Game Development Reference
In-Depth Information
Combining Equations (6.5) and (6.6) results in an equation relating an angular impulse to
a resulting change in angular momentum.
(
)
τ
=− =
LL I
ω ω
−
(6.30)
1
0
1
0
Equation (6.30) states that in the absence of a net applied torque, angular momentum of
an object, or of a system of objects, is constant. This concept is known as the
conservation of
angular momentum
.
Exercise
3.
A figure skater with her arms stretched wide spins at 2 revolutions per second. If she pulls her arms
tightly against her body, causing her moment of inertia to decrease from 2.0
kg-m
2
to 1.6
kg-m
2
, how
fast will she spin when her arms are next to her body?
Collisions with Friction
Up to this point in the chapter we have dealt with frictionless collisions. In reality, assuming
that a collision is frictionless is only strictly valid for
direct impact collisions
. As shown in
Figure 6-12, a direct impact collision is one in which the line of action for the collision passes
through the center of mass of the two objects, and the velocity vectors of the two objects are
parallel to the line of action. After a direct impact collision, the two objects immediately separate,
and the collision only affects the velocity along the line of action of the collision.
Figure 6-12.
Velocity and line of action are in the same direction for direct impact collisions.
The other general type of collision is an
oblique
or glancing impact. As shown in Figure 6-13,
an oblique collision is one in which the velocity vectors of the two objects aren't aligned with
the line of action.
