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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...