# Center of mass and moments

• kieranl
In summary, Kieran was trying to find the centre of mass for a lamina with a given density, but he was confused about how to convert coordinates to polar. He eventually figured out that he needed to stay with (x,y) coordinates, and that it took a lot of effort to do so.f

## 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

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 :yuck:), so the easiest thing is to stay with the (x,y) coordinates. 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.