SUNY Geneseo Department of Mathematics

Mass and Moment

Thursday, April 7

Math 223 03
Spring 2016
Prof. Doug Baldwin

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Mass and Moments
- Section 15.6
  - “Moment” = mass weighted by distance
  - Density = δ(x,y,z)
  - Mass formula
  - Center of mass and first moment formulas
    $M_{yz} = integral over D of x times delta; x bar = M_{yz}/M$
  - Moment of inertia
- Examples
  - Indiana Jones and the Pyramid of Silliness
    - Mass of pyramid?
    - Making it balance?
      $M = integral from 0 to 1 of integral from -z to z of integral from -z to z of e^x+e^y+z; M_{yz} = integral w/ same bounds of x times density$
    - muPad calculations for these integrals
    - Moment of inertia if it spins around z axis?
    - What about spinning around z = 1, y = 1 edge?
    - muPad evaluation of integral for I_z
Next
- Line integrals of scalar functions
- Read section 16.1