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Welcome to the presentation
on moments.

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So just if you were
wondering, I have

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already covered moments.

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You just may not have recognized
it, because I

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covered it in mechanical
advantage and torque.

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But I do realize that when I
covered it in mechanical

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advantage and torque, I think
I maybe over-complicated it.

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And if anything, I didn't cover
some of the most basic

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moment to force problems that
you see in your standards

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physics class, especially
physics classes that aren't

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focused on calculus or going
to make you a mechanical

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engineer the very next year.

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So we did that with-- why did
I write down the word

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"mechanical?" Oh yeah,
mechanical advantage.

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If you do a search for
mechanical advantage, I cover

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some things on moments
and also on torque.

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So what is moment of force?

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Well, it essentially is the
same thing as torque.

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It's just another word for it.

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And it's essentially force times
the distance to your

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axis of rotation.

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What do I mean by that?

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Let me take a simple example.

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Let's say that I have
a pivot point here.

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Let's say I have some type
of seesaw or whatever.

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There's a seesaw.

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And let's say that I were to
apply some force here and the

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forces that we care about-- this
was the exact same case

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with torque, because there's
essentially the same thing.

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The forces we care about
are the forces that are

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perpendicular to the distance
from our axis of rotation.

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So, in this case, if we're here,
the distance from our

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axis of rotation is this.

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That's our distance from
our axis of rotation.

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So we care about a perpendicular
force, either a

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force going up like that or a
force going down like that.

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Let's say I have a force
going up like that.

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Let's call that F, F1, d1.

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So essentially, the moment of
force created by this force is

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equal to F1 times d1, or the
perpendicular force times the

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moment arm distance.

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This is the moment
arm distance.

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That's also often called the
lever arm, if you're talking

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about a simple machine, and I
think that's the term I used

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when I did a video on
torque: moment arm.

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And why is this interesting?

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Well, first of all, this force
times distance, or this moment

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of force, or this torque, if it
has nothing balancing it or

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no offsetting moment or torque,
it's going to cause

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this seesaw in this example to
rotate clockwise, right?

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This whole thing, since it's
pivoting here, is going to

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rotate clockwise.

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The only way that it's not going
to rotate clockwise is

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if I have something keep-- so
right now, this end is going

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to want go down like that, and
the only way that I can keep

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it from happening is if I exert
some upward force here.

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So let's say that I exert some
upward force here that

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perfectly counterbalances, that
keeps this whole seesaw

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from rotating.

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F2, and it is a distance d2
away from our axis of

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rotation, but it's going in a
counterclockwise direction, so

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it wants to go like that.

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So the Law of Moments
essentially tells us, and we

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learned this when we talked
about the net torque, that

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this force times this distance
is equal to this force times

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this distance.

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So F1 d1 is equal to F2 d2, or
if you subtract this from both

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sides, you could get F2 d2 minus
F1 d1 is equal to 0.

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And actually, this is how we
dealt with it when we talked

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about torque.

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Because just the convention with
torque is if we have a

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counterclockwise rotation, it's
positive, and this is a

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counterclockwise rotation
in the example

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that I've drawn here.

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And if we have a clockwise
rotation, it has a negative

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torque, and that's just the
convention we did, and that's

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because torque is a
pseudovector, but I don't want

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to confuse right now.

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What you'll see is that these
moment problems are actually

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quite, quite straightforward.

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So let's do a couple.

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It always becomes a lot easier
when you do a problem, except

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when you try to erase
things with green.

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So let's say that --
let me plug in real

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numbers for these values.

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Let me erase all of this.

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Let me just erase everything.

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There you go.

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All right, let me draw
a lever arm again.

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So what we learned when we
learned about torque is that

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an object won't rotate if the
net torque, the sum of all the

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torques around it, are zero,
and we're going to apply

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essentially that same
principle here.

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So let's do it with masses,
because I think that helps

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explain a lot of things and
makes this seesaw example a

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little bit more tangible.

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Let's say I have a 5-kilogram
mass here, and let's say that

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gravity is 10 meters
per second squared.

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So what is the downward
force here?

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What is the downward force?

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It's going to be the mass times
acceleration, so it's

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going to be 50 Newtons.

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And let's say that the distance,
the moment arm

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distance or the lever arm
distance here, let's say that

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this distance right
here is 10 meters.

