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### Coefficient of Friction

The coefficient of friction (μ), is a measure of the amount of friction existing between two surfaces. A low value of coefficient of friction indicates that the force required for sliding to occur is less than the force required when the coefficient of friction is high.

The value of the coefficient of friction is given by:

Transposing gives:

Frictional force = μ × Normal force

The direction of the forces given in this equation is as shown in the below figure.

The coefficient of friction is the ratio of a force to a force, and hence has no units.

Typical values for the coefficient of friction when sliding is occurring, i.e. the dynamic coefficient of friction, are:

• For polished oiled metal surfaces less than 0.1,
• For glass on glass 0.4,
• For rubber on tarmac close to 1.0.

In general, The coefficient of friction (μ) for dynamic friction is a little less than that for static friction.

However, for dynamic friction (μ) increases with speed; additionally, it is dependent on the area of the surface in contact.

In some applications, a low coefficient of friction is desirable, for example, in bearings, pistons moving within cylinders, on ski runs, and so on. However, for such applications as force being transmitted by belt drives and braking systems, a high value of coefficient is necessary.

Instances where frictional forces are an advantage include:

1. Almost all fastening devices rely on frictional forces to keep them in place once secured, examples being screws, nails, nuts, clips and clamps.
2. Satisfactory operation of brakes and clutches rely on frictional forces being present.
3. In the absence of frictional forces, most accelerations along a horizontal surface are impossible; for example, a person’s shoes just slip when walking is attempted and the tyres of a car just rotate with no forward motion of the car being experienced.