Yesterday I asked why there's no name for a unit of momentum. Today I have answers. Plus, if you read all the way to the end, I have a genuinely constructive suggestion.
First things first, in case you have no idea what I'm talking about. In the metric system—officially known as SI—there are three basic quantities: the meter, the kilogram, and the second.¹ Everything else is derived from those three. For example, force = mass * acceleration, so:
F = ma
a = distance / seconds²
Therefore, F = mass * distance / seconds²
One unit of force = 1 kg * 1 meter / 1 second²
This quantity is called a newton, named after Isaac Newton. Lots of other things have names too: ohm, watt, lumen, joule, and so forth. Click here for a list.
Momentum is a critically important quantity, equal to mass * velocity. So why wasn't it ever given a name? I did several minutes of research on this question, and the most authoritative sounding answer came from a commenter at Stack Exchange called Conifold. He or she explains that there were two waves of standardization and naming:
The second wave, started in the 1860s and formalized by the 1880s in both SI and its competitor CGS, was meant to catch up with developments in thermodynamics and electromagnetism, and gave us ohms, volts, farads, watts, etc. Kilograve was renamed into kilogram and became the unit of mass. The unit of force was named dyne in CGS (from Greek dynamis — force) and newton in SI.
....The unit for power, watt, was suggested even before joule, by Siemens in 1882, to replace Watt's own horsepower used to measure the output of steam engines. Siemens was an electric engineer. Joule himself was honored by a unit name for determining the mechanical equivalent of heat. Momentum was out of luck.
In other words, momentum has no name because no one ever bothered to give it one. However, another commenter, jkien, tells us that it was given a name in the CGS system
In 1887 a committee of the British Association was appointed for the purpose of "considering the desirability of introducing uniform nomenclature for the fundamental units of mechanics of co-operating with other bodies engaged in similar work.” The committee issued a series of questions to members, and collected their replies. The result was that in 1888, when the committee met at Bath, they were able, amid much difference of opinion, to agree as to the desirability of introducing names for the C. G. S. units of velocity, momentum,
and pressure; the names suggested being, kine, bole, and barad respectively.
So in the CGS system, a single unit of momentum is the bole. It never caught on and goes entirely unused today.
Long story short, there's no special reason that there's no name for a unit of momentum. There just isn't. But this prompts an obvious question: What should it be, and how do we get it adopted?
Let's take the second question first. The problem is that traditionally these units are named after people who had something to do with discovering or theorizing about them. But momentum goes back a long way, and everyone associated with it is a dead white man. This is boring and will get no one excited.
So what if we proposed naming it after a woman? That would not only be well deserved, but it would get the attention and support of lots of people. But who should it be?
By chance there's an excellent candidate. The importance of momentum in physics is not so much in the quantity per se, but in the fact that it's always conserved. When a rocket throws off propellant in one direction (down), the rocket goes in the other direction (up) because the total momentum of the system must be conserved.²
But why must it be conserved? In 1915, a brilliant German mathematician named Emmy Noether proved that all conservation laws can be expressed as symmetries. In particular, conservation of momentum is a consequence of the symmetry of space. This was a critical contribution to physics.
So I propose that the unit of linear momentum be named a noether. Who's with me?³
¹There's a competing system called CGS, in which the three basic units are the centimeter, the gram, and the second. It is little used.
²In case you're curious, this is also part of the explanation for how airplanes work. The shape of the wing forces air downward at considerable speed, which means the airplane is forced upward. When these are balanced, the plane travels at a steady altitude.
³We can argue about angular momentum some other time.
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Sign me up for Team Noether.
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"¹There's a competing system called CGS, in which the three basic units are the centimeter, the gram, and the second. It is little used."
This isn't actually correct. For the three most common units used (distance, mass, time) the two are used interchangeably. The cgs and the SI are basically the same system just on a different scale of the metric system, and thus both are used accordingly to the needs.
Want to measure distance between cities? Use Kilometers.
Want to measure distance between to points at home? Use meters.
Want to measure things on a blueprint or other smallish thing? Use centimeters.
That is the simplicity of the metric system, that depending on the scale, for the most part you can easily avoid having to use fractions or decimal points because there is a corresponding full unit in either direction of the scale.
For more field specific units like force, energy, pressure, or electromagnetism. The SI named unit is indeed preferred in general over the cgs unit, but here again it is a matter of scale (since all of these units are derived from the basic three), so in some fields or applications the CGS units are still used. It's all dependent on the specific need or personal preference.
I think it's more that the prefixes are inconsistent than anything else - "metre" doesn't match up with "kilo-gram" in a useful way, and nor does 'centimetre' work with 'gram'. (Also, that "second" derives from an entirely different number base system doesn't help either.)
There are other differences between CGS and SI, particularly when it comes to electromagnetism. CGS uses two different ways (plus a third, hybrid, way) of dealing with charges and currents and fields. SI tries to unify all of this, at the cost of adding a couple of additional constants (vacuum permittivity and permeability), but at least you don't end up with square roots of centimetres and the like, as you do in CGS.
The gas law constant, R, would always throw me off--you can (could) find it expressed in different units of pressure (atm, mm of Hg, anyone?). Also, atm has be re-defined recently (meaning past 30 or so years 😉
Anoether esoteric post.
I foresee some significant misunderstandings. Please sir, may I have a noether?
+1
😉
That does highlight another issue, if the noether is used as a unit, what would its symbol be? "N" is taken. It could be called noethers and use Ns, though that could be confused with impulse, N*s.
Obvs. choice would be Œ.
While acknowledging the sexist bias that calls women by their first names where men are called by surnames, I confess that "emmy" is a better unit.
This was going to be my suggestion! The "emmy" because it is catchy and easy to say. And it could be abbreviated as the "e."
Except . . . there is that stupid TV awards show with that name. And some might object that using a first name might seem disrespectful.
On second thought, I'm with Kevin on "noether," which could be abbreviated as "nt" or "nr".
"Emmy" said aloud sounds like m times e.
1. She has no place with the gods. Newton, Faraday, Watt, they’re kind of in a class of their own
2. Isn’t momentum confusing enough without adding an additional layer of abstraction and indirection? I’d much prefer if expressing units in terms of base SI units became even more common
I know this is half tongue in cheek but hope this doesn’t become a hobby horse. Then again what am I gonna do about it, you do you Kev
On the contrary, Noether's Theorem is one of the driving forces behind modern theoretical physics. The Standard Model exists because of it.
On top of that, she's an important figure in the history of mathematics as well.
"Kine"? It already means "cattle."
"Bole" The trunk of a tree. No wonder those two were non-starters. As for "barad", no comment.
" When a rocket throws off propellant in one direction (down), the rocket goes in the other direction (up) because the total momentum of the system must be conserved."
That is just false, because it ignores gravity. The force that is used to accelerate the gases down needs to match the sum of the force of gravity and added momentum of the rocket.
For a flying plane, the pplave doesn't gain momentum upwards even though it accelerates air downwards, because the force for this acceleration matches the force of gravity.
To preserve the momentum in these systems you need to include Earth and its momentum in the system.
The atmospheric pressure we experience at the surface is slightly higher because of all those big aluminum particles supported in the air by the smaller molecules.
That is just false, because it ignores gravity.
No, it doesn't. Kevin's statement is perfectly correct. That gravity acts on an object doesn't negate the general principle.
Which general principle?
The conservation of momentum does not apply when there is gravity, unless you include the momentum of the body thet causes the gravity (Earth in this case). In other ways, conservation of momentum applies only only to close systems, and the plane and air under gravity are not a close d system (because they interact with Earth via gravity).
There's also Émilie du Châtelet. So maybe the unit can be the Emm.
Although in the early 18th century the concepts of force and momentum had been long understood, the idea of energy as transferable between different systems was still in its infancy and would not be fully resolved until the 19th century. It is now accepted that the total mechanical momentum of a system is conserved and none is lost to friction. Simply put, there is no 'momentum friction' and momentum can not transfer between different forms, and particularly there is no potential momentum. Emmy Noether later proved this to be true for all problems where the initial state is symmetric in generalized coordinates. Mechanical energy, kinetic and potential, may be lost to another form, but the total is conserved in time.
The Du Châtelet contribution was the hypothesis of the conservation of total energy, as distinct from momentum. In doing so, she became the first to elucidate the concept of energy as such, and to quantify its relationship to mass and velocity based on her own empirical studies. Inspired by the theories of Gottfried Leibniz, she repeated and publicized an experiment originally devised by Willem 's Gravesande in which balls were dropped from different heights into a sheet of soft clay. Each ball's kinetic energy - as indicated by the quantity of material displaced - was shown to be proportional to the square of the velocity. The deformation of the clay was found to be directly proportional to the height the balls were dropped from, equal to the initial potential energy.
https://en.wikipedia.org/wiki/%C3%89milie_du_Ch%C3%A2telet
Kevin will also be pleased to learn that Noether was a protege and colleague of his own kitty's namesake, the German mathematician David Hilbert. Hilbert overcame the objections of conservative members of the university faculty in Goettingen and hired her as the first female privatdozent (unsalaried lecturer) in the university's mathematical institute, at the time the premier math department in the world. Unable to earn tenure and forced out of her job when the Nazis took power, she left for the US and took a position at Bryn Mawr College near Philadelphia. Einstein tried to get her appointed to the Institute of Advanced Study, calling her the most brilliant mathematician of her generation, but she declined and remained at Bryn Mawr where she enjoyed working with female students. She died suddenly in 1935 from post-operative complications following surgery to remove some benign uterine cysts.
