- #1

opticaltempest

- 135

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Here is the problem:

http://img141.imageshack.us/img141/3830/problemsm5.jpg

Is it possible to determine this moment of inertia in this problem using double integrals of the form:

http://img172.imageshack.us/img172/1219/momented0.jpg

I could do this problem using double integrals if the region R was a solid circle using [tex]x^2+y^2=R^2[/tex] and then simplifying the integration by switching to polar coordinates. However, the region is a hoop whose width is infinitely thin.

How do I modify my region R in order to take into account the "uniform thin hoop" that has no width? Is there a way I could evaluate a hoop of width [tex]\Delta R[/tex] and find moment of inertia in terms of [tex]\Delta R[/tex] then let find the limiting value as [tex]\Delta R[/tex] approaches zero?

If I used that approach, what would I use for the density of the infinitely thin hoop?

http://img141.imageshack.us/img141/3830/problemsm5.jpg

Is it possible to determine this moment of inertia in this problem using double integrals of the form:

http://img172.imageshack.us/img172/1219/momented0.jpg

I could do this problem using double integrals if the region R was a solid circle using [tex]x^2+y^2=R^2[/tex] and then simplifying the integration by switching to polar coordinates. However, the region is a hoop whose width is infinitely thin.

How do I modify my region R in order to take into account the "uniform thin hoop" that has no width? Is there a way I could evaluate a hoop of width [tex]\Delta R[/tex] and find moment of inertia in terms of [tex]\Delta R[/tex] then let find the limiting value as [tex]\Delta R[/tex] approaches zero?

If I used that approach, what would I use for the density of the infinitely thin hoop?

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