# Search results

1. ### What's Wrong with My Line of Reasoning? Calculating a Hollow Sphere's Moment Inertia

I don't see any abuse of terminology in the way you derive dA because for me it is pretty good. I would be glad if you can point out which terminology you abused. Ah, I got it now! Please let me show you that I have understood your derivation below: dA=\pi (r+(r+dr))\sqrt{dz^2+dr^2}...
2. ### What's Wrong with My Line of Reasoning? Calculating a Hollow Sphere's Moment Inertia

Ah, what a good way to check whether a model is correct or not! I was riveted in finding the moment inertia of a solid and hollow sphere so that I forgot to validate the underlying model. Thank you for pointing this out. Infinitely short conical frustums never came to my mind before...
3. ### What's Wrong with My Line of Reasoning? Calculating a Hollow Sphere's Moment Inertia

Hi Ho! Thank you very much for reading my line of reasoning. Although it seems long and complicated, the idea is actually very simple, isn't it? I don't get the reason why the fact that the ring in the second case does not have unit radius affects the calculation in any way. Isn't that...
4. ### What's Wrong with My Line of Reasoning? Calculating a Hollow Sphere's Moment Inertia

Hi Ho! I know that many books show the way to derive the moment inertia of a solid and a hollow sphere in many ways, each according to the lines of reasoning of their authors. I also have my own line of reasoning that I have successfully applied in finding the moment inertia of a solid...
5. ### Dy/dx: must dx be the independent variable?

Hi Ho! If y=\sin x, \frac{dy}{dx}=\frac{d(\sin x)}{dx}=\cos x. If x=\sin y, y=\arcsin x, and therefore \frac{dy}{dx}=\frac{d(\arcsin x)}{dx}=\frac{1}{\sqrt{1-x^2}}. But, if x=\sin y, can \frac{dy}{dx} be done as \frac{dy}{dx}=\frac{dy}{d(\sin y)}=\frac{1}{\frac{d(\sin...
6. ### Limit x->-infinity (x/(z^2+x^2)^0.5) = ?

Hi Ho! :smile: Mmmm... I have a problem with this one: \lim_{x\rightarrow-\infty} \frac{x}{\sqrt{z^2+x^2}} Using a computer graphics tool, I found that the result should be -1 by looking at the generated graph. But if I do it by hands, I find 1 as follows...