Game Development Reference
friction force is equal to the coefficient of friction. If you assume that the collisions are
such that the kinetic coefficient of friction is applicable, then this ratio is constant.
µ k = F f / F n
Here, F f is the tangential friction force and F n is the normal impact force. You can extend
this to say that the ratio of the tangential impulse to normal impulse is equal to the
coefficient of friction.
Consider the collision between the golf club head and golf ball illustrated in Figure 5-6 .
Figure 5-6. Golf club-golf ball collision
In the upper velocity diagram, v - represents the relative velocity between the ball and
club head at the instant of impact, v + represents the velocity of the ball just after impact,
v t- and v t+ represent the tangential components of the ball velocity at and just after the
instant of impact, respectively.
If this were a frictionless collision, v t- and v t+ would be equal, as would the angles α and
θ. However, with friction the tangential velocity of the ball is reduced, making v t+ less
than v t- , which also means that α will be less than θ.
The lower force diagram in Figure 5-6 illustrates the forces involved in this collision
with friction. Since the ratio of the tangential friction force to the normal collision force
is equal to the coefficient of friction, you can develop an equation relating the angle φ
to the coefficient of friction.
tan φ = F f / F n = µ
In addition to this friction force changing the linear velocity of the ball in the tangential
direction, it will also change the angular velocity of the ball. Since the friction force is