Finding Center of Mass for a Lamina in First Quadrant

[kieranl]

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 I am confused about how to go about this problem. I don't know how to convert this to polar. The question is related to the lecture on polar integrals so I am assuming that's what has to be done?

The Attempt at a Solution

 

[tiny-tim]

Hi kieranl!

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 I am confused about how to go about this problem. I don't know how to convert this to polar. The question is related to the lecture on polar integrals so I am assuming that's 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 ), so the easiest thing is to stay with the (x,y) coordinates.

 

[Enzo]

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 got to 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.