- #1

MeMoses

- 129

- 0

## Homework Statement

Find the center of mass of the lamina which occupies if the density at any point is proportional to the distance from the origin.

36 <= x^2+y^2 <= 81, y >= 0

## Homework Equations

## The Attempt at a Solution

Rewrote it in polars to get 6<r<9. The x is clearly 0 as you can see from symmetry, but I can't get y. The total mas should be 45pi/2 takeing the integral of r dr d(theta) with 0<theta<pi and 6<r<9. And to find y I need to take the Momentx/mass, but I am not getting the right answer. For momentx I took the double integral of r**2*sin(theta) with the same limits to get 342. Can you see where I'm going wrong. Also density=k*r but that just leaves an extra k on mass and Mx which cancel. Any help would be great