The normal force is one component of the contact force between two objects, acting perpendicular to their interface. The frictional force is the other component, acting parallel to the plane of the interface between objects.

Friction tends to oppose any relative motion between objects, acting at the surfaces in contact.

If there is relative motion, the frictional force is the kinetic force of friction.

If there is no relative motion, the frictional force is the static force of friction.

Let's say you're standing still and you then start to walk forward across a flat floor. Which force of friction is involved? Which direction is it?

1. Static friction, acting opposite to the way you're walking.
2. Static friction, acting in the direction you're walking.
3. Kinetic friction, acting opposite to the way you're walking.
4. Kinetic friction, acting in the direction you're walking.

Because your foot does not slip on the floor, the frictional force is static friction.

To determine the direction think about what would happen if there was no friction. When you pushed against the floor your foot would slide backwards. Friction opposes this, and acts forwards. Static friction is the force that propels you forward.

Push a book across a table. The kinetic force of friction, f_k is the force that brings the book to rest, opposing the motion.

f_k is proportional to the normal force:

f_k = μ_k N

μ_k is known as the coefficient of kinetic friction. It is a dimensionless number that depends only on the two surfaces in contact. Typical values are 0.1 - 1.0, but could be higher or lower.

Static friction can be much less intuitive than kinetic friction. For a book at rest on a flat table, where the only other forces are the force of gravity and the normal, the static force of friction is zero. If you then push horizontally with a small force, static friction establishes an equal-and-opposite force that keeps the book at rest.

As you steadily increase your force, the force of friction increases to match you. Eventually your force exceeds the maximum force of friction, and the book moves.

The maximum force of static friction, f_s, is given by:

f_{s max} = μ_s N

μ_s is known as the coefficient of static friction.

μ_s ≥ μ_k. In other words, it is harder to start something moving than it is to keep it moving once it's moving.

Static friction can be difficult to deal with because in general:

f_s ≤ μ_s N

We will often deal with the limiting case, involving the maximum force of static friction, but always think before writing down

f_{s max} = μ_s N. We will deal with cases where f_s < μ_s N .