Game Development Reference

In-Depth Information

Now, the total weight of the body is:

W
total
= W
car
+ W
driver
+ W
fuel

W
total
= 17,500 N + 850 N + 993 N = 19,343 N

To get the mass of the body, you simply divide the weight by the acceleration due to

gravity.

M
total
= W
total/
g = 19,343 N /(9.81 m/s
2
) = 1972 kg

The next mass property we want is the location of the center of gravity of the body. In

this example we will calculate the centroid relative to the global origin. We will also apply

the first moment formula twice, once for the
x
coordinate and again for the
y
coordinate:

X
cg
body
= {(x
cg car
)(W
car
) + (x
cg driver
)(W
driver
) + (x
cg fuel
)

(W
fuel
)} / W
total

X
cg body
= {(30.50 m)(17,500 N) + (31.50 m)(850 N) + (28.00 m)

(993 N)} / 19,343 N

X
cg
body
= 30.42 m

Y
cg
body
= {(y
cg car
)(W
car
) + (y
cg driver
)(W
driver
) + (y
cg fuel
)

(W
fuel
)} / W
total

Y
cg body
= {(30.50 m)(17,500 N) + (31.00 m)(850 N) + (30.50 m)

(993 N)} / 19,343 N

Y
cg
body
= 30.52 m

Notice that we used weight in these equations instead of mass. Remember we can do

this because the acceleration due to gravity built into the weight value is constant and

appears in both the numerator and denominator, thus canceling out.

Now it's time to calculate the mass moment of inertia of the body. This is easy enough

in this 2D example since we have only one rotational axis, coming out of the paper, and

thus need only perform the calculation once. The first step is to calculate the local

moment of inertia of each component about its own neutral axis. Given the limited

information we have on the geometry and mass distribution of each component, we

will make a simplifying approximation by assuming that each component can be rep‐

resented by a rectangular cylinder, and will thus use the corresponding formula for

moment of inertia from
Figure 1-5
. In the equations to follow, we'll use a lowercase
w

to represent width so as to not confuse it with weight, where we've been using a capital

W
.

I
o car
= (m/12) (w
2
+ L
2
)