Friction review

Review the key concepts, equations, and skills for friction, including how to find the direction and magnitude of the friction force.

Key terms

Term (symbol)Meaning
Friction ($F_f$ or $f$)A contact force that resists sliding between surfaces.
Kinetic friction ($F_{f,k}$ or $f_k$)Friction when an object slides along a surface. Direction is opposite the object’s sliding direction and is parallel to the contact surface.
Static friction ($F_{f,s}$ or $f_s$)Friction that prevents an object from sliding along a surface. Direction stops the object from sliding against another surface and is parallel to the contact surface.
Coefficient of friction ($\mu$)A number typically between $0$ and $1$ that describes the roughness between two surfaces, where $0$ is slippery and $1$ is very rough. A unit-less ratio of the frictional force to the normal force. The static friction coefficient $\mu_s$ is for surfaces that are not sliding, while kinetic $\mu_k$ is for sliding surfaces.
If $\mu$ is greater than $1$, that means the force that resists the sliding is greater than the normal force.
An example where $\mu > 1$ is velcro. In this case, the two surfaces are a little more complex in how they interact.
For beginning physics courses (AP Physics 1, AP Physics C, or entry level college physics courses), $\mu$ only ranges from 0 to 1. This still covers a wide variety of real world situations.

Equations

EquationSymbol breakdownMeaning in words
$\lvert \vec{F_{f,k}} \lvert = \mu_k \lvert \vec{F_N} \lvert$$F_{f,k}$ is kinetic friction, $\mu_k$ is coefficient of kinetic friction, $F_N$ is normal forceKinetic friction magnitude is directly proportional to the normal force magnitude and the roughness between the sliding surfaces.
$\lvert \vec{F_{f,s}} \lvert \leq \mu_s \lvert \vec{F_N} \lvert$$F_{f,s}$ is static friction, $\mu_s$ is coefficient of static friction, $F_N$ is normal forceStatic friction magnitude is directly proportional to the normal force magnitude and the roughness between the sliding surfaces.
$\mu = \dfrac { \lvert \vec{F_f }\lvert }{\lvert \vec{F_N} \lvert }$$F_f$ is friction, $\mu$ is coefficient of friction, $F_N$ is normal forceThe coefficient of friction is the ratio of the magnitude of frictional force divided by the normal force magnitude.

How to find direction of friction force

Static friction prevents sliding

Static friction is the force holding an object in place on an incline, such as the cheese in Figure 1. The friction force points against the direction that the object would slide without friction. Static friction keeps gravity from pulling the cheese down the incline.
Figure 1. Cheese resting on an incline because static friction holds it in place.
Another example of static friction comes when objects are moving. When you are walking, static friction pushes in the direction of you are trying to move (see Figure 2 below). The foot pushes on the ground, and without friction the foot would slide backwards (like walking on ice). Static friction pushes in the direction that prevents your foot from sliding, which results in forward motion.
Figure 2. Direction of static friction on a shoe walking forward. Static friction pushes the person forward. Shoe image courtesy of Pixabay.

Kinetic friction acts opposite the object’s sliding direction

Kinetic friction always opposes the object’s sliding direction. As seen in Figure 3 below, if an object is moving up an incline, the force of friction $f_k$ points down the incline. If the object is moving down an incline, the $f_k$ points up the incline.
Figure 3. Kinetic friction $f_k$ direction for a block of cheese sliding on an incline with velocity $v$.

How to determine magnitude of friction force

Friction is determined by the two surfaces in contact, and how tightly the two surfaces are pushed together (normal force $F_N$).
• Coefficient of friction ($\mu$): this describes the roughness between two surfaces. A high coefficient of friction produces more friction.
• Normal force ($F_N$): squeezing surfaces together more tightly increases the friction. This is one reason why heavy objects are harder to slide across the ground.
These factors of friction are reflected in its generalized equation:
$\lvert \vec{F_f} \lvert \leq \mu \lvert \vec{F_N} \lvert$
Friction for a given object isn’t always just one value though, it can change. Let’s learn how by imagining a person pushing a refrigerator as shown in Figure 4 below. When we push an initially resting refrigerator with an external applied force $F_\text {app}$ and start it moving, both static and kinetic friction push back on the object at different times.
Figure 4. Horizontal forces acting on a refrigerator being pushed with increasing applied force $F_\text {app}$.

Static friction

Initially static friction $F_{f,s}$ prevents the refrigerator in Figure 4 from moving. But as we continue applying more and more force $F_\text {app}$, eventually the refrigerator begins sliding. This is because static friction has a maximum value that it can reach before it lets an object begin sliding. As long as $\lvert F_\text {app} \lvert \leq \lvert F_{f,s_{max}} \lvert$, then the refrigerator remains at rest. This is described by the equation below:
$\lvert \vec{F_{f,s}} \lvert \leq \mu_s \lvert \vec{F_N} \lvert$

Kinetic friction

Once an object begins to slide, kinetic friction $F_{f,k}$ acts with a constant amount to resist the sliding motion:
$\lvert \vec{F_{f,k}} \lvert = \mu_k \lvert \vec{F_N} \lvert$

Common mistakes and misconceptions

People often mistake the coefficient of friction $\mu$ for the frictional force $F_f$. The coefficient of friction is a number that describes the interactions between the surfaces, it is not a force. In order to find the friction force, $\mu$ has to be multiplied by the normal force on the object.