Dimension of Angle: Learn LL^-1 from Course Book

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SUMMARY

The dimension of angle is defined as [LL^-1], indicating that angles are dimensionless quantities. When measured in radians, angles represent the ratio of arc length to radius, a concept rooted in high school geometry. This dimensionless nature remains consistent across different measurement units, with only conversion factors varying. The discussion highlights a common misunderstanding in educational materials regarding the dimensionality of angles.

PREREQUISITES
  • Understanding of basic geometry concepts, particularly the relationship between arc length and radius.
  • Familiarity with the concept of dimensional analysis in physics.
  • Knowledge of measurement units, specifically radians and degrees.
  • Basic mathematical skills for ratio calculations.
NEXT STEPS
  • Explore the concept of dimensionless quantities in physics.
  • Learn about the applications of radians in trigonometry and calculus.
  • Research the differences between various angle measurement units, including degrees and gradians.
  • Study dimensional analysis techniques in scientific contexts.
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Students in physics and mathematics, educators seeking to clarify concepts of angle measurement, and anyone interested in the foundational principles of geometry.

HussanAli
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In my course I am curios to know how the dimension of angle becomes [LL^-1]. The following pic is taken by course book.



http://i42.tinypic.com/iy2y3r.jpg
 
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When angles are measured in radians, they are simply the ratio of arclength divided by radius ... as taught in high school geometry, at least in the USA.
 
An important note to make is that regardless of the units you're using to measure an angle, its dimensions are still the same, none. :) The only difference is a conversion factor.
 
Redbelly98 said:
When angles are measured in radians, they are simply the ratio of arclength divided by radius ... as taught in high school geometry, at least in the USA.
Thanks that helps :!) . What a damn books in Pakistan they taught.
 

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