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Understanding Center of Mass in Spherical Coordinates

Learn how to calculate center of mass with example problems in spherical coordinates. Includes mass calculation of various geometric shapes. Explore the density equations in polar coordinates for accurate results.

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Understanding Center of Mass in Spherical Coordinates

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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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