Lecture 26: Spherical coordinates; surface area. View the complete course at: ocw.mit.edu/18-... License: Creative Commons BY-NC-SA More information at ocw.mit.edu/terms More courses at ocw.mit.edu
"How many of you have seen spherical coordinates before?" *Half the class raise their hands* "I see that's not very many." - The legendary Auroux, 2007
The Einstein field equations state that the superpostion principle will not work on gravitational fields. So using the formulas at ~41min wouldn't take relativity into consideration :)
Spherical cap of radius r and height h: pi*(h^2)*(3r-h)/3. Radius r is the radius of the sphere, not of the cap. Here r=1 and h=1-1/sqrt(2) which gives the answer. My HP-50g gives it as (8-5*sqrt(2))*pi/12 which is the same that was on the lecture. Personally I don't like roots in denominators in answers.
Good explanation but the convention for letters assigned to angles (phi, theta) is different to the more usual one . Theta, usually is used for the angle from z-axis
Because in z-axis thing are diffirent than x and y axiis. In z-axis you go with your angle in both dirextion at the same time so 90 degrees in z-axis is like 180 degrees in x-axis & y-axis so 1 rev. will be equal to 180 degrees not 360 I hope that answered your question..
Because of the simmetry, the force exerted by all the particles in the direction of positive and negative x and y cancel out each other, and only the net force exerted in the Z direction is doing an atraction to the mass little-m.
