- #1
chetzread
- 801
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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
- Start date
In summary, the conversation discusses the use of polar and azimuthal coordinates in representing points in 3D space. It also clarifies the role of the angles θ and φ in the equations x = p(cosθ)(sinφ) and y = p(sinθ)(cosφ), as well as the location of point P in relation to the x-axis. The conversation also mentions the importance of accurately representing coordinates and avoiding miscommunication in physics.
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
- 23
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
- 801
- 1
really? then where is p?Mr-R said:
P is on the same line as x-axis, am i right?
- #4
Mr-R
- 123
- 23
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
Homework Helper
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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
Staff Emeritus
Science Advisor
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Education Advisor
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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
Science Advisor
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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 !
FAQ: Triple integral in polar coordinate
What is a triple integral in polar coordinates?
A triple integral in polar coordinates is a mathematical tool used to calculate the volume of a three-dimensional object that is defined using polar coordinates. It involves integrating over a region in the xy-plane and taking into account the radius and angle of the object.
Why is a triple integral in polar coordinates useful?
A triple integral in polar coordinates is useful because it allows us to solve for the volume of objects that are more easily described using polar coordinates, such as spheres, cones, and cylinders. It also simplifies calculations for objects with circular symmetries.
How is a triple integral in polar coordinates different from a regular triple integral?
A triple integral in polar coordinates is different from a regular triple integral because it uses polar coordinates instead of Cartesian coordinates. This allows us to describe and solve for the volume of objects that are not easily defined using Cartesian coordinates.
What are the steps for solving a triple integral in polar coordinates?
The steps for solving a triple integral in polar coordinates are as follows:
- Identify the region of integration in the xy-plane.
- Set up the integrand, taking into account the polar coordinates.
- Integrate over the region of integration, using the limits of integration in terms of polar coordinates.
- If necessary, convert the result back to Cartesian coordinates.
What are some real-world applications of triple integrals in polar coordinates?
Triple integrals in polar coordinates have many real-world applications, such as calculating the volume of a lake or pond, determining the mass and center of mass of a solid object, and calculating the electric flux through a cylindrical surface. They are also used in fields such as physics, engineering, and astronomy to solve various problems involving three-dimensional objects and their properties.