Game Development Reference
In-Depth Information
v
r
Figure 3-8.
An object traveling in circular motion has continually changing velocity vector.
Even though the velocity magnitude of the object may be constant, the directional compo-
nents of velocity are continually changing. If we consider the circular motion in a two-dimensional
Cartesian coordinate system, when the object is at the top of the circle, all of the velocity is in
the x-direction and there is no velocity in the y-direction. When the object travels 90 degrees
around the circle, all the velocity will now be in the y-direction.
The only way the velocity components can continually change in this manner is if there is
a continuous acceleration of the object and therefore a continuous force upon the object. This
force is known as a
centripetal force
. The centripetal force,
F
C
, is a function of the mass of the
object,
m
, the square of the velocity magnitude (that is, speed) of the object,
v
, and the radius
of the circle,
r
.
2
mv
F
=
(3.12)
C
r
The direction of centripetal force is towards the center of the circle. Centripetal force is not
limited to objects traveling along circular trajectories. You will encounter centripetal force in
your game programming whenever you model an object traveling along a curved path. When a
car drives around a curve in the road, the friction generated between the tires and the road
must balance the centripetal force generated by the car traveling around the curve. The centripetal
force is an inverse function of the radius of curvature, which is why it is harder to drive around
a sharp curve than a gentle one. Centripetal force is also a function of the square of velocity, so
when you approach a sharp curve it's a good idea to slow down.
Exercise
4.
A satellite is able to orbit a planet because the centripetal force generated by the motion of the satellite balances
the gravitational pull on the satellite from the planet. Using what you know about centripetal and gravitational
force, compute the radius of the moon's orbit. The mass of Earth is 5.974
e
+24
kg
and the mean orbital velocity
of the moon is 1023
m/s
.
Force Balances and Force Diagrams
You have learned that when a net external force is applied to an object that the object will
accelerate in direction of the applied force. However, when calculating how a body will react to
