- #1
chetzread
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Homework Statement
why x is p(cosθ)(sinφ) ? and y=p(sinθ)(cosφ)?
z=p(cosφ)
As we can see, φ is not the angle between p and z ...
Triple integral in polar coordinate
- Thread starter chetzread
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SUMMARY
The discussion centers on the representation of coordinates in polar and spherical systems, specifically the equations x = ρ cos(θ) sin(φ), y = ρ sin(θ) cos(φ), and z = ρ cos(φ). Participants clarify that φ is the angle between the z-axis and the line from the origin to the point in space, not between p and z. The conversation emphasizes the importance of understanding the distinction between the Greek letters ρ (rho) and φ (phi) in these contexts, as well as the proper interpretation of diagrams related to these coordinate systems.
PREREQUISITES- Understanding of polar and spherical coordinate systems
- Familiarity with trigonometric functions and their applications
- Knowledge of Greek letters used in mathematics, specifically ρ (rho) and φ (phi)
- Ability to interpret mathematical diagrams accurately
- Study the derivation of spherical coordinates from polar coordinates
- Learn about the applications of spherical coordinates in physics and engineering
- Explore the differences between polar and cylindrical coordinate systems
- Review common mistakes in interpreting coordinate diagrams and how to avoid them
Students studying calculus, physics enthusiasts, and anyone seeking to deepen their understanding of coordinate transformations in three-dimensional space.
why x is p(cosθ)(sinφ) ? and y=p(sinθ)(cosφ)?
z=p(cosφ)
As we can see, φ is not the angle between p and z ...
- #2
Mr-R
- 123
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Why would you think that?
Well, as I see it, ##\phi## is the angle between ##z## and ##\rho##.
Well, as I see it, ##\phi## is the angle between ##z## and ##\rho##.
- #3
chetzread
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really? then where is p?Mr-R said:
P is on the same line as x-axis, am i right?
- #4
Mr-R
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chetzread said:
Nope it is not on the same axis as x. If that was the case then the equation ##x^2+y^2+z^2=\rho^2## wouldn't make sense.
If you are bothered by the provided diagram then just look up another one from another source
- #5
ehild
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- #6
Irene Kaminkowa
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https://www.physicsforums.com/members/chetzread.597855/
You had better start from 2D - the polar coordinates, trying to understand, why x = ρ cos Θ and y = ρ sin Θ.
You had better start from 2D - the polar coordinates, trying to understand, why x = ρ cos Θ and y = ρ sin Θ.
- #7
vela
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That's a really bad figure. No wonder you're confused. Check out the page ehild linked to.chetzread said:
By the way, ##\rho## is the Greek letter rho. It's not P nor p.
- #8
BvU
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Can I also point out that physicists use ##\theta## for the polar angle and ##\phi## for the azimuthal angle ?
Much more consistent with the cylindrical ##(\rho,\phi,z)## coordinate system
So: stay alert to avoid miscommunication !
Much more consistent with the cylindrical ##(\rho,\phi,z)## coordinate system
So: stay alert to avoid miscommunication !
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