# Friction and Couples: Understanding Coefficients

• Hashiramasenju
In summary, the question is whether it is possible to find the magnitude of the frictional couple if given the coefficient of friction between the inner surface of the pulley and its axle. The problem involves a system with a light inextensible string, two particles of mass m and 4m, and a rough pulley. The initial angular acceleration of the pulley needs to be determined and the weight distribution of the pulley on the axle will likely be at a point. To solve this problem, the friction equation can be used with the friction coefficient and normal force acting on the wall of the pulley by the axle.
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 ?

## The Attempt at a Solution

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.

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.

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 ?

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.

## 1. What is friction and how does it affect objects?

Friction is a force that resists the relative motion or tendency to motion between two surfaces in contact. It can affect objects by slowing down or stopping their motion, as well as causing wear and tear on the surfaces.

## 2. What is a coefficient of friction and how is it calculated?

A coefficient of friction is a dimensionless quantity that represents the amount of friction between two surfaces. It is calculated by dividing the force of friction by the normal force, which is the force perpendicular to the surface of contact.

## 3. How does the coefficient of friction vary between different surfaces?

The coefficient of friction can vary greatly between different surfaces, as it depends on factors such as the texture, roughness, and material of the surfaces. For example, the coefficient of friction between rubber and concrete is higher than that between ice and ice.

## 4. What is a couple and how does it relate to friction?

A couple is a pair of forces that act on an object in opposite directions but not along the same line. In the context of friction, couples refer to the forces that act on an object in opposite directions due to the friction force between the object and the surface it is in contact with.

## 5. How can understanding coefficients of friction help in real-life applications?

Understanding coefficients of friction is crucial in many real-life applications, such as designing tires for cars and creating non-slip surfaces for floors. It also helps in predicting the behavior of objects in different situations, such as the braking distance of a car on a wet road.

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