# Talk:Angular frequency

WikiProject Physics (Rated Start-class, High-importance)

## x vs r

The equations for linear acceleration are using x instead of r as defined above them. FIX IT~! 155.33.109.3 (talk) 19:45, 2 October 2009 (UTC)

I've separated the confusing text into sections and added an explanation of x. It wasn't really the same as the r above, though there is an analogy - should we explain it here? Dbfirs 08:44, 25 June 2010 (UTC)
This article mixes wrongly two different physical concepts and their quantities: One is angular velocity (a.k.a. angular speed), which is a property of angular motion. Its vector is the angular velocity vector. The other concept and its scalar quantity is angular frequency (a.k.a. circular frequency), which is a property of periodical or oscillatory motion. In other words, a frequency is a frequency and not a velocity or speed! Unfortunately, the notation of both quantitites is ω, which, I think, brings about this confusion. Hence the article angular velocity needs to be generalized to angular velocity vector plus its scalar quantity angular velocity (a.k.a angular speed), while this article angular frequency should deal only with periodical (frequency) behavior. I think the angular frequency Gif is not suited to depicture this adequately, because frequency is not about turning angles, but about general periodic behavior. Astroflash (talk) 14:17, 10 January 2016 (UTC)
We have a separate article on angular velocity. Would it be better if angular speed redirected to that article, then this one can concentrate on the oscillatory aspect. There are, of course, close connections between the two concepts. Dbfirs 17:42, 10 January 2016 (UTC)
Of course I'm aware of the angular velocity article. Yes, I'd propose to redirect angular speed to angular velocity. But my key point is that in either of the two, or better in both, articles the widespread fallacy to muddle these two concepts should be addressed. Astroflash (talk) 19:45, 10 January 2016 (UTC)
To be concrete, there are two lines of physical reasoning:
- Concept "periodic behavior" (quantity "frequency" ν) --> "harmonic periodic behavior" (= harmonic oscillation) by Fourier analysis sinωt, cosωt --> interpretation of ω as a linear projection of circular motion, hence ω=2πν, (notion "circular frequency" = "angular frequency")
- Concept "motion" (quantity "velocity vector") --> "relative motion" (quantities "radial velocity", dr/dt, and "angular velocity"="angular speed", ω=dθ/dt) --> circular motion (dr/dt=0, ω=const)
Only at this lowest level of circular motion the two concepts osculate. I think this line of reasoning should be mapped somehow on wikipedia articles.
--- Astroflash (talk) 04:44, 11 January 2016 (UTC)
There seems to be a consensus that angular speed should redirect to angular velocity, so I've done that. An alternative would be to have a disambiguation page with links to both articles. I agree with your separation of concepts, though we should not lose sight of the close connections. Do you think that many people do get muddled? Would you like to start modifying the articles to clarify the difference between the concepts? Dbfirs 08:37, 11 January 2016 (UTC)
Well, this is a disadvantage of the english Wikipedia, namely that it doesn't provide big pictures of physical concepts, but only mathematical explanation of terms. E.g. I'm missing in the article of relative motion the basic physical concept of angular motion and radial motion, rather the full power of mathematical transformations is presented. Such an approach scares beginners.
Once angular speed is redirected to angular velocity I don't see the need for any disambiguation. What's left to do is to clarify in the angular frequency article that ω is a true frequency describing the change of an abstract phase angle in the complex phasor plane and that it is NOT related to a change of a physical angle (with a link to angular velocity). Only in the case of physical circular motion there exists a relation between both, hence circular frequency. Inversely, one should mention in the circular motion article that there is a relation to circular frequency (redirected to angular frequency)
--- Astroflash (talk) 16:40, 11 January 2016 (UTC)

## Angular speed

Currently, we have a redirect from "angular speed" to this article. I believe that the article should be under the heading "angular speed" because that is the more general term, with "angular frequency" being one particular way to measure angular speed. This is a fairly minor point. What does anyone else think? Dbfirs 22:36, 13 March 2011 (UTC)

I suggest that angular speed should redirect to angular velocity instead. :-) --Steve (talk) 05:20, 14 March 2011 (UTC)
I've no objection, though we would need to expand the lead, or add a section for the redirect, to explain that angular speed is just the magnitude of the angular velocity vector. Dbfirs 07:13, 14 March 2011 (UTC)
I think angular frequency should stay it's own article, as it's often used as a measure in other oscillations as well, being a shorthand for 2*pi*f. That being said, I agree that angular speed should redirect to angular velocity, as it's just the magnitude of the vector. Kyrsjo (talk) 13:58, 27 May 2014 (UTC)
That has now been done (see above), but do we need further clarifications? Dbfirs 16:57, 11 January 2016 (UTC)

## Connections to Oscillatory motion

Angular frequency, as defined in the beginning of the main article, is primarily related to rotating objects. Below I have attempted to elucidate the geometrical connection between a rotating object and oscillatory motion/behavior. My first attempt at modifying the main article was done in haste and was of very poor quality. That modification was undone by another user (and rightfully so). I have therefore decided to stage my modification here for criticism. My intention is to add this section before the "Examples" section in the main article. In doing so, the "Examples" section will most likely be adjusted to better reflect this connecting idea. Jatosado (talk) 02:48, 25 March 2013 (UTC)

Connections to Oscillatory motion

Circular motion is geometrically related to oscillatory motion. A circle is described from the Pythagorean theorem

${\displaystyle r={\sqrt {x^{2}+y^{2}}}\quad }$

in polar coordinates x and y have a sinusoidal form,

${\displaystyle x=r\cos \theta \,}$
${\displaystyle y=r\sin \theta \,}$

where ${\displaystyle \theta }$ is the angle of revolution. In the case where the angle of revolution increases with time, as for a rotating object, the angle can be expressed in terms of an angular frequency, i.e.,

${\displaystyle \theta =\omega t}$

which then allows x and y to be written as,

${\displaystyle x=r\cos \omega t\,}$
${\displaystyle y=r\sin \omega t\,}$

Here the x and y coordinate each execute sinusoidal motion in time. It is in this sense that an oscillating object, which may strictly move linearly, can be described as having an angular frequency in time if, in that case, its motion too is sinusoidal. — Preceding unsigned comment added by Jatosado (talkcontribs) 02:48, 25 March 2013 (UTC)

Please compare this with Circle#Equations. Specifically, the first equation is the equation of a circle centered at the origin, not the Pythagorean theorem. The second set of equations is the parametric form of the first equation, which should not be confused with the equation of a circle in polar coordinates, which does not involve the Cartesian coordinates x and y. The term "angle of revolution" seems confusing and should be avoided. Do you mean angle of rotation? The last sentence should be backed up by a reference if possible. Isheden (talk) 20:43, 25 March 2013 (UTC)
Your second pair of equations describes the conversion from polar to cartesian coordinates, see Polar_coordinate_system#Converting_between_polar_and_Cartesian_coordinates. Isheden (talk) 20:58, 25 March 2013 (UTC)
See also Simple harmonic motion, especially Uniform circular motion in the Examples section. Isheden (talk) 21:12, 25 March 2013 (UTC)