Using rotating vector to draw sine waves

[Emilyjoint]

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??

 

[truesearch]

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

 

[xAxis]

Yes, everyone has to follow it. Otherwise it wouldn't be convention, would it?

 

[truesearch]

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.

 

[the_emi_guy]

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.

 

[Philip Wood]

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 ...