Medium level calculation of center of mass

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Homework Help Overview

The discussion revolves around calculating the center of mass for a given problem involving linear and surface densities, specifically in the context of integrating over a circumference and a disk. The participants are exploring the application of integration techniques and coordinate systems in their calculations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the mass using linear density for a circumference and surface density for a disk, questioning the correctness of their methods and the necessity of using spherical coordinates versus Cartesian coordinates.

Discussion Status

Some participants provide feedback on the approaches mentioned, indicating that the principles are correct but expressing uncertainty about the specific calculations without seeing them. There is a suggestion that spherical coordinates might be easier, but Cartesian coordinates are also viable with the right substitutions.

Contextual Notes

There is a mention of an attached file that presumably contains the question, which is currently missing from the discussion. This may affect the clarity of the problem being addressed.

eileen6a
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Homework Statement




~

Homework Equations



integration

The Attempt at a Solution


for a) i use linear density and calculate the mass of circumference and integrate it bottom to top. is it riight?any other methods?
for b) i use surface density and calcuate the mass of disk and intergrate bottom to top is it right?any other methods?

also do i need to use spherical coordinate? is it exceedinly difficult to use cartisian?
 
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hi eileen! :smile:

erm :redface:where did the question go? :confused:
 
why disappear? the file as attached thx~
 

Attachments

hi eileen! :smile:

(wouldn't it have been quicker just to type the question? :confused:)
eileen6a said:
for a) i use linear density and calculate the mass of circumference and integrate it bottom to top. is it riight?

correct in principle, but difficult to say whether you're actually doing it right without seeing the calculation :wink:
for b) i use surface density and calcuate the mass of disk and intergrate bottom to top is it right?any other methods?

if by "disk" you mean "hemispherical shell", yes

and there's no other method that uses (a)
also do i need to use spherical coordinate? is it exceedinly difficult to use cartisian?

spherical is easier, but Cartesian will also work, so long as you know your trig substitutions for the integral :smile:
 

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