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How to calculate dA of a circle

  1. Jun 7, 2012 #1
    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 [itex]dm=\frac{M.dA}{A}=\sigma .dA[/itex] and [itex]dA=R.dR.d\theta[/itex].


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

    Thanks!
     
    Last edited: Jun 7, 2012
  2. jcsd
  3. Jun 7, 2012 #2
    This is a calculus question.

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

    You almost had it with [itex]dA = r \; dr[/itex], but you need to account for the angle. Think of it like this: start at a point [itex](r,\theta)[/itex]. From there, add a small radial distance [itex]dr[/itex] and a small angle [itex]d\theta[/itex]. Doing so should define a small rectangle. One side is just [itex]dr[/itex], 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 [itex]r \; d\theta[/itex].

    The small differential area [itex]dA[/itex] is then just the product of the two side lengths of the (nearly) rectangular shape we have: [itex](dr)(r \; d\theta) = r \; dr \; d\theta[/itex].
     
  4. Jun 7, 2012 #3
    Yes, sorry I was thinking about a disc. I think I got it now! Thank you for the answer and sorry for posting this question in the wrong forum.
     
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