PHYS 121 Mechanics
Chapter 0
Chapter 0
MECHANICS:
The Motion of Bodies and how the Motion Depends on the
Forces Acting on those Bodies
WHAT IS A
BODY
?
For this course, we usually refer to blocks of wood, cars, air particles,
planets, even people, etc.
This is something fairly solidly held together (even rigid) so that
when we talk about its position, we have some idea of where the body is.
The location or
position of a blob of ink spilled onto the floor is harder to describe, although we will talk about
flexible bodies like ropes before long (and short ropes before long ones).
WHAT IS
MOTION
?
To talk about motion, we start with the body’s
position
and how it
changes in time.
So we need the
velocity
(the time rate of change of position), and, because
of the interaction story you’ll read below, we also need the
acceleration
(the time rate of
change of velocity) of the body.
By the way, the position implies the coordinate location of
some point defined on the body (a great choice will be the “center of mass” – see much later).
This also brings us to digress about basic units of position and time measurements (meters,
seconds, and all that).
Units:
The primary units are SI meters
m
, seconds
s
, and kilograms
kg
for lengths, times, and
masses (SI
System Internationale where we will use “
≡
≡
” to mean “defined by” or “equivalent to” or
“means”). The littler units come in the “cgs” system and are centimeters cm, seconds, and grams g (1m
= 100cm, 1kg=1000g). We’ll say more about units in a moment, including a really ugly discussion that
many people even avoid because it seems so awful.
WHAT IS
FORCE
?
Well, a body
accelerates
(changes its velocity, as we said) because there
is some
interaction
between it and another body (some influence on its motion due to another
body).
Why?
Well, this is what is behind Newton’s laws.
We think a neat way to start this
introductory physics course in mechanics is to show you Newton’s three laws straightaway.
Why?
Well, because everything we do in this course can be explained, can be derived, from
them.
We describe the strength and direction of this interaction by "numbers."
In our full three-
dimensional (3D) world, there are three numbers needed for each position, velocity, and
acceleration, in view of the three directions, which defines “vectors” for each.
(We will have a
more detailed discussion of vectors as we go.)
We thus have a vector associated with the
interactions; force is the name we use for this vector.
The vector corresponding to the three interaction numbers is the "force" vector
.
[
F
F
G
G
is a nice
notation connected to the fact that the 3 numbers (the “components” in all three directions) also
can be described in terms of a direction and a magnitude.
So we often use
,
r
G
v
G
,
a
G
for the
position, velocity, and acceleration, too.]
The idea that a body accelerates only if there is some
interaction on it can be rephrased in two equivalent ways:
VECTOR STATEMENT: