MIT
18 02 -
Lecture 26
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Lecture 26 Spherical coordinates distance to the origin angle from the x axis in the xy plane angle with z axis Converting to cylindrical r sino 0 0 z coso Cartesian x rcos0 coso cos0 y rsin0 sino sin0 z z coso We can parameterize a unit sphere by 0 o sinocos0 sinosin0 coso Volume of a unit ball 4 3 We know that V 1 V But what is V in spherical coordinates V sino p 0 o V 2 sino o 0 p 2 0 p 4 p 4 3 Gravitation assuming M is a point like object F Gravitation assuming M is spread out with a density x y z F Gm Force in z direction F F Gm Gm cososino p 0 o Limits of integration o 0 2 0 0 2 p 0 sphere sphere
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