Game Development Reference
In-Depth Information
Summary
In this chapter, you learned the basics of the physics of colliding bodies. Starting with the
concepts of linear momentum and impulse of force, equations were developed that compute
the post-collision velocities from a linear collision. You learned about how a coefficient of resti-
tution is used to characterize the efficiency of the collision and about inelastic and perfectly elastic
collisions. In addition to linear momentum and impulse, the subjects of angular momentum
and impulse were discussed. You learned how friction between colliding objects can cause the
objects to spin.
Some of the key concepts to take away from this chapter are as follows:
•
The change in velocity that results from a collision can be characterized by a linear or
angular impulse.
•
The post-collision velocities of two objects after a collision can be determined from the
principle of conservation of momentum and the coefficient of restitution for the collision.
•
For frictionless collisions, only the velocity in the direction of the line of action of a collision
is affected by the collision. The other velocity components normal to the line of action
are unchanged.
•
For collisions that involve friction, the resulting frictional impulse reduces the magnitude
of the velocity in the direction normal to the line of action and causes the objects to spin.
•
If a sphere rolls without sliding at the end of a frictional impulse, the angular velocity of
the sphere will be equal to 5/7 the initial velocity normal to the line of action divided
by the radius of the sphere.
We will use our knowledge of collision physics in the next chapter when we explore the
physics of sports. The spin caused by frictional collision plays a crucial role in golf, soccer,
tennis, baseball, and many other sports as well.
Answers to Exercises
1.
The line of action for the collision is along the x-axis so only the x-components of velocities
for the two objects will be affected by the collision. The post-collision x-direction veloc-
ities can be computed from Equations (6.14a) and (6.14b).
(
)
10.99
+
1
−
0.81
20
m/s
v
′ =
+
5
= −
5.65
1
x
10
10
(
)
10.91
+
9
−
0.9
m/s
′
v
=
20
+
5
=
7.85
2
x
10
10
