ShmoopTube

00:03

Here’s your shmoop du jour, brought to you by “riding a motorcycle.”

00:07

It’s…just like riding a bike. But with the added near-certainty of serious injury.

00:13

A bicycle that has tires with a diameter of 2 feet travels half a mile.

00:18

How many rotations does each tire make? There are 5,280 feet in one mile.

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Round answer to the nearest whole number.

00:27

So what we’re looking for is the number of rotations…

00:31

Well, cleverly, let’s call that… n.

00:33

That n for…number of rotations.

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All right, we want to know how many times the full circle rotates over the course of its journey,

00:42

so the circumference of the tire… times n… equals a half a mile.

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If there are 5,280 feet in a mile, then in a half mile that's...

00:53

5,280 over 2...that's 2,640.

00:58

We know the circumference of a circle is diameter times pi...

01:03

…so 2 – the diameter of our tire…times pi times n…equals 2,640.

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We want n by itself, so we divide both sides of the equation by 2 pi to get n equals 2,640 over 2 pi.

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Now it’s time to put our calculator to work.

01:24

2,640 divided by 2 pi comes out to 420.38…

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or, when rounded to the nearest whole number… 420 rotations.

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Wow… you had so much fun counting tire rotations you barely even remember how you got here.

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