## Units

For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.

Moderators: gmalivuk, Moderators General, Prelates

lu6cifer
Posts: 230
Joined: Fri Mar 20, 2009 4:03 am UTC
Location: That state with the all-important stone

### Units

So, a unit like m/s--meters per second--means that if I run at 5 meters per second, I will travel 5 meters every second. But, then what does something like a Newton-meter mean? How would you explain that as I did with m/s?

Edit: "I will travel 5 meters per second" instead of "I will travel 4 meters per second"...I think I switched around the numbers while posting. Thanks for the catch Squid Tamer
Last edited by lu6cifer on Sun Sep 13, 2009 2:55 am UTC, edited 1 time in total.
lu6cifer wrote:"Derive" in place of "differentiate" is even worse.

doogly wrote:I'm partial to "throw some d's on that bitch."

Squid Tamer
Posts: 220
Joined: Fri Apr 03, 2009 3:59 am UTC
Location: Over there
Contact:

### Re: Units

Wouldn't you travel 5 meters in one second, if you were going 5 m/s?

Anyway, the newton meter is a unit of torque, which is rotational force.
A newton is a unit of force, and a newton-meter is the torque of one newton pushing the end of a lever 1 meter long.

You can (usually?) substitute a division as "per", so that m/s means meters per second, and g/cm^3 means grams per cubic centimeter.

lu6cifer
Posts: 230
Joined: Fri Mar 20, 2009 4:03 am UTC
Location: That state with the all-important stone

### Re: Units

But, I was talking about in general, how do you 'visualize' units such as newton-meter or newton-second, or joule-second?
lu6cifer wrote:"Derive" in place of "differentiate" is even worse.

doogly wrote:I'm partial to "throw some d's on that bitch."

thoughtfully
Posts: 2253
Joined: Thu Nov 01, 2007 12:25 am UTC
Location: Minneapolis, MN
Contact:

### Re: Units

A Newton-meter is the same unit as a Joule also, or units of work/energy. The amount of work done applying a force of one newton over a distance of a meter.

Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.
-- Antoine de Saint-Exupery

Seraph
Posts: 343
Joined: Mon Jul 16, 2007 4:51 pm UTC

### Re: Units

thoughtfully wrote:A Newton-meter is the same unit as a Joule also, or units of work/energy. The amount of work done applying a force of one newton over a distance of a meter.

If you follow the BIPM recommendations, a Newton-meter is a measure of torque, and a Joule is a measure of work/energy. While they may be dimensionally equivalent, it isn't a good idea to equate the two, as they measure two different things. Specifically Torque is a vector, while energy is a scaler.
Last edited by Seraph on Sun Sep 13, 2009 4:32 am UTC, edited 1 time in total.

You, sir, name?
Posts: 6983
Joined: Sun Apr 22, 2007 10:07 am UTC
Location: Chako Paul City
Contact:

### Re: Units

lu6cifer wrote:But, I was talking about in general, how do you 'visualize' units such as newton-meter or newton-second, or joule-second?

1 newton is the force it takes to give an 1 kg object an acceleration of 1 m/s^2.
1 newton meter is the torque required to give an object with moment of inertia 1 kg m^2 an angular accleration of 1 rad / s^2.
I edit my posts a lot and sometimes the words wrong order words appear in sentences get messed up.

Cup of Dirt
Posts: 75
Joined: Wed Jul 08, 2009 3:22 am UTC

### Re: Units

I think those numbers should be the same.

But, to answer your question, it's pretty much the same thing with more complicated units. For example, a Newton-meter (also known as a Joule) is a unit of energy, or work. So you have done one Joule of work if you exert a constant force of one Newton on an object over a distance of one meter, as long as the direction of motion and the force you exert are in the same direction. But you have to be careful, because a Newton-meter is also a unit of torque, which is basically the angular equivalent of force. If you have a wrench a meter long gripping a bolt, and you exert a Newton of force on the end of the wrench, perpendicular to the wrench itself, then you are exerting one Newton-meter of torque. Energy and torque are very different things, so the precise meaning of a term like "Newton-meter" depends on context.

