Understanding about differentials?

[DannyPhysika]

Homework Statement

Problem 7.29:

http://cas.umkc.edu/physics/wrobel/phy240/Homework 5.pdf

Homework Equations

dr= R d(theta)

The Attempt at a Solution

I don't understand how to get R d(theta) = dr from the last part of the question, any explanation about how it works is appreciated.

 

[clementc]

It's a formula from radian measure. Basically if you have the angle $$\theta$$ in radians, you can find the arc length by the formula:
$$l=r\theta$$
So if you have a differential amount of $$\theta$$, you can find a differential amount of arc length which is just $$dl=rd\theta$$