Timeline for Why revolutions (or turns) are dimensionless?
Current License: CC BY-SA 4.0
11 events
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| Jul 30, 2019 at 11:14 | comment | added | BioPhysicist | @Dale Right, and I feel like that is what the OP might be getting at. What is the reasoning behind this subjective convention. Your answer is still good though. No worries. | |
| Jul 30, 2019 at 11:11 | comment | added | BioPhysicist | @alephzero Yes, sorry I used the wrong word. My point is still the same point | |
| Jul 30, 2019 at 11:10 | comment | added | alephzero | @AaronStevens The title of the OP says "dimensions" not "units". Units and dimensions are two different things. Miles and millimeters are different units, but they both have the same dimension - length. Similarly for radians and turns of revolutions | |
| Jul 30, 2019 at 11:05 | comment | added | Dale | @Aaron Stevens I understand but the point is that it is a convention. There is no real “why” for conventions. Once you have established that something is a convention then all why questions disappear, except as historical trivia. | |
| Jul 30, 2019 at 10:39 | comment | added | Dale | @roy212 when you are measuring angles you are also comparing how many of a standard pattern are in an angle. That is what any measurement does. Turns and radians are both angle patterns against which we can count and compare. The dimensionality is a matter of convention, just as the size of the pattern. | |
| Jul 30, 2019 at 4:36 | comment | added | BioPhysicist | I agree with everything you say here, but I feel like it misses the point. The OP is asking why we make revolutions unitless. They are not asking if it's valid to give revolutions units. | |
| Jul 30, 2019 at 4:18 | comment | added | roy212 | When I measure a pole I'm also counting. I'm counting how many meters there are compared to the standard unit. Why isn't the same when counting revolutions? I don't think that there is a "revolution pattern" or a "radian pattern" to compare with. But I wonder why isn't possible to make such a pattern. | |
| Jul 30, 2019 at 3:55 | comment | added | Dale | Good point. I have added a paragraph specific to “turns” and “revolutions”. Note that there is no requirement that they be dimensionless. | |
| Jul 30, 2019 at 3:54 | history | edited | Dale | CC BY-SA 4.0 |
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| Jul 30, 2019 at 3:48 | comment | added | rob♦ | Note that the question is about revolutions ("turns") rather than radians. The radian is dimensionless because it's a ratio; a number of turns is dimensionless because it's a thing that you count. The defining logic is in the same section of the SI brochure, but the two angular measures (radians and revolutions) are dimensionless for slightly different reasons. | |
| Jul 30, 2019 at 3:19 | history | answered | Dale | CC BY-SA 4.0 |