Game Development Reference

In-Depth Information

These laws form the basis for much of the analysis in the field of mechanics. Of particular

interest to us in the study of dynamics is the second law, which is written:

F = ma

where
F
is the resultant force acting on the body,
m
is the mass of the body, and
a
is the

linear acceleration of the body's center of gravity. We'll discuss this second law in greater

detail later in this chapter, but before that there are some more fundamental issues that

we must address.

Units and Measures

Over years of teaching various engineering courses, we've observed that one of the most

common mistakes students make when performing calculations is using the wrong units

for a quantity, thus failing to maintain consistent units and producing some pretty wacky

answers. For example, in the field of ship performance, the most commonly misused

unit is that for speed: people forget to convert speed in knots to speed in meters per

second (m/s) or feet per second (ft/s). One knot is equal to 0.514 m/s, and considering

that many quantities of interest in this field are proportional to speed squared, this

mistake could result in answers that are as much as 185% off target! So, if some of your

results look suspicious later on, the first thing you need to do is go back to your formulas

and check their dimensional consistency.

To check dimensional consistency, you must take a closer look at your units of measure

and consider their component dimensions. We are not talking about 2D or 3D type

dimensions here, but rather the basic measurable dimensions that will make up various

derived
units for the physical quantities that we will be using. These basic dimensions

are
mass
,
length
, and
time
.

It is important for you to be aware of these dimensions, as well as the combinations of

these dimensions that make up the other derived units, so that you can ensure dimen‐

sional consistency in your calculations. For example, you know that the weight of an

object is measured in units of force, which can be broken down into component di‐

mensions like so:

F = (M) (L/T
2
)

where
M
is mass,
L
is length, and
T
is time. Does this look familiar? Well, if you consider

that the component units for acceleration are (
L/T
2
) and let
a
be the symbol for accel‐

eration and
m
be the symbol for the mass of an object, you get:

F = ma