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14.4 Center of Mass

14.4 Center of Mass. Note: the equation for this surface is ρ = sin φ (in spherical coordinates). Example 1. Find the mass of the triangular lamina with vertices (0,0), (0,3), and (2,3) given that the density at (x,y) is ρ (x,y) = 2x + y. Solution to Example 1.

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14.4 Center of Mass

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  1. 14.4 Center of Mass Note: the equation for this surface is ρ= sinφ (in spherical coordinates)

  2. Example 1 Find the mass of the triangular lamina with vertices (0,0), (0,3), and (2,3) given that the density at (x,y) is ρ(x,y) = 2x + y

  3. Solution to Example 1

  4. Example 2 (hint convert to polar coordinates) Find the mass of the lamina corresponding to the first-coordinate portion of the circle

  5. Finding Center of Mass

  6. Example 3 Find the center of mass of the lamina corresponding to the given parabolic region

  7. Example 3 solution part 1

  8. "A mathematician is a blind man in a dark room looking for a black cat which isn't there." -- Charles Darwin (quoted by Jaime Escalante in the film, STAND and DELIVER)

  9. Figure 14.37

  10. Figure 14.39

  11. Figure 14.40

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