Average distance on a sphere | MIT 18.02SC Multivariable Calculus, Fall 2010

[@parkershaw8529]

Upper half solid sphere, volume wise is a cylinder MINUS an inverted cone (same diameter and height). Assuming constant density, volume and mass are interchangeable. The center of mass of a cylinder is at half height, the center of mass of cone is quarter height from the base. Mass of the cylinder is 3x of the cone. So the center of the mass for the half ball is the combined center of mass of positive cylinder and negative cone, should be 3/8 of the height (radius) of the half ball from base (if my calculation is correct). Let me write a program to verify it.

[@parkershaw8529]

#include #define N (1000) int main() { size_t count = 0, sum = 0; for (int ix = -N; ix

[@sighmaniacrotmg6530]

A better way to do the boundary equation is to expand (z-1)^2 then you easily see that rho squared = 2z

[@MarkSummersCAD]

Very nice video. Anyone take the time to compute the solution of the triple integral?

[@markjarrodhughes]

I got 53/20 - 4/5*Sqrt[2] which is 1.519. Not 100% certain I didn't screw something up though.

[@sllaurella]

@@markjarrodhughes thank you. mathematicians forget that we (mortals) need a number as a solution jaja

[@schlast8311]

why are you not setting origin at center of sphere? and where is the solution ?

[@hanktian5186]

Why does distance satisfy that equation? Does it have anything to do with the mass point?

[@NeelSandellISAWESOME]

If you want to find the average value of a function in 2D, your formula is 1/b-a * integral(f(x)dx)). What you are doing here is 2D/1D = 1D. In this example, you want to go 4D/3D = 1D

[@ismailsevimli6424]

@@NeelSandellISAWESOME Thanks

[@labibbidabibbadum]

"Maybe I'm beating a dead horse..." Er, no. Please feel free to provide all the scaffolding you like.

[@sb_dunk]

Nanny McPhi

[@TheBlundert4ker]

Is anyone else off-put by the unusually large chalk?

[@jyothishkumar3098]

I actually liked it :D