I have always loved this - it really puts things into a different perspective. I also really like movies, so the visuals accompanying this make this reading of Pale Blue Dot so much more potent.
Ahah! Now I see exactly where I went wrong; I can now see two ways to solve the problem. I can set it up as you suggested, with a line with the equation y=h(1-\frac{x}{r} ) and then use my "formula" to integrate from 0 to r.
I_{y}=2\pi\rho\int_a^b yx^3\ dx
I_{y}=2\pi\rho\int_0^r...
I realize I have only been here for about two days... but it is really refreshing to find a community such as this online, and to see that it can be accessed for free. I would also like to thank the people who donate their time here.
Hmm, I was probably unclear in explaining how I set up the problem. Since the book I am using only covers plain old two-variable equations (no multivariable stuff like z^2=x^2+y^2), the only way I know how to calculate volumes of solids is to rotate equations (or the areas bounded by those...
Homework Statement
Find the moment of inertia of the right circular cone or radius r and height h with respect to its axis, and in terms of its mass.
*As of this point, I am supposed to use solids of revolution, and so I need to rotate a line about an axis, and find the moment of inertia with...