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What I want to do
now is figure out,

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what's the minimum
speed that the car has

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to be at the top of this
loop de loop in order

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to stay on the track?

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In order to stay in
a circular motion.

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In order to not
fall down like this.

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And I think we
can all appreciate

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that is the most difficult part
of the loop de loop, at least

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in the bottom half
right over here.

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The track itself
is actually what's

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providing the centripetal force
to keep it going in a circle.

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But when you get
to the top, you now

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have gravity that is
pulling down on the car,

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almost completely.

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And the car will have to
maintain some minimum speed

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in order to stay in
this circular path.

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So let's figure out what
that minimum speed is.

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And to help figure
that out, we have

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to figure out what the radius of
this loop de loop actually is.

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And it actually does not
look like a perfect circle,

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based on this little screen
shot that I got here.

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It looks a little
bit elliptical.

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But it looks like the radius
of curvature right over here

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is actually smaller
than the radius

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of the curvature of the
entire loop de loop.

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That if you made
this into a circle,

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it would actually be maybe
even a slightly smaller circle.

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But let's just assume, for
the sake of our arguments

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right over here, that this
thing is a perfect circle.

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And it was a perfect
circle, let's think

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about what that
minimum velocity would

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have to be up here at the
top of the loop de loop.

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So we know that the magnitude
of your centripetal acceleration

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is going to be equal
to your speed squared

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divided by the
radius of the circle

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that you are going around.

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Now at this point
right over here,

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at the top, which is
going to be the hardest

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point, the magnitude
of our acceleration,

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this is going to be 9.81
meters per second squared.

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And the radius,
we can estimate--

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I copied and pasted
the car, and it

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looks like I can get it to stack
on itself four times to get

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the radius of this
circle right over here.

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And I looked it up on the
web, and a car about this size

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is going to be about
1.5 meters high

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from the bottom of the
tires to the top of the car.

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And so it looks like--
just eyeballing it

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based on these copying
and pasting of the cars,

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that the radius of this
loop de loop right over here

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is 6 meters.

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So this right over
here is 6 meters.

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So you multiply both
sides by 6 meters.

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Or actually, we could keep
it just in the variables.

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So let me just rewrite
it-- just to manipulate it

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so we can solve for v. We have
v squared over r is equal to a.

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And then you multiply
both sides by r.

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You get v squared is
equal to a times r.

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And then you take the principal
square root of both sides.

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You get v is equal to
the principal square root

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of a times r.

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And then if we plug
in these numbers,

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this velocity that we
have to have in order

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to stay in the circle is going
to be the square root of 9.81

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meters per second
squared, times 6 meters.

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And you can verify that
these units work out.

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Meters times meters is meter
squared, per second squared.

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You take the square
root of that,

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you're going to get
meters per second.

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But let's get our calculator
out to actually calculate this.

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So we are going to get
the principal square root

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of 9.81 times 6 meters.

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It gives us-- now here's
our drum roll-- 7.67.

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I'll just round to three
significant digits,

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7.67 meters per second squared.

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And significant digits
is a whole conversation,

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because this is just a very,
very rough approximation.

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I'm not able to measure
this that accurately at all.

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But I get roughly 7
point-- I'll just round,

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7.7 meters per second.

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So this is approximately
7.7 meters per second.

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And just to give a sense
of how that translates

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into units that we're used
to when we're driving cars,

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we can convert 7.7
meters per second.

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If we want to say how many
meters we go to an hour,

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well, there's 3,600
seconds in an hour.

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And then if you want to
convert that into kilometers--

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this will be in meters--
you divide by 1,000.

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One kilometer is
equal to 1,000 meters.

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And you see here,
the units cancel out.

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You have meters, meters,
seconds, seconds.

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You're left with
kilometers per hour.

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So let's actually
calculate this.

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And so we get our
previous answer.

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We want to multiply
it times 3,600

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to figure out how many
meters in an hour.

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And then you divide
by 1,000 to convert it

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to kilometers per hour.

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So you divide by 1,000.

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And we get 27.6
kilometers per hour.

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So this is equal
to 27.6 kilometers

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per hour, which is
surprisingly slow.

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I would have thought
it would have

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to be much, much, much faster.

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But it turns out, it does not
have to be much, much faster.

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Only 27.6 kilometers per hour.

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Now the important
thing to keep in mind

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is this is just fast
enough, at this point,

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to maintain the circular motion.

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But if this were a perfect
circle right over here,

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and you were going at exactly
27.6 kilometers per hour,

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you would not have much
traction with the road.

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And if you don't have much
traction with the road,

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the car might slip
and might not be

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able to actually
maintain its speed.

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So you definitely
want your speed

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to be a good bit larger
than this in order

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to keep a nice
margin of safety--

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in order to especially
have traction

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with the actual loop
de loop, and to be

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able to maintain your speed.

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Now what I want to
do in the next video

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is actually time the car to
figure out how long does it

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take it to do this loop de loop.

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And we're going to assume
that it's a circle.

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And we're going
to figure it out.

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And we're going to
figure out how fast

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it's actual average velocity
was over the course of this loop

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de loop.