Recent content by thetasaurus

As you said, I get the correct solution when I get rid of the second and third dr's. That error is probably due to the fact that I don't actually know what I'm doing, but how can I mathematically justify omitting them? When is it ever okay to just get rid of stuff?

Homework Statement Despite the fact that this started as an extended AP Physics C problem, I turned it into a calc problem because I (sort of) can. If it needs to be moved please do so. There is a hollow solid sphere with inner radius b, outer radius a, and mass M. A particle of mass m...

Not sure if this topic belongs here, but here goes. Homework Statement From the AP physics C 1995 test there is a problem that gives the potential energy curve U(x). With F=-\frac{dU}{dx} in one variable, F(x)=-\frac{a}{b}+\frac{ba}{x^{2}} Where a and b are constants. Now I need to get...

I'd love it if both formulas were the same, then they'd be all orderly and look nice. Evidently you're right that my look-alike formula is working against me, and as of now I have (reluctantly) accepted this fact. However I'm still curious if anyone can prove why it doesn't work, or where I...

He derived it for me (as he did for the Cartesian formula as well) and I agree that it makes perfect sense. However I don't understand why the way I did it doesn't work. I know that the Pythagorean method is valid, but it seems to me like the geometric way I came up with should work as well.

I would agree with you yet we are able to calculate the area using this method with a non-constant r as a function of θ. My question is why doesn't this work for arc length. Technically r even is constant... the tiny sliver of the curve represented by dθ is such a small angle/sector/arc...

It is known that the area of a sector of a polar curve is \frac{1}{2}\int r^{2} d \theta This of course comes from the method of finding the area of an arc geometrically, by multiplying the area of the circle by the fraction we want \frac{\theta}{2\pi}\pi r^{2} Today I learned how...