Can you derive a formula for the critical angle when pulling a thread roll?

[JukuJohannes]

Homework Statement

Hello, the question itself is pretty abstract.
When pulling a thread roll, there is an critical angle, where the thread does not start to unwind itself. Instead, the thread roll itself starts to move.
Derive an formula for determining that critical angle.

Homework Equations

Most probably it is about using the Newtons' first law, as the angular acceleration and speed remains constant (0).

The Attempt at a Solution

I think the final formula will include centermass conception and radius of the thread-roll. But I have no idea, from where to start..

 

[kuruman]

To start unwinding (i.e. change its state of rotational motion), the thread roll needs to have a net torque applied to it about the axis of rotation. So if the torque is zero about the axis of rotation, the thread roll will not start unwinding. Start from there.