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Newton's First Law tells
us that an object at rest

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will stay at rest, and object
with a constant velocity

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will keep having that
constant velocity

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unless it's affected by
some type of net force.

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Or you actually could say an
object with constant velocity

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will stay having a
constant velocity

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unless it's affected
by net force.

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Because really, this
takes into consideration

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the situation where
an object is at rest.

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You could just have
a situation where

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the constant velocity is zero.

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So Newton's First
Law, you're going

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to have your constant velocity.

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It could be zero.

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It's going to stay being
that constant velocity

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unless it's affected,
unless there's

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some net force that acts on it.

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So that leads to the
natural question,

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how does a net force affect
the constant velocity?

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Or how does it affect of
the state of an object?

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And that's what Newton's
Second Law gives us.

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So Newton's Second
Law of Motion.

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And this one is maybe
the most famous.

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They're all kind of
famous, actually.

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I won't pick favorites here.

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But this one gives us
the famous formula force

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is equal to mass
times acceleration.

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And acceleration is
a vector quantity,

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and force is a vector quantity.

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And what it tells us--
because we're saying,

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OK, if you apply
a force it might

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change that constant velocity.

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But how does it change
that constant velocity?

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Well, let's say I have
a brick right here,

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and it is floating in space.

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And it's pretty nice for us
that the laws of the universe--

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or at least in the classical
sense, before Einstein

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showed up-- the laws of
the universe actually dealt

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with pretty simple mathematics.

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What it tells us is if
you apply a net force,

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let's say, on this
side of the object--

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and we talk about net force,
because if you apply two forces

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that cancel out and that
have zero net force, then

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the object won't change
its constant velocity.

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But if you have a
net force applied

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to one side of this
object, then you're

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going to have a net acceleration
going in the same direction.

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So you're going to have
a net acceleration going

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in that same direction.

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And what Newton's
Second Law of Motion

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tells us is that acceleration
is proportional to the force

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applied, or the force
applied is proportional

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to that acceleration.

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And the constant
of proportionality,

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or to figure out what you have
to multiply the acceleration by

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to get the force, or what you
have to divide the force by

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to get the acceleration,
is called mass.

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That is an object's mass.

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And I'll make a
whole video on this.

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You should not confuse
mass with weight.

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And I'll make a whole
video on the difference

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between mass and weight.

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Mass is a measure of
how much stuff there is.

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Now, that we'll
see in the future.

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There are other things
that we don't normally

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consider stuff that
does start to have mass.

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But for our classical, or at
least a first year physics

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course, you could
really just imagine

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how much stuff there is.

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Weight, as we'll see
in a future video,

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is how much that stuff
is being pulled down

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by the force of gravity.

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So weight is a force.

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Mass is telling you how
much stuff there is.

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And this is really neat that
this formula is so simple,

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because maybe we could have
lived in a universe where force

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is equal to mass squared
times acceleration times

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the square root of acceleration,
which would've made all

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of our math much
more complicated.

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But it's nice.

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It's just this constant
of proportionality right

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over here.

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It's just this nice
simple expression.

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And just to get our feet wet
a little bit with computations

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involving force, mass,
and acceleration,

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let's say that I have a force.

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And the unit of force
is appropriately

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called the newton.

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So let's say I have a
force of 10 newtons.

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And just to be clear, a
newton is the same thing

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as 10 kilogram meters
per second squared.

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And that's good that a newton
is the same thing as kilogram

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meters per second squared,
because that's exactly what you

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get on this side of the formula.

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So let's say I have a
force of 10 newtons,

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and it is acting on a mass.

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Let's say that the
mass is 2 kilograms.

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And I want to know
the acceleration.

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And once again, in this video,
these are vector quantities.

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If I have a positive
value here, we're

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going to make the assumption
that it's going to the right.

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If I had a negative value, then
it would be going to the left.

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So implicitly I'm
giving you not only

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the magnitude of the
force, but I'm also

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giving you the direction.

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I'm saying it is to the
right, because it is positive.

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So what would be acceleration?

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Well we just use f equals ma.

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You have, on the
left hand side, 10.

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I could write 10
newtons here, or I

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could write 10 kilogram
meters per second squared.

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And that is going to be
equal to the mass, which

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is 2 kilograms times
the acceleration.

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And then to solve
for the acceleration,

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you just divide both
sides by 2 kilograms.

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So let's divide the
left by 2 kilograms.

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Let me do it this way.

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Let's divide the
right by 2 kilograms.

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That cancels out.

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The 10 and the 2, 10
divided by 2 is 5.

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And then you have kilograms
canceling with kilograms.

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Your left hand side, you get
5 meters per second squared.

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And then that's equal
to your acceleration.

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Now just for fun, what happens
if I double that force?

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Well then I have 20 newtons.

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Well, I'll actually work it out.

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Then I have 20 kilogram
meters per second squared

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is equal to-- I'll
have to color code--

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2 kilograms times
the acceleration.

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Divide both sides by 2
kilograms, and what do we get?

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Cancels out.

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20 divided by 2 is 10.

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Kilograms cancel kilograms.

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And so we have the
acceleration, in this situation,

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is equal to 10 meters
per second squared

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is equal to the acceleration.

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So when we doubled the force--
we went from 10 newtons

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to 20 newtons-- the
acceleration doubled.

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We went from 5 meters
per second squared

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to 10 meters per second squared.

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So we see that they are
directly proportional,

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and the mass is that how
proportional they are.

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And so you could imagine what
happens if we double the mass.

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If we double the mass in this
situation with 20 newtons,

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then we won't be dividing
by 2 kilograms anymore.

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We'll be dividing
by 4 kilograms.

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And so then we'll have 20
divided by 4, which would be 5

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and would be meters
per second squared.

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So if you make the mass
larger, if you double it,

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then your acceleration
would be half as much.

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So the larger the mass
you have, the more force

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you need to accelerate it.

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Or for a given force, the less
that it will accelerate it,

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the harder it is to change
its constant velocity.

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