Friction and Couples: Understanding Coefficients

[Hashiramasenju]

Homework Statement

Usually in any question will the magnitude of the couple(friction) be given or is it possible to find the couple from the co efficient of friction between the rotating object and the axis ?

Homework Equations

The Attempt at a Solution

 

[Kinta]

Can you please be more specific about what the problem statement is and what information you're given about the system? If you don't have a particular problem in mind, make one up.

 

[Hashiramasenju]

Here is the Question but i want to know whether we can find the frictional couple if we are given the coefficient of friction between the axis and the pulley(if there is such a thing)
A light inextensible string has a particle of mass m attached to one end and a particle of mass 4m attached to the other end. The string passes over a rough pulley which is modeled as a uniform circular disc of radius a and mass 2m, as shown in Figure 2.
The pulley can rotate in a vertical plane about a fixed horizontal axis which passes through the centre of the pulley and is perpendicular to the plane of the pulley. As the pulley rotates, a frictional couple of constant magnitude 2mga acts on it.
The system is held with the string vertical and taut on each side of the pulley and released from rest. Given that the string does not slip on the pulley, find the initial angular acceleration of the pulley.

 

[Kinta]

So your question is more one of intrigue rather than one regarding difficulty solving the problem? If that's the case, then my guess would be that it is possible to find the magnitude of the frictional couple if given that coefficient of friction between the inner surface of the pulley and its axle. I haven't worked such a problem myself, but an initial thought of mine would be to wonder how the pulley's weight on the axle from the hanging masses would be distributed (whether it'd all be at one point or if it would go like a function of position in the plane of the pulley).

 

[Hashiramasenju]

Yup tomorrows my exam and i am self studying but do you have any idea about how to calculate it ?

 

[Kinta]

If your exam is in an introductory physics course, the weight distribution of the pulley on the axle will likely be at a point. You could then just use the good old friction equation $F_{\mu} = \mu F_N$ with $\mu$ the friction coefficient and $F_N$ the normal force acting on the wall of the pulley by the axle. This friction force acts as a torque adding to those contributed by the hanging masses.