How to know which coefficient of friction to use? I need to find the friction force acting on a body with known mass using the coefficient of static or kinetic friction. The formula for friction force is
$$F = \mu N$$
Which coefficient of friction should I use for parameter $\mu$?
 A: In the case of static friction, the equation equals the maximum possible static friction $f_{s-max}$ before motion is impending, and is
$$f_{s-max}=\mu_{s}N$$
where $\mu_s$ is the coefficient of static friction.
Up until the applied force equals the maximum possible static friction force, the static friction force is a variable is equal and opposite to the applied force.
Once motion (sliding between the surfaces) begins, friction changes from static friction to kinetic friction, or
$$f_{k}=\mu_{k}N$$
Where $\mu_k$ is the coefficient of kinetic friction and where, in general, $\mu_{k}<\mu_s$. Kinetic friction is typically considered constant, at least at low speeds.
If the object exhibits pure rolling, only static friction is required to prevent slipping when an external force or torque is applied to the rolling object.
Hope this helps.
A: As you mention in your post, the friction force magnitude is proportional to the normal force $f = \mu n$, where $\mu$ is coefficient of friction. The friction force acts along the surface and always in the direction opposite to the (relative) motion.
The static friction acts when relative velocity between the body and the surface is zero. It is defined via coefficient of static friction $\mu_s$. Note that $\mu_s n$ will actually give you the maximum magnitude of the static friction force. This means that the static friction force is
$$f_s \leq \mu_s n$$
and its actual value depends on other forces acting on the body. See figure below for graphical explanation of this principle.
When the relative velocity is not zero, the kinetic friction acts on the body and the static friction is zero. The kinetic friction magnitude is defined via coefficient of kinetic friction $\mu_k$ which is assumed to be constant, i.e. it does not depend on velocity. Note that in general $\mu_k < \mu_s$.
The explained friction force model is just a simplification of what actually happens on molecular level which works well in most cases. However, you could expect to see more complex behavior in reality, such as kinetic friction dependence on velocity etc.

Source: H. D. Young, R. A. Freedman, "University Physics with Modern Physics in SI Units", 15th ed., 2019.
A: If the two surfaces in contact are sliding past each other use the coefficient of kinetic friction.  If they are not moving relative to each other use the coefficient of static friction.
Note that the equation $F=\mu N$ is for kinetic friction.  The case for static friction is a bit more subtle.  For static friction you could say $F_{s_{max}} = {\mu}_s N $ or $F_s \le {\mu}_s N$.  This is because the magnitude of the force of static friction is only as great as it needs to be to prevent slipping.
