1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Units and equation for volume

  1. Aug 22, 2014 #1
    1. The problem statement, all variables and given/known data

    moi.jpg


    In the equation dm = δ x 2∏rLdr

    Where δ = density, and

    2∏rL = volume

    How is it that the volume can be 2∏rL? The units of r is (metres) and the units of L is (metres) which leads to m2 (Area)

    Should it not be ∏r2L for volume?


    3. The attempt at a solution

    My reasoning that it's 2∏rL is because dm and dr are infinitesimally small such that the circle formed doesn't really have a surface area as such and therefore the volume is simply the circumference multiplied by the length...but that still doesn't make it a "volume"

    Can anyone explain?

    Thanks
     
  2. jcsd
  3. Aug 22, 2014 #2

    jedishrfu

    Staff: Mentor

    Looks like you forgot the units of dr which is also meters.

    The 2*pi*r*L is the area of a cylinder so 2*pi*r*l*dr is a volume element with dimensions of meters^3
     
  4. Aug 22, 2014 #3
    You forgot to include the thickness dr in your calculation of volume. It has units of metres.

    This way of setting up an integral by considering infinitesimally small quantities is something you'll find to be very common in a lot of physics texts. It's not mathematically rigorous, but it's often a useful heuristic.

    If you want some intuition on how it works in a more mathematical setting, try looking up the definition of the integral as the limit of a Riemann sum.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Units and equation for volume
Loading...