration. Writing up the equations for the linear acceleration this was possible to find. However! Is (1) really correct? Because what about the friction in the small wheels of the wagon. Don't their friction also contribute to the linear acceleration of the system yet not the angular?

 

[rcgldr]

small wheels on wagon. Don't their friction also contribute to the linear acceleration of the system yet not the angular?

I think you're supposed to assume the wheels of the wagon have zero angular inertia, and that the cylinder driven wagon is free of any losses of energy. You could also assume the wagon has no wheels and is frictionless.

Is (1) really correct?

Try to find another equation that relates to friction force.

 

[aaaa202]

Yes okay, the assignment actually stated that explicitly, but I didn't know how to interpret it. Specifically it said, that the angular intertia was so little it could be neglected. Ahh well. But won't they always contribute with the same force to drive the linear movement as the big, heavy cylinder?
EDIT: No wait, of course they won't - I get it now - ty so much :)