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Density and intergrals

  1. Jan 31, 2005 #1
    I've ran aground on my physics 4a homework.

    Consider a solid disk of mass M=15.6kg and areal density =Dx3. Determine the value D if the radius of the disk is 0.25m.

    I solved the problem before it: (a)Consider a two meterstick of mass M=8.2kg and linear density =Cx5. Determine the value C.

    by taking the intergral of the linear density and setting it equal to the mass and plugging in 2 meters for the x and solving for C.

    Changing the object to a disk from a meter stick somehow destroys the problem from me and I can't figure out what to do to get it to work. I've tried finding area pi(r)^2 using the radius that gave, and i've tried circumferance 2pi(r).

    What I'm I missing?
  2. jcsd
  3. Jan 31, 2005 #2


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    Could it be that x in Dx3 stands for the radius of the disk? In this case, you can proceed exactly as with the stick; integrating the surface density from 0 to 0.25m (and 0 to 2pi) and then solve for D.
    Last edited: Jan 31, 2005
  4. Jan 31, 2005 #3


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    I start again...

    Use the fact that the mass is the surface integral of the areal density over the whole surface. I.e.

    [tex]M = \iint_{surface} \sigma dA[/tex]

    And use the fact that the areal density is given to you as a function of the radius to integrate in polar coordinate. Recall that in polar coordinate, the area element is [itex]dA = rdrd\theta[/itex].
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