Friction in a contact between a pulley and a string

[Elleboys]

Homework Statement

I need to find a formula for the friction in the system.
I had a disk and a pulley connected to a rotation sensor on each side.
I wrapped a pulley with a string and there was a small mass attached to the bottom.
As I let that mass fall, it would fall and spin a pulley.
What would be the formula for the friction in the system?

*Given variables are T, Hanging mass, pulley radius, disk mass, disk radius, and angular acceleration

Homework Equations

Torque = I(mr^2)*(angular acceleration)
Fnet = Fg-T-Ff

The Attempt at a Solution

 

[Simon Bridge]

Welcome to PF;
Does the string slip over the pulley?

How is friction usually figured out?