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Center of mass and moments

  • Thread starter kieranl
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  • #1
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Homework Statement



A lamina has the shape of the region in the first quadrant that is bounded by the graphs of y = sinx and y= cosx, between x = 0 and x = π/4. Find the centre of mass if the density is δ(x,y) = y.

Homework Equations



I know all the equations for moments and center of mass but im confused about how to go about this problem. I dont know how to convert this to polar. The question is related to the lecture on polar integrals so im assuming thats what has to be done???

The Attempt at a Solution

 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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Hi kieranl! :smile:
A lamina has the shape of the region in the first quadrant that is bounded by the graphs of y = sinx and y= cosx, between x = 0 and x = π/4. Find the centre of mass if the density is δ(x,y) = y.

I know all the equations for moments and center of mass but im confused about how to go about this problem. I dont know how to convert this to polar. The question is related to the lecture on polar integrals so im assuming thats what has to be done???
Noooo …

you only convert coordinates if it makes the job easier …

for example, if the density function was δ(r,θ) …

in this case, δ = y (and also sin(rsinθ) is horrible :yuck:), so the easiest thing is to stay with the (x,y) coordinates. :wink:
 
  • #3
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Heya Kieranl

This is like your third curtin engineering question you've posted, so i'll assume you're probably doing mechanical engineering?

Alls I gotta say is that this one took me like 5 pages of working out. I double checked it with maple so I know its right, but maybe i did it in some really long and complicated way. I didnt convert to polar format, although I wasnt sure if I was supposed to. I was just left with 4 integrals which I had to solve step by step.
 

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