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Spherical Coordinates01:23

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Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...
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Anodic Stripping Voltammetry (ASV), Cathodic Stripping Voltammetry (CSV), and Adsorptive Stripping Voltammetry (AdSV) are electrochemical techniques used to determine trace amounts of analytes in solution. These methods involve applying a potential to an electrode and measuring the resulting current.
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Newton's law of gravitation describes the gravitational force between any two point masses. However, for extended spherical objects like the Earth, the Moon, and other planets, the law holds with an assumption that masses of spherical objects are concentrated at their respective centers.
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A spherical capacitor consists of two concentric conducting spherical shells of radii R1 (inner shell) and R2 (outer shell). The shells have  equal and opposite charges of +Q and −Q, respectively. For an isolated conducting spherical capacitor, the radius of the outer shell can be considered to be infinite.
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A charge distribution has spherical symmetry if the density of charge depends only on the distance from a point in space and not on the direction. In other words, if the system is rotated, it doesn't look different. For instance, if a sphere of radius R is uniformly charged with charge density ρ0, then the distribution has spherical symmetry. On the other hand, if a sphere of radius R is charged so that the top half of the sphere has a uniform charge density ρ1 and the bottom half has a...
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Related Experiment Video

Updated: Feb 13, 2026

Reconstitution of Basic Mitotic Spindles in Spherical Emulsion Droplets
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Forceless Sadowsky strips are spherical.

E L Starostin1, G H M van der Heijden1

  • 1Department of Civil, Environmental & Geomatic Engineering, University College London, Gower Street, London WC1E 6BT, United Kingdom.

Physical Review. E
|March 18, 2018
PubMed
Summary

Thin elastic ribbons naturally form spherical shapes, offering new models for biopolymers and nanomaterials beyond traditional wormlike chain descriptions. This research identifies broader energy functionals with similar spherical tendencies.

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Area of Science:

  • Physics
  • Materials Science
  • Nanoscience

Background:

  • Classical wormlike chain models are insufficient for describing certain ribbonlike objects.
  • Developable elastic strips require specific energy minimization principles.

Purpose of the Study:

  • To investigate the geometric properties of thin rectangular ribbons.
  • To explore the tendency of these ribbons to form spherical shapes.
  • To identify a broader class of energy functionals exhibiting this property.

Main Methods:

  • Analysis of energy-minimizing configurations for the Sadowsky functional.
  • Mathematical modeling of narrow, developable elastic strips.
  • Characterization of forceless solutions.

Main Results:

  • Thin rectangular ribbons, as defined by the Sadowsky functional, exhibit a natural propensity to form spherical shapes.
  • Forceless solutions for these ribbons are found to lie on a sphere.
  • A wider range of energy functionals demonstrating this spherical tendency has been identified.

Conclusions:

  • The findings provide a new theoretical framework for understanding ribbonlike structures in biophysics and nanoscience.
  • The identified functionals offer alternative models for systems not amenable to classical descriptions.
  • This work advances the understanding of the geometry and mechanics of elastic ribbons.