There's an important distinction to make
between cause and effect when analyzing
the motion of objects.
There are two very separate questions that we can ask.
The first is, how does a particular object move?
This is a purely descriptive geometrical question
that we're asking.
What does the geometry of the motion look like?
If we were to draw its trajectory
as a function of time, what's the shape of that trajectory?
The study of the geometry of motion of a trajectory
is referred to as kinematics.
The second question we can ask is, why does an object
move the way it does?
Why does the kinematic description of the trajectory
look the way it does?
This concerns what the causes are of the motion
and of the changes in that motion.
The study of the cause behind the changes of motion
is called dynamics.
Newton's Second Law of Motion connects these two questions.
When we write F equals ma, this is more than just
a mathematical identity.
Physically, we're connecting two very different questions.
And we can symbolize that by dividing the equation
into its two sides.
The right-hand side, the ma side,
is essentially asking the question of how, how
does the object move?
What does that motion look like?
It's a description, a geometric description
of the object's motion.
The left-hand side of the equation, where the forces are,
answers the question of why, why does the object
move the way it does?
What causes the motion to change?
These are very different conceptually.
And the remarkable thing about Newton's Second Law, in fact,
one of Newton's signature accomplishments
was to realize that these two questions can
be connected in this way through Newton's Second Law of Motion.
Since these are very different issues,
we'll examine them separately in our course.
We'll begin this week by looking at kinematics in one and two
dimensions, basically learning how
to describe the geometric motion of an object
and its trajectory.
We'll follow that by discussing the dynamics of the motion,
examining why an object's motion changes when forces are applied
through a discussion of Newton's laws and their applications.