consider a lamina whose boundary is defined by the parametric form r(theta)=1+cos thetaml.the coordinate of the CM (Xcm,Ycm) of this lamina is
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Answer:
5.6.1 Use double integrals to locate the center of mass of a two-dimensional object.
5.6.2 Use double integrals to find the moment of inertia of a two-dimensional object.
5.6.3 Use triple integrals to locate the center of mass of a three-dimensional object.
We have already discussed a few applications of multiple integrals, such as finding areas, volumes, and the average value of a function over a bounded region. In this section we develop computational techniques for finding the center of mass and moments of inertia of several types of physical objects, using double integrals for a lamina (flat plate) and triple integrals for a three-dimensional object with variable density. The density is usually considered to be a constant number when the lamina or the object is homogeneous; that is, the object has uniform density.