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Let's say that I have
another mass.

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Let's say it's a 25 kilogram--
no, that's too much.

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Let's say it's 10 kilograms.
Let's say I have

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a 10-kilogram mass.

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And I want to place it some
distance d from the fulcrum or

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from the axis of rotation so
that it completely balances

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this 5-kilogram mass.

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So how far from the axis of
rotation do I put this

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10-kilogram mass?

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This is the distance, right?

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Because we actually carry
the distance to the

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center of the mass.

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Well, how much force
is this 10-kilogram

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mass exerting downwards?

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Well, it's 10 kilograms times 10
meters per second squared,

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it's 100 Newtons.

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This is acting what?

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This is acting clockwise,
right?

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This one's acting clockwise
and this one's acting

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counterclockwise, right?

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So they are offsetting
each other.

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So we could do it a
couple of ways.

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We could say that 50 Newtons,
the moment in the

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counterclockwise direction, 50
Newtons times 10 meters, in

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order for this thing to not
rotate has to be equal to the

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moment in the clockwise
direction.

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And so the moment in the
clockwise direction is equal

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to 100 Newtons times some
distance, let's call that d,

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100 Newtons times d, and
then we could just

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solve for d, right?

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We get 50 times 10 is 500.

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500 Newton-meters is equal
to 100 Newtons times d.

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That's 100.

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Divide both sides by 100, you
get 5 meters is equal to d.

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So d is equal to 5.

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That's interesting.

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And I think this kind of
confirms your intuition from

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playing at the playground that
you can put a heavier weight

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closer to the axis of rotation
to offset a light weight

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that's further away.

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Or the other way to put it is
you could put a light weight

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further away and you kind of get
a mechanical advantage in

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terms of offsetting the
heavier weight.

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So let's do a more difficult
problem.

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I think the more problems we
do here, the more sense

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everything will make.

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So let's say that we have
a bunch of masses.

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Actually, let's not
do it with masses.

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Let's just do it with forces
because I want to

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complicate the issue.

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So this is the pivot.

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And let's say I have a force
here that's 10 Newtons going

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in the clockwise direction, and
let's say it is at-- let's

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say if this is 0, let's say that
this is at minus 8, so

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this distance is 8, right?

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Let's say that I have another
force going down at 5 Newtons.

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And let's say that its
x-coordinate is minus 6.

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Let's say I have another force
that's going up here, and

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let's say that it
is 50 Newtons.

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This might get complicated.

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50 Newtons, and it's at minus
2, so this distance

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right here is 2.

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Let's say that I need to figure
out-- and I'm making

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this up on the fly.

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Let's say that I have another
force here that is 5 Newtons.

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No, let's make it a weird
number, 6 Newtons, and this

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distance right here
is 3 meters.

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And let's say that I need to
figure out what force I need

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to apply here upwards or
downwards-- I actually don't

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know, because I'm doing this on
the fly-- to make sure that

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this whole thing
doesn't rotate.

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So to make sure this whole
thing doesn't rotate,

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essentially what we have to
say is that all of the

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counterclockwise moments or all
of the counter clockwise

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torques have to offset all
of the clockwise torques.

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And notice, they're not
all on the same side.

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So what are all of the things
that are acting in the

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counterclockwise direction?

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So counter clockwise
is that way, right?

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So this is acting
counterclockwise, this is

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acting counterclockwise,
and that's it, right?

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So the other ones
are clockwise.

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And we don't know this one.

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Let's assume for a second.

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We could assume either way.

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And if we get a negative, that
means it's the opposite.

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So let's assume that this is a--
all of the clockwise ones

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I'll do in this dark brown.

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Let's assume this is clockwise,
let's assume that

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this is clockwise, and let's
assume that our mystery force

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is also clockwise.

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All of the counterclockwise
moments have to offset all the

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clockwise moments.

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So what are the counterclockwise
moments?

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Well, this one's
counterclockwise, so it's 10

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Newtons, 10 times its distance
from its moment arm.

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We said it's 8, because it's
at the x-coordinate minus 8

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from 0, so it's 10
times 8, plus 50.

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This is also counterclockwise
times 6, 50 times 6, and those

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are all of our counterclockwise
moments and

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that has to equal the
clockwise moments.

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So clockwise moments,
let's see.

