Mechanics 2: Linear and Rotational Dynamics - 3D Math Primer for Graphics and Game Development - page 570

In the first scenario, there is more friction available than necessary to
stop the sliding. However, as the angle of inclination increases, the nor-
mal component of gravity decreases, which reduces the amount of friction
available. Meanwhile, as the perpendicular component of gravity is de-
creasing, the lateral component is increasing, which makes the bowl want
to slide. The force of static friction must counter this lateral component
if the bowl is to remain in equilibrium. The center image shows the crit-
ical angle at which the lateral force of gravity is exactly equal to the to
the maximum amount of friction. On the right, we imagine that we have
tilted the table while holding the bowl in place, and then let go of the
bowl. The maximum available friction is being applied, but it's less than
was available in the center picture due to the decrease in the normal force
and isn't enough to overcome the increased lateral component of gravity.
Just after this picture was taken, friction switched from static mode into
kinetic mode, the bowl slid off the table and shattered, and a cartoon
cleaning robot scurried in through a little door in the wall to clean up the
mess.
Calculating kinetic friction is essentially identical to static friction. The
only difference is that we replace the subscript s with a k.

Kinetic Friction

f k = k n. (12.6)

The direction of the force of kinetic friction is always opposed to the relative
motion of the surfaces. (Remember, according to Newton's third law, there
are actually two forces, one pushing against the bowl, and the other against
the table, and they are in opposite directions.) As we said earlier, the
coe cient of kinetic friction is usually less than the coe cient of static
friction. Thus, if we increase the angle of the table ever so slowly so that
static friction is just overcome, the petunias will begin to accelerate, based
on this difference between kinetic and static friction. Coulomb's primary
contribution to the theory, sometimes called Coulomb's law of friction, was
that the force of kinetic friction does not depend on the relative velocities
of the surfaces, so, unlike static friction, there is no distinction between the
effective force and the maximum force.
Notice that the amount of area that the two objects are in contact does
not appear in Equations (12.5) or (12.6). For example, let's say we repot the
petunias in a taller bowl with a smaller footprint but the same weight. We
have reduced the surface area where the bowl and table are in contact, but