Those examples are pretty straightforward, but sometimes units just don't have an easily understandable meaning. A good example is G, the gravitational constant, which comes in units of m3/(kg*s2). Those units are what they are because of G's role in Newton's law of gravity:

$F = \frac{Gm_1m_2}{r^2}$

G is basically the exchange rate between a gravitational force on one hand, and the masses of two objects and their distance on the other. So multiplying [imath]m_1m_2/r^2[/imath] by G must have the effect of making the right hand side have units of force. You can write Newtons as kilogram*meters/second2, and verify for yourself that G must have those units. That's kind of the only significance.
"Why can't people see things the way they are?"
"Because that's the way they are. Why can't you see that?"

PM 2Ring
Posts: 3713
Joined: Mon Jan 26, 2009 3:19 pm UTC
Location: Sydney, Australia

### Re: Units

Seraph wrote:While they may be dimensionally equivalent, it isn't a good idea to equate the two, as they measure two different things.

So I shouldn't be using picohectares to measure fuel consumption and should instead use litres per 100 kilometres? Boring!

Posts: 5654
Joined: Wed Jun 11, 2008 11:03 am UTC
Location: The Netherlands

### Re: Units

PM 2Ring wrote:
Seraph wrote:While they may be dimensionally equivalent, it isn't a good idea to equate the two, as they measure two different things.

So I shouldn't be using picohectares to measure fuel consumption and should instead use litres per 100 kilometres? Boring!

Picohectares would be a good way of expressing litres per 100 kilometres. But fuel consumption (rather: efficiency) is usually given in kilometers per liter, which has dimension m^-2. So it wouldn't work.

It's pretty hard to find two nice units that combine to m^-2. You could express it in kilolux per millilumen I suppose. Or Teratesla per Megaweber.
It's one of those irregular verbs, isn't it? I have an independent mind, you are an eccentric, he is round the twist
- Bernard Woolley in Yes, Prime Minister

PM 2Ring
Posts: 3713
Joined: Mon Jan 26, 2009 3:19 pm UTC
Location: Sydney, Australia

### Re: Units

PM 2Ring wrote:So I shouldn't be using picohectares to measure fuel consumption and should instead use litres per 100 kilometres? Boring!

Picohectares would be a good way of expressing litres per 100 kilometres. But fuel consumption (rather: efficiency) is usually given in kilometers per liter, which has dimension m^-2. So it wouldn't work.
That depends where you live. Litres per 100 kilometres has been the standard in Australia for several decades, since we went metric.

From http://en.wikipedia.org/wiki/Fuel_efficiency
Fuel economy is usually expressed in one of two ways:

* The amount of fuel used per unit distance; for example, litres per 100 kilometres (L/100 km). In this case, the lower the value, the more economic a vehicle is (the less fuel it needs to travel a certain distance); this is the notation generally used across Europe.

* The distance travelled per unit volume of fuel used; for example, kilometres per litre (km/L) or miles per gallon (MPG), where 1 MPG (imperial) = 0.354013 km/l. In this case, the higher the value, the more economic a vehicle is (the more distance it can travel with a certain volume of fuel). This notation is popular in the USA and the UK (MPG), India and Latin America (km/L).

1 picohectare is the area of a 0.1mm x 0.1mm square. I like the image of a vehicle consuming a fuel "stream" measured this way.

thoughtfully
Posts: 2253
Joined: Thu Nov 01, 2007 12:25 am UTC
Location: Minneapolis, MN
Contact:

### Re: Units

PM 2Ring wrote:1 picohectare is the area of a 0.1mm x 0.1mm square. I like the image of a vehicle consuming a fuel "stream" measured this way.

It's 0.1 mm2, or the area of a square [imath]\sqrt{0.1} \approx .316[/imath] mm on a side.

Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.
-- Antoine de Saint-Exupery

PM 2Ring
Posts: 3713
Joined: Mon Jan 26, 2009 3:19 pm UTC
Location: Sydney, Australia

### Re: Units

thoughtfully
Posts: 2253
Joined: Thu Nov 01, 2007 12:25 am UTC
Location: Minneapolis, MN
Contact:

### Re: Units

I couldn't puzzle out the right query for Google, so I Did The Math(tm). I botched the first step
10000 m2 in a hectare is 1e4 m2, not 1e5 m2.

Perfection is achieved, not when there is nothing more to add, but when there is nothing left to take away.
-- Antoine de Saint-Exupery

Posts: 5654
Joined: Wed Jun 11, 2008 11:03 am UTC
Location: The Netherlands

### Re: Units

PM 2Ring wrote:
Fuel economy is usually expressed in one of two ways:

* The amount of fuel used per unit distance; for example, litres per 100 kilometres (L/100 km). In this case, the lower the value, the more economic a vehicle is (the less fuel it needs to travel a certain distance); this is the notation generally used across Europe.

Interesting. I am from Europe, and I've never seen this used anywhere. Very strange. What countries are supposed to do this?
It's one of those irregular verbs, isn't it? I have an independent mind, you are an eccentric, he is round the twist
- Bernard Woolley in Yes, Prime Minister

You, sir, name?
Posts: 6983
Joined: Sun Apr 22, 2007 10:07 am UTC
Location: Chako Paul City
Contact:

### Re: Units

PM 2Ring wrote:
Fuel economy is usually expressed in one of two ways:

* The amount of fuel used per unit distance; for example, litres per 100 kilometres (L/100 km). In this case, the lower the value, the more economic a vehicle is (the less fuel it needs to travel a certain distance); this is the notation generally used across Europe.

Interesting. I am from Europe, and I've never seen this used anywhere. Very strange. What countries are supposed to do this?

I hear it all the time in Sweden.
I edit my posts a lot and sometimes the words wrong order words appear in sentences get messed up.

Zamfir
I built a novelty castle, the irony was lost on some.
Posts: 7594
Joined: Wed Aug 27, 2008 2:43 pm UTC
Location: Nederland

### Re: Units

Diadem wrote:Interesting. I am from Europe, and I've never seen this used anywhere. Very strange. What countries are supposed to do this?

It's the standard in all countries of the EU, I think. I thought you were from the Netherlands too? Look for example here:
http://www.volkswagen.nl/home/modellen/polo/easyline/technische_gegevens/0,18339,Polo_Easyline_D0Lnl,00.html. It gives 5.5 l/100km as average value.

In this case, the lower the value, the more economic a vehicle is (the less fuel it needs to travel a certain distance)

The "it goes down" part is not the main reason to prefer this method of notation. The point it that l/100km is a linear relationship to the cost and pollution for a given distance, while km/l is linear to the distance you can travel on one tank. The second used to be important, but the first is much more important nowadays.
Improvements from 6l/100km to 5 to 4 to 3 are all the same reduction in cost and pollutants. But the other notation, 16.6km/l to 20km/l to 25 km/l to 33,3km/l, suggests that moving from a 16.6km/l to a 20km/l car is not much of an improvement at all, and as a result people with inefficient cars tend to underestimate the improvements they can get by buying a more efficient vehicle.

jaap
Posts: 2094
Joined: Fri Jul 06, 2007 7:06 am UTC
Contact:

### Re: Units

Zamfir wrote:
Diadem wrote:Interesting. I am from Europe, and I've never seen this used anywhere. Very strange. What countries are supposed to do this?

It's the standard in all countries of the EU, I think. I thought you were from the Netherlands too? Look for example here:
http://www.volkswagen.nl/home/modellen/polo/easyline/technische_gegevens/0,18339,Polo_Easyline_D0Lnl,00.html. It gives 5.5 l/100km as average value.

