Recent content by Limecat

Thanks for the chin-up. I don't know how normal this is, but my multivariable calc I've sorta-kinda forgotten now. I'll rememner terms like stokes' theorem, curvature, etc but I won't know how to do them again until I flip through my math text (I don't sell my texts) and then I"ll go oh yeah...

I'm sure that's part of it; the pressure to get good grades. And classes sometimes feel like they go too fast.. or like I said originally, I leave lecture not knowing what I was just taught.

I'm that way with a lot of things.

I said I'm trying to DERAIL the fail train. NOT stay on it. I have no idea about the blowing off homework. I always feel i should be doing something meaningless instead of my homework. Like browsing an internet forum (I'm not talking about this one) When I say I can't wait to study x y z...

Or at least... that's how it seems... I'm an Astronomy Major. In the summer, I'm all 'I can't wait to study x y and z!' and then two weeks into the semester, I'm just, 'meh. My homework can burn in hell' Completely unmotivated and don't know my future outlook. I pass my courses with average...

cos(0) is just 1...

No, if you do it by x y z, you got to do it a bit differently.. I explained in my other reply that you don't have to do it in x y z (unless you want to be extra rigorous with your math). It's because the mass is uniformly distributed, which means that the centre of mass is directly above the...

oops. I left out a \delta in the numerator. Make sure you have a \delta there when you do the actual calculation. I added it to the reply

for \phi not quite. \phi goes from zero (which is at the top of a sphere, if we're thinking of a full sphere for example's sake) to pi (which is the bottom of the sphere) In this case, we have half a sphere so... ;)

denominator: \frac{\delta 4\pi r^3}{3}\frac{1}{2} numerator: m_{1}r_{1} + m_{2}r_{2} + ... m = \delta V; dm = \delta dV (since \delta is constant) so now numerator becomes \int\int\int rdm = \int\int\int r\delta dV dV for a sphere is r^2 sin\phi drd\phi d\vartheta and...

I've only done it in spherical coordinates... probably not the best way if the density isn't a constant. But since the density IS constant, you can assume that the centre of mass lies somewhere along the vertical axis. To find the centre of mass of something, you need to do (m1x1 + m2x2 + ...) /...

My physics is a bit rusty... but I'm not sure how I would do that in 3 separate components like you've written there... but then I can't quite get the math to work out right doing a single triple integral in spherical coordinates. I know that the centre of mass should be above the middle of the...

No you don't need to do any integration for the denominator. The density is constant. The mass of the hemisphere is just the volume of a sphere divided by two, and then multiplied by the density

No. Horizontally, it's just F = kx.

The denominator is just the mass of the hemisphere.