Game Development Reference
In-Depth Information
Table 4-2.
Moments of Inertia for Some Common Objects
Object
Axis of Rotation
Moment of Inertia
2
5
mr
2
Solid sphere of radius
r
Through the center of the sphere
2
3
mr
2
Spherical shell of radius
r
Through the center of the sphere
1
2
mr
2
Cylinder of radius
r
and length
l
Through the ends of the cylinder
1
1
2
2
ml
+
mr
Cylinder of radius
r
and length
l
Through the middle of the cylinder
12
4
Perpendicular axis through the
center of the ring
2
mr
Ring of radius
r
1
2
mr
2
Ring of radius
r
Through the diameter of the ring
Rigid Body Motion
So far in this chapter, we have looked at translational and rotational motion separately. It's
time now to put the two together to describe what is known as
rigid body motion
—the general
motion of an object that is traveling through space and rotating at the same time. Combined
rotational and translational motion will happen quite frequently in game programming situ-
ations. When a pitcher throws a baseball, it will be spinning as it flies towards the catcher
(unless it is a knuckleball). Golf balls, tennis balls, footballs, and hockey pucks will usually be
tumbling or spinning as they travel through the air.
Fortunately, while the overall motion of an object, like the flight of a curveball, can seem
quite complicated, for modeling purposes the overall motion can be separated into transla-
tional and rotational components, and the two components can be analyzed independently.
To separate the translational and rotational motion components, we need to be familiar with a
concept known as the
center of mass
, discussed next.
Center of Mass
According to Newton's second law, the acceleration of an object is a function of the mass of the
object and the external forces applied to the object. The size of the object does not enter into
the equation. The acceleration of a basketball will be the same as that of a marble if the two
objects have the same mass and are subject to the same net external force.