In the Netherlands, technical specs or other official numbers not part of a sales pitch will always be in litres/100km, but people will colloquially almost always say something like "1 op 20", meaning 1 litre takes you 20 kilometres. Literally that means "1 over 20", so it is dividing it the same way around, but it is really no different to saying it is 20km per litre.

mr-mitch
Posts: 477
Joined: Sun Jul 05, 2009 6:56 pm UTC

### Re: Units

If my memory of the sticker on the cars at car dealerships are correct, Australia also uses L/100km to indicate efficiency. I've planned to work this value out for my car using my trips to uni, but I can't be bothered.

eSOANEM
:D
Posts: 3652
Joined: Sun Apr 12, 2009 9:39 pm UTC
Location: Grantabrycge

### Re: Units

Zamfir wrote:
Diadem wrote:Interesting. I am from Europe, and I've never seen this used anywhere. Very strange. What countries are supposed to do this?

It's the standard in all countries of the EU, I think. I thought you were from the Netherlands too? Look for example here:
http://www.volkswagen.nl/home/modellen/polo/easyline/technische_gegevens/0,18339,Polo_Easyline_D0Lnl,00.html. It gives 5.5 l/100km as average value.

Not in England. Here we use miles per gallon. Of course that's probably because the government made a complete hash of going metric.
my pronouns are they

Magnanimous wrote:(fuck the macrons)

gmalivuk
GNU Terry Pratchett
Posts: 26767
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

### Re: Units

Zamfir wrote:The point it that l/100km is a linear relationship to the cost and pollution for a given distance, while km/l is linear to the distance you can travel on one tank. The second used to be important, but the first is much more important nowadays.

Except in big countries like the US, which might have something to do with why we still do it in the distance per fuel manner.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

Zamfir
I built a novelty castle, the irony was lost on some.
Posts: 7594
Joined: Wed Aug 27, 2008 2:43 pm UTC
Location: Nederland

### Re: Units

gmalivuk wrote:Except in big countries like the US, which might have something to do with why we still do it in the distance per fuel manner.

Nah, it's just ingrown tradition, and the awkwardness of the "per 100km" part. Even though all the official notes here are in l/100km, people still talk about km/l ( or as Jaap says, "1 op 15").

Carnildo
Posts: 2023
Joined: Fri Jul 18, 2008 8:43 am UTC

### Re: Units

Zamfir wrote:The "it goes down" part is not the main reason to prefer this method of notation. The point it that l/100km is a linear relationship to the cost and pollution for a given distance, while km/l is linear to the distance you can travel on one tank. The second used to be important, but the first is much more important nowadays.

Maybe in Europe that's the case, but out here in the Wild West, where you see signs like "next services 92 miles", the distance you can travel on a tank still matters.

PM 2Ring
Posts: 3713
Joined: Mon Jan 26, 2009 3:19 pm UTC
Location: Sydney, Australia

### Re: Units

gmalivuk wrote:
Zamfir wrote:The point it that l/100km is a linear relationship to the cost and pollution for a given distance, while km/l is linear to the distance you can travel on one tank. The second used to be important, but the first is much more important nowadays.

Except in big countries like the US, which might have something to do with why we still do it in the distance per fuel manner.

Australia is a big country, too, but people here seem to have accepted the volume/distance form. I suspect that those who grew up with miles per gallon would still feel more comfortable with that measurement. OTOH, the conversion between the two forms isn't so amenable to mental arithmetic. Especially when you're over 50.

Tass
Posts: 1909
Joined: Tue Nov 11, 2008 2:21 pm UTC
Location: Niels Bohr Institute, Copenhagen.

### Re: Units

I prefer stating the fuel economy as an area or inverse area. 20km/l comes out as 0.05 mm2. Or equivalently 20 per square millimeter. :p

PM 2Ring
Posts: 3713
Joined: Mon Jan 26, 2009 3:19 pm UTC
Location: Sydney, Australia

### Re: Units

Tass wrote:I prefer stating the fuel economy as an area or inverse area. 20km/l comes out as 0.05 mm2. Or equivalently 20 per square millimeter. :p

Join me in the Great Picohectare Revolution! You know you want to.