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Newton's first law tells
us about the motion

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of isolated bodies.

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By an "isolated body," we mean
one on which the net force

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is 0, one that's isolated
from all interactions

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to as great a
degree as possible.

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Newton's first law states
that an isolated body

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moves in a straight line
at constant velocity

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and will continue to do so as
long as it remains undisturbed.

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Note that that constant
velocity might be 0.

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So for example, a body at
rest-- an isolated body at rest

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will remain at rest
if left undisturbed.

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An isolated body moving
at constant velocity

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will continue to move
at a constant velocity

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as long as it
remains undisturbed.

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It turns out that it's
always possible to define

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a coordinate system in
which an isolated body moves

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at constant velocity, perhaps 0.

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Such a coordinate system is
called an "inertial coordinate

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system."

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So another way of stating
Newton's first law

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is that inertial
coordinate systems exist.

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Now, it's worth
pointing out that not

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all useful coordinate
systems are inertial.

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The ones that aren't we call
"non-inertial coordinate

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systems."

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As an example, imagine that I am
standing in an elevator that's

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accelerating upward.

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If we defined a
coordinate system that

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moves with the elevator,
that coordinate system

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is accelerated with respect
to an observer who is at rest.

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In that accelerated
coordinate system,

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an isolated body would not
move at a constant velocity.

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So there are
applications where using

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non-inertial coordinate
systems is convenient.

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However, in this course,
we will concentrate

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on inertial coordinate systems
in which isolated bodies move

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at a constant velocity.

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What if the body
is not isolated?

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If a force acts
on a body, then it

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will accelerate in
proportion to that force.

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In particular, for a
point like constant mass,

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Newton's second law tells
us that the vector force

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is equal to the mass times
the vector acceleration.

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So in other words, the
acceleration caused by a force

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is proportional to that
force and the constant

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of proportionality is the mass.

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And there are two
important points

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I want to make about
Newton's second law.

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The first is that
forces always involved

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real physical interactions.

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Something must be
acting on the object.

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If nothing is acting
on the object,

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if the object is
isolated, then we

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know-- from Newton's first law--
that an isolated body never

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accelerates in an
inertial frame.

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It moves at constant velocity.

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So the only way
to have an object

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move with a velocity
that's changing--

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that is, to have
an acceleration--

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is to have a force acting on it.

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And Newton's second law tells
us exactly how that works.

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The second point
I want to make is

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that this statement of Newton's
second law, F equals ma,

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is actually a special case.

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It's for the special case of
a constant point like mass.

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More generally, Newton's second
law is written as the force

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is equal to the time
derivative of the momentum, p.

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Now, we'll talk about momentum
later in this course in more

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detail, but I'll just tell
you that the momentum,

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for a point like
mass, is defined

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as the mass times the velocity.

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Now, for a point
mass that's constant,

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these two equations
are exactly identical.

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If you take the derivative of m
times v where m is a constant,

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you just get m
times the vector a.

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And you get the
first equation back.

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So it's just a fancier way
of writing the same thing.

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It doesn't convey
any new information.

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So why do we talk about this
as being the more general form?

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It's because this second
form of Newton's second law

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can be generalized to a system
of particles or a system

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where mass is flowing and the
mass of something is changing.

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You can't describe
that by F equals ma,

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but it's always true that, for
a given system, F equals dp/dt.

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And we'll see how that works
in more complicated mass flow

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problems later in the course.