Game Development Reference
In-Depth Information
F a
=
(3.3a)
x
x
F a
=
(3.3b)
y
y
F a
=
(3.3c)
z
z
In Equation (3.3a), the quantity
a
x
is the acceleration in the x-direction. Dividing a force
into directional components allows for a more refined analysis of the effects of the given force
on an object. If the force is directed in the x-direction, the acceleration will be in the x-direction
as well, and there will be no change in velocity in the y- or z-direction.
Sometimes you will have directional components of a force and will need to compute the
overall magnitude of the force. The magnitude of a force vector is equal to the square root of
the sum of the square of the directional components.
FFFF
=++
2
2
2
(3.4)
x
y
z
Most of the time in this topic we will use the Cartesian frame of reference with the x- and
y-directions parallel to the surface of the earth and the z-direction normal to it. The Cartesian
frame of reference is the best choice for problems involving linear motion. If a model involves
circular or rotational motion, like modeling the spin of a golf ball for instance, it usually makes
more sense to use either the spherical or cylindrical coordinate systems where a vector is split
into angular components.
Types of Forces
In very simplistic terms, a force is something that pushes or pulls on an object with the poten-
tial to change the motion of the object. When a baseball player hits a baseball, the bat imparts
a force to the ball. When a gun is fired, the gunpowder charge imparts a force to the bullet. In
this section, we will discuss in more detail four special types of forces that will be a part of many
of the physical models you will use as a game developer—gravitational, friction, spring, and
centripetal force.
Gravitational Force
One of the many disciplines that Newton applied himself to was a study of the motion of celestial
objects. It was known at that time that the moon traveled in a nearly circular orbit around the
earth. From his first law of motion, Newton knew that the only way the moon could circle the
earth is if there was a force directed toward the earth acting on the moon. Without the presence
of such a force, the moon would fly off into space.
Newton eventually came to the conclusion that there was a
gravitational force
between
the earth and the moon. He then generalized this finding to say that there was a gravitational
force,
F
G
, between any two objects that was proportional to the masses of the objects,
m
1
and
m
2
, and inversely proportional to the square of the distance between them,
r
.
Gm m
F
=
12
2
(3.5)
G
r
