14.4 Center of Mass

Note: the equation for this surface is ρ= sinφ(in spherical coordinates)

Example 1Find 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

Example 2 (hint convert to polar coordinates)

Find the mass of the lamina corresponding to the first-coordinate portion of the circle

Finding Center of Mass

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

Example 3 solution part 1

"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)

Figure 14.37

Figure 14.39

Figure 14.40