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Polar and Cylindrical Coordinates

Polar and Cylindrical Coordinates

The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.

Polar Coordinates

Polar Coordinates

The polar coordinate system offers an alternative to the Cartesian coordinate system for specifying points in a plane, using a distance and an angle instead of x and y coordinates. This system is particularly advantageous in situations involving circular or rotational symmetry, such as in physics or engineering problems involving waves, oscillations, or orbital paths.Defining Polar CoordinatesIn polar coordinates, a point is represented as P(r, ��), where r is the radial distance from a fixed...

Graphs of Polar Equations

Graphs of Polar Equations

The polar coordinate system represents points using a distance from a central point (the pole) and an angle from a reference direction (the polar axis). Unlike rectangular coordinates, polar coordinates are ideal for graphing curves with radial symmetry or periodic behavior.Some general forms of graphs in polar coordinates include the following:Equation of a Circle (Centered at the Pole):A graph where the radius remains constant for all angles traces a circle centered at the pole:Equation of a...

Curvilinear Motion: Polar Coordinates

Curvilinear Motion: Polar Coordinates

In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position with respect to time...

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Related Experiment Video

Updated: Jun 7, 2026

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy (iPALM)

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy (iPALM)

Published on: December 1, 2016

Technique for accurate stellar polarimetry using CCD cameras.

G Novak, T Jarrett

|November 2, 2010

Summary

This study introduces a new charge-coupled device (CCD) polarimetry technique for measuring stellar polarization. The method corrects for atmospheric transparency variations, offering improved accuracy for astronomical observations.

Area of Science:

Astronomy and Astrophysics
Observational Cosmology

Background:

Stellar polarization measurements are crucial for understanding interstellar dust and magnetic fields.
Existing CCD polarimetry techniques face challenges with atmospheric transparency variations.

Purpose of the Study:

To present a novel CCD polarimetry technique for stellar polarization data acquisition.
To demonstrate the technique's ability to correct for atmospheric transparency fluctuations.
To highlight the integration capabilities with existing photometric systems.

Main Methods:

Utilized a 0.9-m telescope at Kitt Peak and a Tek 2048 CCD camera.
Employed a novel method involving measurements through polarizing filters to correct for atmospheric transparency.
Analyzed stellar polarization data, considering both bright and faint star regimes.

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

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Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy (iPALM)

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy (iPALM)

Published on: December 1, 2016

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Main Results:

Achieved polarization measurement uncertainties of 0.3-0.5% for bright stars in hour-long sequences.
Identified Poisson noise as the limiting factor for fainter stars.
Demonstrated the technique's robustness against residual atmospheric transparency effects.

Conclusions:

The developed CCD polarimetry technique effectively measures stellar polarization.
The method offers significant advantages, including ease of integration into existing photometric systems.
This technique enhances the accuracy and efficiency of astronomical polarimetric surveys.