求解Find the center of mass of the solid between the spheres x

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/11/09 03:36:57

求解Find the center of mass of the solid between the spheres x2 + y2 + z2 = 1 and
Find the center of mass of the solid between the spheres x2 + y2 + z2 = 1 and
x2 + y2 + z2 = 9 if the density is proportional to the distance from the origin.

平方写好一点,我还以为是x2只是一个变量.
答案应该是原点（0,0,0）.
x^2+y^2+z^2=1 是个半径为1的小球,中心座落在原点.
x^2+y^2+z^2=9 是个半径为3的稍微大点的球,中心也是座落在原点.
靠观察就知道两球之间的solid的中心也是在原点.
你也可以用微积分做,我懒得去做了.如果你微积分好的话,这题不难.用spherical coordination去做,不要用cartesian coordination.做法是每个点的moment总和除以每个点mass的总和.要做三次,每一次计算moment跟据一个axis.

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