Noether was a professor of Mathematics at Göttingen when Maria Goeppert-Mayer attended.
https://en.wikipedia.org/wiki/Maria_Goeppert_Mayer
(Goeppert-Mayer already has a unit for two-photon absorption, her doctoral thesis, named after her)
I like better the names of the units of acceleration!!
Jerk
Snap
Crackle
and
Pop!!!
so a killa-Snap is a Pop? or are we going all Wayan brothers on this?
These are the names of the successive derivatives of acceleration with respect to time. They aren't units of acceleration; they're not units at all.
Why have a unit name for momentum when velocity and acceleration don't even have unit names?
+10. For at least one Noether hater out there, she was instrumental in early exploration of algebraic structures - groups/rings/modules as well as a lot of other stuff. Most people don't know of her importance because a) she's a woman and there was no effort to canonize her back in the day, and b) you have to know a bit of math before you can understand what she did. How do you explain the descending chain condition in words a conservative Republican can understand?
Yes, a highly significant figure. Among other things, she helped to invent algebraic topology — not an easy matter to explain to the layman.
BTW, in re Kevin's explanation for how airplanes work, I gotta ask, what, no love for Bernoulli?
I don't think there is a massive flow of high speed air directed downward from an airplane's wings, but I only had 1 semester of college physics around the time that Nixon was president. This seems like a better explanation of lift:
https://www.cam.ac.uk/research/news/how-wings-really-work
Exactly. The plane isn't thrust upward. The air has to move faster across the top of a curved wing, creating a pressure difference -- lower pressure above the wing and higher pressure below. The wing is basically sucked upward.
It still push the air down, though not "high speed downwards". Without pushing down it cannot egenrate force upwards, which is what is needed to keep the plane from going down because of gravity.
There is a very simple reason momentum has no unit name. It is always there but very rarely used in a formula (torque is different matter). It also has no direct use in everyday life. Most of the unit names that have stuck and are in actual use have at least some use in daily life.
Good luck making the Noether stick!
cgs is what's (mostly) used in astrophysics. cm, g, s, erg, gauss. What's a few more powers on the exponents? These then get mixed in with other "sensible" units like Angstrom and Hz. A few astro-particular units like parsec/kpc/Mpc/Gpc or Jansky (a flux per unit frequency, although I think you'll see milli-Jansky used more often). Lots of relative units like solar mass, or Eddington luminosity (which is mass dependent, and technically composition dependent). And then a whole lot of even crazier units like magnitudes in specific wavelength filter bands, Crab units (an X-ray flux measurement, which is both energy and observing instrument dependent), and then a whole host of things like "equivalent hydrogen column" (a measure of the amount of absorbing material, in units of cm^{-2}, if you were measuring the hydrogen, which you are not, where the value is going to depend upon an implicit assumed set of atomic cross sections and a set of assumed elemental abundances relative to hydrogen). It's all kind of crazy. But SI, not used that much.
I always liked the system used by high energy physicists, where the speed of light c = 1. E = Mc^2 then turns into E = M, and mass and energy have the same unit of measure.
And Planck's constant h-bar = 1 too, so time and distance can be in units of 1/energy.
The rate of change of acceleration is known as the "jerk".
True. And running around without clothes on is known as the "streak".
Long ago I too wanted there to be a name for a unit of momentum. At some point I realized that using Newton-Seconds (Ns) as the units made more sense.
The unit for Force has Seconds squared on the bottom. Momentum just has Seconds on the bottom. So if you just multiply Force (N) times Time (s) you get Momentum (Ns). You can also call it Mass (kg) times Velocity (m/s) to get (kg m/s). This is the same units as (Ns).
Things became much clearer to me when I started thinking of momentum in terms of Newton-Seconds. If something has momentum of 100 Ns that means if you apply an opposing force of 1 Newton for 100 seconds then the object will have no momentum. Or 10 N for 10 s, or 10,000 N for .01 s, etc.
And if you apply a force of 2 N for 20 seconds to something with no momentum, it will then have a momentum of 40 Ns. After thinking about momentum this way I understood it much better and stopped thinking we needed another unit.
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I propose her name for the unit of angular momentum because one good turn deserves a Noether.
Ouch! Well-played, Sir Madam, well-played.