WEBVTT
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This is College Physics
Answers with Shaun Dychko.
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This trailer wheel is rotating
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and it's going to rotate
through a certain angle *theta*,
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and we're going to figure out
what that angle is in radians
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because after we have radians we can
multiply that by the radius of the wheel
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to get the total arc
length traveled.
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That arc length is the distance
traveled by the trailer wheel.
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So we have this definition
for change in angle.
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It is the arc length
divided by the radius
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and this *d* up here is the diameter
of the wheel, it's not distance.
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That's diameter and we divide
that by two to get the radius.
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So we have 0.575 meters
radius for the wheel
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and we'll rearrange this
formula to solve for *delta s*
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by multiplying both sides by *r*.
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We get *delta s* which is the distance
traveled by the trailer wheel
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is the change in the angle
multiplied by its radius.
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So we have two hundred thousand
revolutions converted into radians
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by multiplying by two pi
radians per revolution
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and we multiply that
by 0.575 meters.
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We get this many meters traveled
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and we multiply that by one
kilometer for every 1000 meters
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and we end up with
723 kilometers
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is what the hub
odometer should read.