Using rotating vector to draw sine waves

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Discussion Overview

The discussion revolves around the use of a rotating vector to draw sine waves, specifically focusing on the convention of anti-clockwise rotation versus clockwise rotation. Participants explore the implications of this convention in both mathematical and practical contexts, including signal processing and three-dimensional representations.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question why the convention dictates anti-clockwise rotation, suggesting it feels unnatural and asking if it is mandatory for everyone to follow.
  • Others argue that the anti-clockwise convention is sensible, as it aligns with the typical representation of a sine wave starting at zero and rising to a maximum.
  • One participant asserts that adherence to the convention is necessary for consistency, emphasizing that a convention implies a standard that must be followed.
  • A participant expresses frustration with a textbook that depicts clockwise rotation, labeling it as unconventional and unsuitable for physics lessons.
  • Another contributor introduces the idea that in signal processing, frequency is treated as a signed number, with anti-clockwise rotation representing positive frequencies and clockwise representing negative frequencies.
  • One participant appreciates the convention for its clarity in three-dimensional contexts, linking anti-clockwise rotation in the x-y plane to a right-handed screw rule and positive z-direction representation.

Areas of Agreement / Disagreement

Participants generally agree that the anti-clockwise convention is widely accepted, but there is disagreement regarding its necessity and the implications of alternative representations, such as clockwise rotation.

Contextual Notes

Some discussions touch on the implications of defining positive and negative directions in various contexts, such as signal processing and three-dimensional geometry, but these points remain unresolved and depend on specific definitions.

Emilyjoint
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We have met the idea that a radius of a circle rotating ANTI-CLOCKWISE can be used to draw a sine wave... I get that... it is a great idea but...why does it have to be rotating anti-clockwise. That seems so un natural to me. We were told it is a convention. Does that mean it is something everyone has to follow??
 
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It is a convention but it is a sensible one!
If you sketch a sine wave it starts at zero and rises up to a max, comes down and goes to a negative max before returning to zero... one cycle...This what you get if you project the radius vector horizontally and you start with the radius as a horizontal line along the x-axis and it rotates anticlockwise
 
Yes, everyone has to follow it. Otherwise it wouldn't be convention, would it?
 
absolutely...unfortunately I have a textbook that shows the vector rotating clockwise...I forbid the use of this book in physics lessons.
All the diagrams in this section of the book are 'upside down' ...not wrong... but unconventional.
 
Emilyjoint,
There is a little more to it than this.
In the signal processing field, frequency is a signed number. This is very common when characterizing modulation. The phaser can rotate either direction, ccw for positive frequencies, cw for negative.
Deciding which rotational direction is positive is analogous to deciding which direction on the x-axis is positive.
 
Last edited:
What I like about the convention is how things appear in 3D... Imagine a set of right-handed axes. Suppose we have rotation in the x-y plane which is anticlockwise when seen from 'above', that is from somewhere with positive z. Then using a right-handed screw rule, the rotation is represented by a (pseudo)vector in the +z direction.

Well, I like it ...
 

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