Game Development Reference
In-Depth Information
In other words, a body at rest will stay at rest unless acted upon by an external force.
Similarly, a body traveling in a straight line, what Newton called a “right line,” will maintain a
constant velocity unless acted upon by an external force. The ability of an object to resist a
change in its motion is called the
inertia
of the object. Newton determined that the inertia of
an object is proportional to its mass. This observation is pretty obvious if you think about it. It's
a lot easier to stop a skateboard than it is to stop a car because the car has a greater mass and
therefore more inertia than the skateboard.
Newton's Second Law of Motion: Force, Mass, and Acceleration
The best known of Newton's laws of motion is his second law, which relates a force applied to
an object to the resulting acceleration of the object. An acceleration represents a change in
velocity, so a net applied force changes the velocity of an object. In the
Principia
Newton wrote
The alteration of motion is ever proportional to the motive force impressed:
and is made in the direction of the right line in which that force is impressed.
Newton's second law says that an acceleration of an object is due to a net external force
applied to the object. Force, therefore, is proportional to acceleration. The inertia of the object,
which is proportional to the mass of the object, resists the acceleration, so the force required to
achieve a given acceleration is proportional to the mass of the object as well. Stated mathemat-
ically, Newton's second law takes a very simple and familiar form:
Fma
=
(3.1)
We can see from Equation (3.1) that a force applied to an object is proportional to the
acceleration of the object. The amount of acceleration due to an applied force depends on the
object's mass. If the same force is applied, a bowling ball with a mass of 5
kg
will accelerate
twice as fast as one with a mass of 10
kg
. It is also important to remember that the force term that
appears in Newton's second law is the net force on an object. If equal forces are applied to an
object in opposite directions, the net force on the object, and therefore its acceleration, is equal
to zero.
The units of force are
pounds
in the English System of Units and (appropriately)
Newtons
in the International System of Units. These units are often abbreviated as
lb
and
N
. As we saw
in Chapter 2, a Newton is equivalent to a
kg-m/s
2
. The units for mass are
kg
in the SI system and
slugs
or
pound
-
mass
in the English system. Acceleration has units of
ft/s
2
in the English system
and
m/s
2
in the SI system. For the most part in this topic, the SI system of units will be used.
SI units are more consistent and easier to work with, and are the standard for scientific endeavors.
If you really want to use English units, you can use the conversion factors given in Chapter 2.
We will use Newton's second law in most of the physics models we will develop throughout
this topic—everything from the motion of bullets to basketballs to boats can be modeled with
the help of Newton's second law.
Weight and Mass
Before we leave the discussion of Newton's second law, let's spend a little time talking about
the distinction between weight and mass. Mass is what is known as an
intrinsic property
of an
object, meaning it is a property that is essential to the object and doesn't change. For example,
