tag:blogger.com,1999:blog-69233306599239202952014-10-02T23:35:29.764-05:00Heart's EightA blog of science, randomness, and the pursuit of happiness.Superflyhttp://www.blogger.com/profile/11175816382939469660noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-6923330659923920295.post-87279149678774939972010-12-16T22:24:00.000-06:002010-12-16T22:24:57.719-06:00FINALSDude... I had 3 tests today, and my candidate fitness assessment for the Air Force Academy. I'm so tired. I also have an interview with MIT tomorrow. Hopefully it will go well... haha of course it will. Time for more math.<img src="http://feeds.feedburner.com/~r/HeartsEight/~4/4aJjuNfG1TM" height="1" width="1" alt=""/>Superflyhttp://www.blogger.com/profile/11175816382939469660noreply@blogger.com6http://heartseight.blogspot.com/2010/12/finals.htmltag:blogger.com,1999:blog-6923330659923920295.post-8462643547347481372010-12-07T22:20:00.002-06:002010-12-07T22:20:59.330-06:00SuggestionsI need some good acoustic guitar songs. Any that would be awesome, you should tell me. Gracias.<img src="http://feeds.feedburner.com/~r/HeartsEight/~4/TvFnQfljATo" height="1" width="1" alt=""/>Superflyhttp://www.blogger.com/profile/11175816382939469660noreply@blogger.com9http://heartseight.blogspot.com/2010/12/suggestions.htmltag:blogger.com,1999:blog-6923330659923920295.post-46703100056172186702010-12-07T00:17:00.001-06:002010-12-07T17:22:32.343-06:00ick-Clay on the Ad-aysYep. That's Pig Latin :P Seriously though. ...I think it's time for bed. Procrastination owned me again. I need more followers. Night everybody.<img src="http://feeds.feedburner.com/~r/HeartsEight/~4/y6aFUxrapVA" height="1" width="1" alt=""/>Superflyhttp://www.blogger.com/profile/11175816382939469660noreply@blogger.com7http://heartseight.blogspot.com/2010/12/ick-clay-on-ad-ays.htmltag:blogger.com,1999:blog-6923330659923920295.post-49404150660773800362010-12-06T21:08:00.002-06:002010-12-07T17:26:48.066-06:00Math and Physics ventures...Well most likely no one will want to see this, but if anyone is interested... Today in Economics I wasn't paying attention to the teacher, but rather I was formulating and deriving the expression for moment of inertia of a hollow sphere. For those of you who don't know, moment of inertia is how hard it is to rotate something about a point or axis.<br /><br />Well here we go. This probably will be really hard to understand because of the lack of symbols... sorry for the inconvenience.<br /><br />int = integral; pi = pi; d = density; m = mass; r = radius; I = moment of inertia; variables = phi, theta, p;<br /><br />I = mr^2<br /><br />Converting to spherical coordinates and integrating we get:<br /><br />I = int[int[int[mr^2,V]]] = int[int[int[(p*sin(phi))^2*p^2*sin(phi),p],phi],theta]<br /><br />p = r in this case.<br /><br />The tricky part was the innermost integral. I realized after thinking for a while that you can't integrate with respect to p because it is infinitesimally small and I don't need the whole radius. Therefore, I converted it into a trivial sum in order to just use the very edge. I also set up my bounds in order to account for the entire sphere.<br /><br />int[int[sum[d*p(i)^4*(sin(phi))^3,i,1,1],phi,0,pi],theta,0,2*pi] where p(1) = r<br /><br />Simplifying to a double integral...<br /><br />int[int[d*r^4*(sin(phi))^3,phi,0,pi],theta,0,2*pi]<br /><br />now some trig subs to make this integrable.<br /><br />d*r^4*int[int[sin(phi)*(1-(cos(phi))^2),phi,0,pi],theta,0,2*pi]<br /><br />simplifies down to:<br /><br />d*r^4*int[4/3,theta,0,2*pi] = (8/3)*pi*d*r^4<br /><br />We can assume a hollow sphere to only have an area: which is 4*pi*r^2<br />And planar density is mass over area<br />And now we substitute<br /><br />(8/3)*pi*(m/(4*pi*r^2))*r^4 = (2/3)*m*r^2<br /><br />Hooray calculus!<img src="http://feeds.feedburner.com/~r/HeartsEight/~4/UltQ6g2nMLE" height="1" width="1" alt=""/>Superflyhttp://www.blogger.com/profile/11175816382939469660noreply@blogger.com3http://heartseight.blogspot.com/2010/12/math-and-physics-ventures.htmltag:blogger.com,1999:blog-6923330659923920295.post-62719019886493521862010-12-06T15:45:00.000-06:002010-12-06T15:45:13.667-06:00Pick Me!Well, I'm home again. I need people to follow me and stuff. That'd be cool. Or not. Whatever. I think it's time for some recreational multi-variable calculus. Who else loves math?<img src="http://feeds.feedburner.com/~r/HeartsEight/~4/efIsTf0nu5o" height="1" width="1" alt=""/>Superflyhttp://www.blogger.com/profile/11175816382939469660noreply@blogger.com5http://heartseight.blogspot.com/2010/12/pick-me.htmltag:blogger.com,1999:blog-6923330659923920295.post-44112434955223671792010-12-05T21:59:00.000-06:002010-12-05T21:59:55.985-06:00ProcrastinationI'm supposed to be reading right now... Well, that's not happening. I've planned on doing so much but find myself in front of the computer when I need something to be done. If anyone ever reads this: procrastinate, yes or no? (Question is meant to be general and is open for interpretation.)<img src="http://feeds.feedburner.com/~r/HeartsEight/~4/8Yt-HZxJjfk" height="1" width="1" alt=""/>Superflyhttp://www.blogger.com/profile/11175816382939469660noreply@blogger.com1http://heartseight.blogspot.com/2010/12/procrastination.htmltag:blogger.com,1999:blog-6923330659923920295.post-64839968586468877882010-12-05T19:54:00.000-06:002010-12-05T19:54:22.609-06:00IntroductionI've never really blogged before and this is kind of just a test run. I don't even know what a blog is really supposed to be. I'm just going to write down random thoughts I have... It's cold outside.<img src="http://feeds.feedburner.com/~r/HeartsEight/~4/f_wC9BmsZMU" height="1" width="1" alt=""/>Superflyhttp://www.blogger.com/profile/11175816382939469660noreply@blogger.com4http://heartseight.blogspot.com/2010/12/introduction.html