Game Development Reference
In-Depth Information
make a ball “stick” on the green. A car engine uses the rotational motion of the driveshaft and
gearbox to transmit power to the wheels. These are just two of the many examples where you
will have to model rotational motion in your game programming.
Let's start our exploration of rotational motion by discussing some terminology. Consider
a flat disk rotating in the counterclockwise direction as shown in Figure 4-7. The origin of the
frame of reference is taken to be the center of the disk. The y-axis is perpendicular to the face
of the disk pointing into the page. The location of a point
P
on the outside of the disk is speci-
fied by the radius of the disk and an angle
q
measured counterclockwise from the x-axis.
z
P(r,θ)
r
θ
x
Figure 4-7.
A schematic of rotational motion
The rate at which the disk is rotating can be expressed in several ways. One way to describe
the rate of rotation is by the frequency,
f
, of rotation, which is the number of revolutions the
disk completes per second. Another way to express the rate of rotation is by the rate at which
the angle
q
changes as a function of time. This quantity is known as the
angular velocity
,
w
.
d
dt
q
w
=
(4.27)
Angular velocity can be expressed in units of
degrees/s
but more commonly is characterized
in units of
radians/s
, sometimes abbreviated as
rad/s
. There are 2
π
radians
in one revolution, so
2
radians
is equal to 360
degrees
. The angular velocity,
w
, is related to the frequency of rotation,
f
, by a factor of 2
π
π
.
wp
=
2
f
(4.28)
Just as translational acceleration is the time rate of change of translational velocity, the
angular acceleration,
α
, is defined as the time rate of change of angular velocity.
d
dt
w
a
=
(4.29)
