Maurice Tutor

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Teaching Since: May 2017
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Education

  • MCS,PHD
    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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  • Professor
    Phoniex University
    Oct-2001 - Nov-2016

Category > Management Posted 04 Mar 2018 My Price 7.00

solid hemisphere of radius

A uniform solid hemisphere of radius R has its flat base in the xy plane, with its center at the origin. Use the result of Problem 10.4 to find the center of mass. [Comment: This and the next two problems are intended to reactivate your skills at finding centers of mass by integration. In all cases, you will need to use the integral form of the definition (10.1) of the CM. If the mass is distributed through a volume (as here), the integral will be a volume integral with dm = ϱ dV.]

Problem 10.4

 

The calculation of centers of mass or moments of inertia usually involves doing an integral, most often a volume integral, and such integrals are often best done in spherical polar coordinates (defined back in Figure 4.16). Prove that

[Think about the small volume dV enclosed between r and r + dr, θ and θ + dθ, and ϕ and ϕ dϕ.] If the volume integral on the left runs over all space, what are the limits of the three integrals on the right?

Figure 4.16

 

Answers

Maurice Tutor
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Status NEW Posted 04 Mar 2018 07:03 PM My Price 7.00

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