Understanding about differentials?

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The discussion focuses on understanding the relationship between arc length and angular displacement in the context of differentials. The formula dr = R d(theta) is derived from the concept that the arc length (l) can be expressed as l = rθ, where θ is in radians. A differential change in angle, dθ, leads to a differential change in arc length, dl = r dθ. The confusion arises in applying this relationship to the problem at hand. Clarification on how to transition from the general formula to the specific differential form is sought.
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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.
 
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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
 

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