# Thread: Double Iterated Integral - Polar Coordinates

1. ## Double Iterated Integral - Polar Coordinates

A thin ring has inner radius 1m, outer radius 3m, and has density directly proportional to the distance from the centre of the ring. In polar coordinates, set up but do not evaluate the double iterated integral to find the moment of intertia about a line tangent to the outside of the ring.

I'm just curious whether I've done this one correctly or not. I've chosen my origin at the centre of the ring and the line tangent to the outside of the ring to be x = 3.

Does anyone see any problems?

2. Bump, still looking for some verification

3. bounds are correct, now i don't see the function which you want to integrate.

4. The function to be integrated is the density. You are told the density is "directly proportional to the distance from the centre of the ring"- that is, kr for some constant k. I don't see where you got "$\displaystyle (3- rcos(\theta))^2$" from.

5. Originally Posted by HallsofIvy
The function to be integrated is the density. You are told the density is "directly proportional to the distance from the centre of the ring"- that is, kr for some constant k. I don't see where you got "$\displaystyle (3- rcos(\theta))^2$" from.
I chose the line tangent to the outside of the ring to be x=3.

So the directed distance from the line x=3 to any point on the ring would be,

(3 -x)

Since we are doing the moment of inertia we square this distance.

So my function for density is r and the distance squared is the,

$\displaystyle (3- rcos(\theta))^2$

Is it clear now? Am I mixing some stuff up?