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?
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.
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)