# Calculating the rotation in radians of a circle rolling x distance

Okay, this is my first attempt at posting a question on this site, so please be forgiving.

Let's say I have a circle with 120cm diameter and it rolls a distance of 1 meter. How do I calculate the rotation it has made in radians?

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Hint: How long is the arc subtended by 1 radian on this circle? (Consider the defintion of radian.)

Then compute how many such arcs the circle will have to "roll through" to go 1 meter.

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A radian is the ratio of the arc of a circle compared to it's radius.

The length of the arc would be the distance rolled and the radius is half your diameter.

distance / radius = radians 100cm / 60cm = 1.6 radians

(Corrected by backwards maths, thanks Zev)

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Your ratio is backwards: one radius length is 60cm, which is less than 1m = 100cm, so it is going through more than 1 radian. The correct answer is $\frac{5}{3}$ radians. –  Zev Chonoles Oct 12 '11 at 11:44