Talk:Angular velocity

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Help with this template Comments: edit – history – watch – refresh (Just a few comments, haven't got time for an in-depth review) Needs more links to related concepts such as angular momentum and angular motion in general. A template grouping the most important concepts in rotational kinetics at the bottom would help too. Real world examples of angular acceleration (I made the suggestion of hula hoops) would help, as well as some examples of fields where calculations using angular velocity are regularly used. Mathematical section is covered quite well A diagram showing velocity resolved into parallel and perpendicular components could be useful in the derivation section Richard001 07:02, 7 December 2006 (UTC)

Contents 1 Help 2 Context 3 rpm 4 Non-circular motion 5 Right hand rule/direction of angular velocity 6 Rewrite

[edit] Help

I think the article should have something like the introduction I've given it. As I see it, Lie algebras provide the explanation of the reason the angular velocity vector behaves as it does. I wish I had found out about them a lot sooner. However, the definition I have given is not correct. I'm trying to think of the right words, but would anyone care to jump in and help?Buster79 09:00, 1 October 2005 (UTC)

[edit] Context

I put a context tag on this page because the introduction launches right into formal mathematical functions without explaining what will happen in non-expert terms or mentioning (anywhere in the article, really) how angular velocity is used in the real world. --Craig Stuntz 20:25, 19 May 2006 (UTC)

Perhaps the introduction should just be scrapped (I won't be offended...). What about "Angular velocity is a quantity which represents the angular speed of a rotation together with its direction, that is, its axis and sense (whether the rotation is clockwise or anticlockwise).", something like the introductory sentence in velocity. Then jump in to the school textbook stuff about vectors. I had hoped my introduction would enlighten; from a certain viewpoint, it's more intuitive to derive it using a derivative than simply to make the definition that the direction of the vector gives the axis of rotation. Still, if it doesn't help, it doesn't help. As to 'used in the real world'? Yep. The article needs a simple example or two. Any physical situation that's at all complicated is probably better treated in angular momentum.Buster79 17:25, 21 May 2006 (UTC)

I mostly agree with this. I personally find the notion of using a derivative for velocity pretty intuitive, but I have no idea what a "special orthogonal linear transformation" or a "skew-adjoint linear transformation" is. Nothing wrong with very technical terms but I don't think they belong in the intro. I suspect a number of people -- middle schoolers and most high schoolers -- who might be interested in the article wouldn't know what a derivative is, either, though, so a "non-math" explanation is also necessary. --Craig Stuntz 02:30, 22 May 2006 (UTC)

Your current revision is much improved; thanks. I think some high schoolers (and below) would still have a problem understanding it, but it's at least understandable to non-mathematics specialists now. Good work, Buster79! --Craig Stuntz 14:19, 2 August 2006 (UTC)

[edit] rpm

In my opinion, revolutions per minute is not a unit of angular velocity or angular frequency, but of frequency. 1 rpm equals 60 Hz.--84.159.248.246 17:06, 20 November 2006 (UTC)

I think that's incorrect. All units used for vector quantities deal only with the magnitude of the measure in question, so "rpm" is a unit for both angular speed and angular velocity. 1 rpm is not the same as 1 Hz. The units of rpm are angle over time. The units of Hz are simply 1 over time, without reference to the angle. -- Slowmover 16:57, 22 November 2006 (UTC)

Where does "rpm" refer to angle? In my opiniion, "revolution" is not a measure of angle but is simply used to specify the kind of things that are counted. --84.159.238.199 17:07, 24 November 2006 (UTC)

One revolution is 360°, or 2π radians, which is a measurement of angle. It is not unit-less. So, 1 rpm is equal to 2π radians per minute, which is possibly easier to recognize as units of angle over time. 1 radian per minute is 1/(2π) rpm, and so on. It's important to see that a revolution is a divisible quantity, like meters or miles. It is measured quantity which can have any real number value, not just integers. -- Slowmover 22:09, 28 November 2006 (UTC)

One thing that just occurred to me is that this is really a semantic argument. The same thing applies to frequency. The units of angle are actually "dimension-less" units, whether radians or revolutions. Circular motion is inherent in the definiton of frequency (since each tick of a clock or the frequency of sound refers to a cycling through a full "revolution" of the available motion). Thus, it probably makes no difference if you talk of angular frequency or angular velocity, except for the vector component. -- Slowmover 22:20, 28 November 2006 (UTC)

Just have a look at the article revolutions per minute. There they say "Revolutions per minute (abbreviated rpm, RPM, r/min, or min−1) is a unit of frequency, commonly used to measure rotational speed, in particular in the case of rotation around a fixed axis." The article about rotational speed says: "Rotational speed tells how many complete rotations there are per time unit, and it is measured in revolutions per second (1/s or Hertz) in the SI System. " (Neither of the articles has been written by me.) --84.159.251.122 09:43, 2 December 2006 (UTC)

[edit] Non-circular motion

is not true in general but only if the motion of the partical is contained in a plane and if that plane contains the origin. In general, ω is neither orthogonal to the position vector r nor to the velocity vector v, so equation (5) is not true. --84.159.248.246 17:24, 20 November 2006 (UTC)

[edit] Right hand rule/direction of angular velocity

While the article describes the direction of angular velocity as being the axis of spinning, it doesn't say anything about what this represents, and what difference it makes whether it is up/down. Perhaps a real world analogy like hula hooping could be used to describe the relevance of this vector. Richard001 06:35, 7 December 2006 (UTC)

[edit] Rewrite

I have resectioned things to make clear the differences between the angular velocity of a particle and the spin angular velocity of a rigid body. Almost all of the contents of the previous page have been included, except the "derivation" section has been shortened. PAR 02:39, 22 January 2007 (UTC)