There are two types of friction:

• Static friction
• Kinetic friction

What is static friction?

• Friction when an object is at rest.
• Example: you push big heavy box on a rough floor yet it refuses to move.

Two equivalent ways to express static friction $f_s$:

$f_{s, max}$ is the maximum possible value of $f_s$ achievable, $\mu_s$ is a dimensionless (no unit) number called the coefficient of static friction, and $F_n$ is the normal force.

What is the coefficient of friction $\mu$?

• Describes the roughness between the box and the floor.
• The rougher the surfaces, the larger is $\mu$, and the higher the value of friction in general.
• $\mu$ is dimensionless (has no units).
• Do not confuse $\mu$ with $f$.
• Two types: $\mu_s$ and $\mu_k$ (see below).

One can see from the simulation above that the static friction is not a fixed number, instead it changes depending on the external force. That is why the relation of $f_s$ is an inequality.

What is kinetic friction

• Friction when an object is in motion.
• The friction coming from the floor on a box sliding is kinetic friction.

Kinetic friction obeys a simple equation (as opposed to an inequality): $\mu_k$ is a dimensionless (no unit) number called the coefficient of kinetic friction, and $F_n$ is the normal force. Once again, the rougher the surfaces, the larger is $\mu_k$, and the higher the value of $f_k$.

We will mostly be dealing with kinetic friction, so for simplicity we will often omit the subscript "$s$" or "$k$" and simply write the equation above as $f=\mu F_n$.

Coefficients of friction for some common materials.

Materials	Static friction $\mu_s$	Kinetic friction $\mu_k$
Shoes on ice	0.1	0.05
Shoes on ice	0.1	0.05
Shoes on wood	0.9	0.7
Wood on wood	0.5	0.3
Stell on steel	0.6	0.3
Stell on steel (lubricated)	0.05	0.03
Rubber on concrete	1.0	0.7

Hooke's Law approximates $F_s$, the force from a spring:

• $k$ is the "spring constant", measured in $N/m$. Basically the "stiffness" of the spring.
• $x$ is the extension of the spring, measured from its equilibrium position.
• $F_{s}$ and $x$ are always opposite in sign because they always point in the opposite directions.

Name	Symbol	Unit	Meaning
Friction	$f$	$ N$	force against motion
Coefficient of friction	$\mu$	no unit	the roughness of the contact surfaces
Spring constant	$k$	$N/m$	stiffness of a spring
Extension	$x$	$m$	displacement of a spring from its equilibrium position
Centripetal acceleration	$a_{cent}$	$m/s^2$	radially inward acceleration of an object undergoing uniform circular motion
Centripetal force	$F_{cent}$	$N$	radially inward force required to keep an object in uniform circular motion