Game Development Reference
In-Depth Information
Because “size doesn't matter” when it comes to Newton's second law, the translational
motion that results from an external force on an object can be modeled as if the object were
shrunk to an infinitesimally small particle located at a point known as the
center of mass
of the
object. For symmetrical objects made from a uniform distribution of material, the center of
mass will be located at the center of the object. For example, the center of mass for a solid
copper sphere would be located at the center of the sphere. The center of mass is also some-
times referred to as the
center of gravity
, because the force of gravity will always act through
the center of mass.
The concept of the center of mass is useful for separating the linear motion of an object
from its rotational motion. When computing the linear motion of an object, Newton's second
law, and the resulting acceleration and velocity, can be applied to the center of mass of the
object. Even if an object is rotating, its center of mass moves as if it were a particle. This can be
very handy when modeling the motion of an object that is rotating in that it allows the separa-
tion of the linear motion computations from the rotational motion computations. For example,
consider the case of a knife being thrown towards a target as shown in Figure 4-10. Even though
the knife may be spinning through the air in what looks like a very complicated motion, if you
could follow the path of the center of mass, you would see that it follows a smooth, parabolic
trajectory.
Figure 4-10.
The center of mass of the knife travels in a smooth curve.
Computing the center of mass for nice, simple, symmetrical objects is quite easy, but what
about more complicated shapes like an airplane? One way to think of the center of mass is that
it is the point of zero net torque. It is this point at which an object will be perfectly balanced in
space. Sometimes the center of mass for a complicated object can be computed analytically or
sometimes it can be found experimentally. An interesting characteristic about the center of
mass is that, depending on the geometry and composition of an object, it's possible for the
center of mass to lie outside of the object. For example, the center of mass of the L-shaped
figure shown in Figure 4-11 is in the empty space between the two legs.
Determination of the center of mass is complicated even further if the object has a nonuni-
form distribution of mass or can change its orientation. The center of mass for a person, for
example, will change if the person bends over or raises her leg. Center of mass considerations
can also be applied to systems of objects. When computing the center of mass of a boat, for
example, it is important to include the contributions due to any passengers who might be on
the boat. If the passengers on the boat move around the deck, the center of mass of the boat
(and possibly the stability of the boat) will change as well.
