# How to calculate dA of a circle

1. Jun 7, 2012

1. The problem statement, all variables and given/known data
Hello! I need to calculate a little fraction (dA) of the area of a circle (mass m and radius R and area A) and I have no idea how to do this.

2. Relevant equations
According to my textbook $dm=\frac{M.dA}{A}=\sigma .dA$ and $dA=R.dR.d\theta$.

3. The attempt at a solution
Well, I tried to analyze the problem and my first thought was $dA=\pi dR^2$. This is obviously wrong so I tried to think a little bit more and this is what I got $dA=R.dR$... wrong again.
PS: is there a problem that I post here very often (create new topics)??

Thanks!

Last edited: Jun 7, 2012
2. Jun 7, 2012

### Muphrid

This is a calculus question.

Why does your circle have mass? Do you mean a disc?

You almost had it with $dA = r \; dr$, but you need to account for the angle. Think of it like this: start at a point $(r,\theta)$. From there, add a small radial distance $dr$ and a small angle $d\theta$. Doing so should define a small rectangle. One side is just $dr$, but the other side, based on the change in angle, depends on how far away you are from the center of the circle: that side length is $r \; d\theta$.

The small differential area $dA$ is then just the product of the two side lengths of the (nearly) rectangular shape we have: $(dr)(r \; d\theta) = r \; dr \; d\theta$.

3. Jun 7, 2012