Solving Volume Problems in Physics: Cartesian vs. Spherical Coordinates

In summary, Cartesian and spherical coordinates are two different ways of defining points in three-dimensional space. They use different equations to calculate volume, with Cartesian coordinates being better suited for rectangular objects and spherical coordinates being better for objects with spherical symmetry. Converting between the two coordinate systems is possible, but may introduce errors. To ensure accuracy, it is important to double-check calculations and use appropriate equations for the chosen coordinate system.
  • #1
twoflower
368
0
Hi,

been solving another volume problem here and though it seemed very straightforward, I'm getting very ugly integrals so it rather seems that I haven't chosen appropriate approach. I scanned how I did it, first in cartesian coordinates:

http://twoflower.matfyz.cz/inc/int.cartesian.jpg"

and then in spherical coordinates:

http://twoflower.matfyz.cz/inc/int.polar.jpg"

Neither of them seems useful...or maybe I'm substituting it wrongly.

A is the set the volume of which I'm trying to compute.

Thank you for any advices.
 
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  • #2
I got it, I really didn't choose the best approach.
 

FAQ: Solving Volume Problems in Physics: Cartesian vs. Spherical Coordinates

What is the difference between Cartesian and spherical coordinates in solving volume problems in physics?

Cartesian coordinates use a three-dimensional rectangular system to define points in space, while spherical coordinates use a combination of radius, polar angle, and azimuthal angle to define points in space. This means that the equations used to calculate volume in Cartesian and spherical coordinates will be different.

Which coordinate system should I use when solving volume problems in physics?

The choice of coordinate system depends on the shape and symmetry of the object being analyzed. Cartesian coordinates are better suited for calculating volumes of rectangular or cuboid objects, while spherical coordinates are better suited for objects with spherical symmetry, such as a sphere or a cone.

Are there any advantages to using spherical coordinates over Cartesian coordinates when solving volume problems?

Yes, spherical coordinates can simplify calculations for objects with spherical symmetry, as the equations used are simpler and involve fewer variables. This can save time and make the calculations more efficient.

Can I convert between Cartesian and spherical coordinates when solving volume problems?

Yes, it is possible to convert between Cartesian and spherical coordinates using appropriate equations. However, it is important to note that the conversion may introduce errors in the calculations, so it is best to stick with one coordinate system throughout the problem.

How do I know if I have solved a volume problem correctly using Cartesian or spherical coordinates?

To ensure the accuracy of your calculations, it is important to double-check your work and use the appropriate equations for the coordinate system you have chosen. You can also compare your results to known values or use mathematical software to verify your answer.

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