Torque in a spool of thread for 3 cases

[ehf]

Homework Statement

(please do not read anything not english)

Homework Equations

torque=r cross T and I alpha

The Attempt at a Solution

I feel that the 3 cases will be different every time but I can't get the hang of the equations.

 

[TomHart]

Do you have another equation that you can use to relate forces and acceleration that might be useful in this type of problem, in addition to ΣΓ = Iα?

I spent a little bit of time looking at Figure 2. One way you can attack this is just to assume direction for linear acceleration (and the corresponding angular acceleration) and direction of the resultant friction force and work from there. However, if you think about it a little bit, you can actually figure out the direction that the spool rolls and the direction of the friction force without having to write out anything. The way to do that is to assume motion in one direction and see if that makes sense. For example, let's assume the direction of linear acceleration for Figure 2 is to the left. Since force T is to the right, what direction would the friction force F have to be to cause acceleration to the left? Well, to the left, of course. And what would the magnitude of F have to be (relative to T) to produce linear acceleration to the left? Well, it would have to be greater than T. Next, look at the directions (and relative magnitudes) of the individual torques produced by forces T and F and see if it is possible for a CCW angular acceleration to result from that.

 

[haruspex]

I can't get the hang of the equations.

When dealing with torques and angular accelerations you need to pick an axis. You can choose any fixed point, or the centre of mass of the rigid body.
If there is a force that you do not know and do not need to determine, you can make life easier by picking a point that is in the line of action of that force. Since it has no moment about that point, it does not appear in the equation.
In the first question, you are asked for the "torque on the spool". What axis would be appropriate? What equation can you write? If it involves unknown forces, create variables to represent them as necessary.)
You must post an attempt.