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What I want to do in this
video is think about the two

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different ways of
interpreting lowercase g.

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Which as we've talked about
before, many textbooks will

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give you as either 9.81
meters per second squared

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downward or towards
the Earth's center.

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Or sometimes it's given with
a negative quantity that

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signifies the direction, which
is essentially downwards,

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negative 9.81 meters
per second squared.

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And probably the
most typical way

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to interpret this value, as
the acceleration due to gravity

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near Earth's surface for
an object in free fall.

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And this is what we're going
to focus on this video.

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And the reason why I'm
stressing this last part

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is because we know
of many objects that

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are near the surface
of the Earth that

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are not in free fall.

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For example, I am near the
surface of the Earth right now,

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and I am not in free fall.

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What's happening to me right
now is I'm sitting in a chair.

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And so this is my chair--
draw a little stick

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drawing on my chair,
and this is me.

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And let's just
say that the chair

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is supporting all my weight.

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So I have-- my legs
are flying in the air.

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So this is me.

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And so what's
happening right now?

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If I were in free fall,
I would be accelerating

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towards the center of
the Earth at 9.81 meters

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per second squared.

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But what's happening is, all
of the force due to gravity

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is being completely
offset by the normal force

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from the surface of the
chair onto my pants,

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and so this is normal force.

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And now I'll make
them both as vectors.

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So the net force in my
situation-- the net force

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is equal to 0, especially
in this vertical direction.

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And because the net
force is equal to 0,

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I am not accelerating towards
the center of the Earth.

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I am not in free fall.

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And because this 9.81
meters per second squared

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still seems relevant
to my situation--

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I'll talk about
that in a second.

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But I'm not an
object in free fall.

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Another way to interpret this
is not as the acceleration

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due to gravity near
Earth's surface

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for an object in free
fall, although it

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is that-- a maybe more
general way to interpret

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this is the gravitational-- or
Earth's gravitational field.

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Or it's really the average
acceleration, or the average,

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because it actually
changes slightly

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throughout the
surface of the Earth.

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But another way to view this, as
the average gravitational field

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at Earth's surface.

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Let me write it
that way in pink.

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So the average gravitational
field-- and we'll

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talk about what a field
means in the physics

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context in a second-- the
average gravitational field

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at Earth's surface.

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And this is a little bit
more of an abstract thing--

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we'll talk about
that in a second--

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but it does help
us think about how

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g is related to
this scenario where

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I am not an object in free fall.

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A field, when you think of
it in the physics context--

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slightly more
abstract notion when

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you start thinking about it
in the mathematics context--

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but in the physics
context, a field

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is just something that
associates a quantity

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with every point in space.

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So this is just a quantity
with every point in space.

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And it can actually be a
scalar quantity, in which case

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we call it a scalar
field, and in which case

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it would just be a value.

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Or it could be a
vector quantity,

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which would be a magnitude
and a direction associated

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with every point in space.

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In which case you are
dealing with a vector field.

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And the reason why
this is called a field

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is, because at near
Earth's surface,

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if you give me a mass--
so for example-- actually,

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I don't know what my
mass is in kilograms.

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But if you're near
Earth's surface

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and you give me a
mass-- so let's say

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that mass right over
there is 10 kilograms--

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you can use g to figure out
the actual force of gravity

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on that object at
that point in space.

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So for example, if this
has a mass of 10 kilograms,

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then we know-- and
this right over here

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is the surface of the Earth, so
that's the center of the Earth.

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So it actually associates
a vector quantity

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whose magnitude,--
so its direction is

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towards the center of the
Earth, and the magnitude

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of this vector quantity is
going to be the mass times g.

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And you could take--
since we're already

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specifying the
direction, we could

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say 9.81 meters
per second squared

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towards the center of the Earth.

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And so in this
situation, it would

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be 10 kilograms times 9.81
meters per second squared.

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Which is 98.1.

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And even this I've
rounded a little bit,

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so it's actually
approximate number.

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98.1 kilogram meters
per second squared

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which is the unit of
force, or 98.1 newtons.

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And this thing might
not be in free fall,

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so this is why g
is relevant even

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in a situation where the
object isn't in free fall.

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g has given us the
force per unit mass--

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the force per mass of
gravity on an object

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near the surface of the Earth.

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Another way to think
about it-- so this

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is the average gravitational
field, and what it's giving

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is force per mass.

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So you give me a mass
near Earth's surface--

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whether it's an
object in free fall

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or not-- you multiply
that mass times g,

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because it's giving
you force per mass,

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and it will give you the
force of gravity acting

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on that object near the
surface of the Earth,

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whether or not
it's in free fall.

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So I just want to make
this little distinction,

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because although g
tends to be referred

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to this way right over here.

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Sometimes you might
encounter a stickler

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who says oh no, no, no, no,
no but g is relevant even when

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an object is not in free fall.

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You obviously can't say
that my acceleration when

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I'm sitting in my chair is
9.81 meters per second squared

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towards the center of the Earth.

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I am not accelerating towards
the center of the Earth.

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And so they'll say,
oh no, no, no, no,

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you can't just call
this acceleration.

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It is true, it is
the acceleration

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when an object is in free fall
near the surface of the Earth--

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if you don't have really air
resistance, if the net force

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really is the force of
gravity-- then this really

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would be the object's
acceleration.

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But it becomes
relevant, and we know

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most objects that we know
of aren't in free fall.

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Obviously, an object in free
fall doesn't stay in free fall

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for long.

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It eventually hits something.

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But we know that
now g is actually

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relevant to all objects.

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It tells us the force
per mass And it's

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tempting to call it
always acceleration--

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because the units
are acceleration--

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but even when you
talk about in terms

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of the gravitational field,
it's still the same quantity.

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It still has the exact same
units, the same magnitude,

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and the same
direction-- it's just

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a different way of viewing it.

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Here, acceleration for
an object in free fall.

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Here, something to
multiply by mass

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to figure out the
force due to gravity.

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