Talk:Angular velocity
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[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)
- 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)
[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)
[edit] Physics/Medicine Perspective
Medical Physics Query: I am not a physicist, just one very curious how the heart works so well for so long. Discovery of Angular Velocity in a living organism was an unexpected find in reading of other areas in this pursuit. 1. Application of living physiology to Angular Velocity is perhaps better appreciated in time phases of a coiled snake readying and striking prey or perceived danger. 2. The snake is a compliant rudimentary tubular organism comprised of many layers of neuromuscle, connective tissue, bone and gas. To most effectively strike prey or respond to threat, the snake recoils itself into the smallest sphere possible. 3. Recoil of the snake enables increasingly favorable numbers of interfaces between the physiologic layers to impart maximum angular velocity towards the target in coil. 4. Sensory input from the snake allows expedient recoil when prey is sighted and suggests this is by no means a passive/relaxation phase. 5. The smallest unit of the heart [muscle] is a [cell] called a [cardiomyocyte]. 6. [Cardiomyocyte]s are decidedly not [particle]s but tend to exhibit some astonishingly similar behavior around a long and short axis. 7. Theory in this area suggests divergent strings of living cardiomyocytes [myocardial muscle mass] grouped and electrically herded around a center liquid [mass] tidally pushed in and out. 8. String theory of myocardial tissue implies anchored and fixed vectors matched 180 degrees to the connective tissue of the heart, namely the heart valves, skeleton of the heart and central body of the heart. 9. Demand driven tidal forward and backward flow begins to describe the number of potential vectors arranged in superimposed angles in solid muscle mass opposed against a viscous, living blood mass. 10. Posit that the [heart/myocardium/cardiac muscle mass] rotates on a long axis clockwise and counterclockwise in layers of muscular sheets arranged one on another from the internal/blood exposed surfaces [endocardium] to the outer/[pericardial space] surfaces [epicardium]. 11. Posit that no single layer turns back or forth on the long axis more than 30 degrees, but all layers in summation turn at least 360 degrees in response to physiologic demand. 12. Thus understood, revolutions per minute around the long axis are readily posited as and extrapolated to time variables [heart rate]. 13. Posit the distal muscular layers of the heart fold and unspread inward to expel blood [systole/pump/ejection fraction= End Systolic Volume/End Diastolic Volume]triggered by sequential concurrent electrical polarization. 14. Volumetric derivation of Systole is perhaps best mathematically stated as Ejection Fraction [EF]. 15. EF is readily extrapolated to [Cardiac Output/CO], first defined by [Adolph Fick]. 16. Posit the proximal muscular layers of the heart unfold and spread outward to impel blood [diastole/sump/] as defined by [Arthur Guyton] guided by sequential electrical depolarization. 17. Posit that superimposed muscular layers engage one another on a plurality of angles around a well defined (mostly plasma) long axis suggesting shear and countershear of angular velocity. 18. Suggest most pragmatic (inexpensive and noninvasive) readily imaged solid long axis definition as Cardiac Apex (south myocardial pole)-Central Body of the Heart [collagen]-(Left AV collagen ring)/ (Right PV collagen ring). 19. Long axis performance physics of the heart are best and first attributed to Robert Hooke. 20. Short axis determinants are most expediently attributed to muscle mass with scarce influence of blood mass. Short axis performance physics of the heart are best and first attributed to Pierre LaPlace. 21. Posit that myocardial layering back and forth of available subsets of cardiomyocytes illustrates principles of shear and subsequent torque generation at work impelling and expelling blood in and out 60-80 times/minute for 60-80 years. 22. Crossing/uncrossing of multiple muscular bands suggests that Francisco Torrent-Guasp was looking ahead and further implies a force multiplier such as Angular Velocity at work within bands of a dedicated systolic heart and a dedicated diastolic heart.--Lbeben (talk) 03:00, 27 May 2008 (UTC)
[edit] Angular Frequency!
The page describes angular frequency, not angular velocity!
Angular frequency has units Hz or s^-1 (or rad*s^-1 if you prefer) and is a measure of the rate of change of the angle. Angular velocity has units m^2*s^-1 and is the tangential velocity × radius. (× = cross product).
Just like angular momentum = tangential momentum × radius and torque (i.e. angular foce) = tangential force × radius.
On the angular momentum page, it says that angular momentum = mass * angular velocity (just like linear momentum = mass * linear velocity), so how can this be if the angular momentum page states that its units are kg m^2 s^-1, and this page says its units are s^-1 ?
--58.167.240.245 (talk) 08:33, 5 June 2008 (UTC)
- Er, the angular momentum page says ang.mom. = moment of inertia * ang.velocity. Moment of intertia has SI units kg m²; thus is consistent with angular velocity having units s-1. Springy Waterbuffalo (talk) 10:45, 5 June 2008 (UTC)
