Asked by: Formerio Marcianes
science space and astronomy

Why do we use cylindrical coordinates?

Last Updated: 15th January, 2020

1 Answer. Basically it makes things easier if your coordinates look like the problem. If you have a problem with cylindrical symmetry, like the magnetic field of a wire, use those coordinates. There are many other systems possible.

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Beside this, why do we use spherical coordinates?

Spherical coordinates determine the position of a point in three-dimensional space based on the distance ρ from the origin and two angles θ and ϕ. If one is familiar with polar coordinates, then the angle θ isn't too difficult to understand as it is essentially the same as the angle θ from polar coordinates.

One may also ask, what is the difference between cylindrical and spherical coordinates? Spherical Coordinates. In the Cartesian coordinate system, the location of a point in space is described using an ordered triple in which each coordinate represents a distance. In the cylindrical coordinate system, location of a point in space is described using two distances (r and z) and an angle measure (θ).

People also ask, what is dS in cylindrical coordinates?

To get dS, the infinitesimal element of surface area, we use cylindrical coordinates to parametrize the cylinder: (6) x = a cos θ, y = a sin θ z = z . Its area dS is the product of its height and width: (7) dS = dz · adθ .

How do you find cylindrical coordinates?

Figure 1: A point expressed in cylindrical coordinates. To convert from cylindrical to rectangular coordinates we use the relations x = r cosθ y = r sinθ z = z. To convert from rectangular to cylindrical coordinates we use the relations r = √ x2 + y2 tanθ = y x z = z.

Related Question Answers

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What is the difference between polar and spherical coordinates?

The polar coordinate system is a 2-dimensional system. Every point in the plane is defined by two numbers. The spherical coordinate system is a 3-dimensional system. Every point in space is define by 3 numbers, 2 angles and the radial distance from the origin.

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What is radial distance in physics?

The radius or radial distance is the Euclidean distance from the origin O to P. The inclination (or polar angle) is the angle between the zenith direction and the line segment OP.

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What is the equation of a sphere?

The general equation of a sphere is: (x - a)² + (y - b)² + (z - c)² = r², where (a, b, c) represents the center of the sphere, r represents the radius, and x, y, and z are the coordinates of the points on the surface of the sphere.

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What is P in spherical coordinates?

The coordinates used in spherical coordinates are rho, theta, and phi. Rho is the distance from the origin to the point. Theta is the same as the angle used in polar coordinates. Phi is the angle between the z-axis and the line connecting the origin and the point.

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What is the point of polar coordinates?

Polar coordinates are used often in navigation as the destination or direction of travel can be given as an angle and distance from the object being considered. For instance, aircraft use a slightly modified version of the polar coordinates for navigation.

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What is azimuthal angle in physics?

In a spherical coordinate system, the azimuth angle refers to the “horizontal angle” between the origin to the point of interest. In math, the azimuth angle is commonly denoted by . However, in physics, the azimuth angle is commonly denoted by .

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Are cylindrical and polar coordinates the same?

Cylindrical coordinates are a simple extension of the two-dimensional polar coordinates to three dimensions. Recall that the position of a point in the plane can be described using polar coordinates (r,θ). The polar coordinate θ is the angle between the x-axis and the line segment from the origin to the point.

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What are the components of cylindrical coordinate?

Cylindrical coordinate surfaces. The three orthogonal components, ρ (green), φ (red), and z (blue), each increasing at a constant rate. The point is at the intersection between the three colored surfaces.

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What does z equal in polar coordinates?

Polar coordinates. The representation of a complex number as a sum of a real and imaginary number, z = x + iy, is called its Cartesian representation. The values x and y are called the Cartesian coordinates of z, while r and θ are its polar coordinates.

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What are the types of coordinates?

Common coordinate systems
  • Number line.
  • Cartesian coordinate system.
  • Polar coordinate system.
  • Cylindrical and spherical coordinate systems.
  • Homogeneous coordinate system.
  • Other commonly used systems.
  • Relativistic coordinate systems.
  • Citations.

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What is surface integrals used for?

Surface integrals are used anytime you get the sensation of wanting to add a bunch of values associated with points on a surface. This is the two-dimensional analog of line integrals. Alternatively, you can view it as a way of generalizing double integrals to curved surfaces.

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What is a coordinate system in physics?

Coordinate systems are used to describe the position of an object in space. A coordinate system is an artificial mathematical tool that we construct in order to describe the position of a real object.

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What is Z in spherical coordinates?

So, given a point in spherical coordinates the cylindrical coordinates of the point will be, r=ρsinφθ=θz=ρcosφ r = ρ sin ? φ θ = θ z = ρ cos ?

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How do you convert to rectangular coordinates?

To convert from rectangular coordinates to polar coordinates, use one or more of the formulas: cosθ=xr, sinθ=yr, tanθ=yx, and r=√x2+y2.

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How do you convert rectangular coordinates to cylindrical coordinates?

To convert from cylindrical to rectangular coordinates we use the relations x = r cosθ y = r sinθ z = z. To convert from rectangular to cylindrical coordinates we use the relations r = √ x2 + y2 tanθ = y x z = z. Example: Convert the point ( 2, 4π 3 ,8 ) from cylindrical to rectangular coordinates.

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How do you find cylindrical coordinates?

Finding the values in cylindrical coordinates is equally straightforward: r=ρsinφ=8sinπ6=4θ=θz=ρcosφ=8cosπ6=4√3. Thus, cylindrical coordinates for the point are (4,π3,4√3). Plot the point with spherical coordinates (2,−5π6,π6) and describe its location in both rectangular and cylindrical coordinates.

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How do you plot cylindrical coordinates?

in cylindrical coordinates:
  1. Count 3 units to the right of the origin on the horizontal axis (as you would when plotting polar coordinates).
  2. Travel counterclockwise along the arc of a circle until you reach the line drawn at a π/2-angle from the horizontal axis (again, as with polar coordinates).

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How do you describe a sphere in cylindrical coordinates?

1 Answer
  1. x2+y2+z2=R2 .
  2. Since x2+y2=r2 in cylindrical coordinates, an equation of the same sphere in cylindrical coordinates can be written as.
  3. r2+z2=R2 .

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What is dV in cylindrical coordinates?

In cylindrical coordinates, we have dV=rdzdrd(theta), which is the volume of an infinitesimal sector between z and z+dz, r and r+dr, and theta and theta+d(theta). As shown in the picture, the sector is nearly cube-like in shape. The length in the r and z directions is dr and dz, respectively.