Game Development Reference

In-Depth Information

(M L
2
L
2
) / (L
3
T
2
)

Canceling dimensions that appear in both the numerator and denominator yields:

M (L/T
2
)

which is consistent with the form shown earlier for resistance,
R
f
. This exercise also

reveals that the empirical term,
C
f
, for the coefficient of friction must be nondimensional

—that is, it is a constant number with no units.

With that, let's take a look at some more common physical quantities that you will be

using along with their corresponding symbols, component dimensions, and units in

both the SI and English systems. This information is summarized in
Table 1-1
.

Table 1-1. Common physical quantities and units

Quantity Symbol Dimensions Units, SI Units, English

Acceleration, linear A L/T
2
m/s
2
ft/s
2

Acceleration, angular α
radian/T
2
radian/s
2
radian/s
2

Density ρ
M/L
3
kg/m
3
slug/ft
3

Force F
M (L/T
2
)
newton, N pound, lbs

Kinematic viscosity ν
L
2
/T m
2
/s ft
2
/s

Length L (or x, y, z) L meters, m feet, ft

Mass m M kilogram, kg slug

Moment (torque)
M
a
M (L
2
/T
2
)
N-m ft-lbs

Mass Moment of Inertia I
M L
2
kg-m
2
lbs-ft-s
2

Pressure P
M/(L T
2
) N/m
2
lbs/ft
2

Time T T seconds, s seconds, s

Velocity, linear V L/T m/s ft/s

Velocity, angular ω radian/T radian/s radian/s

Viscosity µ M/(L T)
N s/m
2
lbs • s/ft
2

a
In general, we will use a capital
M
to represent a moment (torque) acting on a body and a lowercase
m
to represent the mass of

a body. If we're referring to the basic dimension of mass in a general sense—that is, referring to the dimensional components of

derived units of measure—we'll use a capital
M
. Usually, the meanings of these symbols will be obvious based on the context in

which they are used; however, we will specify their meanings in cases where ambiguity may exist.

Coordinate System

Throughout this topic we will refer to a standard,
right-handed
Cartesian coordinate

system when specifying positions in 2D or 3D space. In two dimensions we will use the

coordinate system shown in
Figure 1-1
(a), where rotations are measured positive coun‐

terclockwise.