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We have 5 Newtons that's going
clockwise times 6.

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5 Newtons.

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Actually, was this 6?

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No, if this is 6, I must have
written some other number here

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that I can't read now.

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How far did I say this was?

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Let's say that this is 2.

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So that 50, let's say this is
2, it's negative 2, because

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that's what it looks like.

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I apologize for confusing you.

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So what were all the
counterclockwise moments?

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This 10 Newtons times its
distance 8, the 50 Newtons

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times this distance, 2.

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Don't get confused
by the negative.

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I just kind of said we're in
the x-coordinate axis or at

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minus 8 if this is 0, but it's
8 units away, right?

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And this 50, its moment arm
distance is 2 units.

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So that has to equal all of
the clockwise moments.

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So the clockwise moments
is 5 Newtons times 6.

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Its distance is 6 and it's
5 Newtons going in

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the clockwise direction.

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And then we have plus
6 Newtons times 3,

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plus 6 times 3.

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And then we're just assuming,
we don't know for sure.

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Let's say we're applying
the force.

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I should have told you
ahead of time so you

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could do this problem.

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Let's say that we're applying
the force at 10 meters away

247
00:12:20,430 --> 00:12:21,480
from our fulcrum arm.

248
00:12:21,480 --> 00:12:23,140
So force times 10.

249
00:12:23,140 --> 00:12:25,240
So now let's just solve
for the force.

250
00:12:25,240 --> 00:12:35,310
We get 80 plus 100 is equal
to 30 plus 18 plus 10F.

251
00:12:35,310 --> 00:12:40,950
We get 180 is equal
to 48 plus 10F.

252
00:12:40,950 --> 00:12:42,500
What's 180 minus 48?

253
00:12:42,500 --> 00:12:50,350
It's 132 is equal to
10F, or we get F is

254
00:12:50,350 --> 00:12:54,780
equal to 13.2 Newtons.

255
00:12:54,780 --> 00:12:59,530
So we guessed correctly that
this is going to be a-- sorry,

256
00:12:59,530 --> 00:13:03,490
this is going to be a-- I keep
mixing up all of the clockwise

257
00:13:03,490 --> 00:13:04,740
and counterclockwise.

258
00:13:04,740 --> 00:13:06,670


259
00:13:06,670 --> 00:13:09,360
This is going to be
a clockwise force.

260
00:13:09,360 --> 00:13:11,540
These were all of the-- sorry,
this is going to be a

261
00:13:11,540 --> 00:13:13,010
counterclockwise force, right?

262
00:13:13,010 --> 00:13:15,040
A clock, this is
counterclockwise.

263
00:13:15,040 --> 00:13:17,140
Let me label that because I
think I said it wrong several

264
00:13:17,140 --> 00:13:19,240
times in the video.

265
00:13:19,240 --> 00:13:23,180
So these go clockwise.

266
00:13:23,180 --> 00:13:26,510


267
00:13:26,510 --> 00:13:29,440
And it's this one
and this one.

268
00:13:29,440 --> 00:13:31,650
And what were the
counterclockwise?

269
00:13:31,650 --> 00:13:34,480
These go counterclockwise.

270
00:13:34,480 --> 00:13:39,830
So we have to apply a 13.10
Newton force 10 meters away,

271
00:13:39,830 --> 00:13:45,380
which will generate 132
Newton-meters moment in the

272
00:13:45,380 --> 00:13:48,410
counterclockwise direction,
which will perfectly offset

273
00:13:48,410 --> 00:13:52,100
all of the other moments, and
our lever will not move.

274
00:13:52,100 --> 00:13:54,280
Anyway, I might have confused
you with all the

275
00:13:54,280 --> 00:13:56,170
counterclockwise/clockwise.

276
00:13:56,170 --> 00:13:58,940
But just keep in mind that all
the moments in one rotational

277
00:13:58,940 --> 00:14:01,270
direction have to offset all
the moments in the other

278
00:14:01,270 --> 00:14:02,510
rotational direction.

279
00:14:02,510 --> 00:14:06,440
All a moment is is the force
times the distance from the

280
00:14:06,440 --> 00:14:11,260
fulcrum arm, so force times
distance from fulcrum arm.

281
00:14:11,260 --> 00:00:00,000
I'll see you in the
next video.