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lu6cifer
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Units

Postby lu6cifer » Sun Sep 13, 2009 12:51 am UTC

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.
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Re: Units

Postby Squid Tamer » Sun Sep 13, 2009 1:31 am UTC

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.

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Re: Units

Postby lu6cifer » Sun Sep 13, 2009 2:57 am UTC

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.

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Re: Units

Postby thoughtfully » Sun Sep 13, 2009 3:01 am UTC

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.
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Re: Units

Postby Seraph » Sun Sep 13, 2009 3:23 am UTC

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.

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Re: Units

Postby You, sir, name? » Sun Sep 13, 2009 4:20 am UTC

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.
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Re: Units

Postby Cup of Dirt » Sun Sep 13, 2009 4:34 am UTC

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:

[math]F = \frac{Gm_1m_2}{r^2}[/math]

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.
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Re: Units

Postby PM 2Ring » Sun Sep 13, 2009 12:20 pm UTC

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!

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Re: Units

Postby Diadem » Sun Sep 13, 2009 3:25 pm UTC

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.
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Re: Units

Postby PM 2Ring » Sun Sep 13, 2009 4:31 pm UTC

Diadem wrote:
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.

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Re: Units

Postby thoughtfully » Sun Sep 13, 2009 4:59 pm UTC

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.
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Re: Units

Postby PM 2Ring » Sun Sep 13, 2009 5:17 pm UTC


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Re: Units

Postby thoughtfully » Sun Sep 13, 2009 6:27 pm UTC

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.

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Re: Units

Postby Diadem » Mon Sep 14, 2009 12:41 am UTC

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?
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Re: Units

Postby You, sir, name? » Mon Sep 14, 2009 12:56 am UTC

Diadem wrote:
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.
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Re: Units

Postby Zamfir » Mon Sep 14, 2009 8:01 am UTC

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.

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Re: Units

Postby jaap » Mon Sep 14, 2009 8:29 am UTC

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.

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Re: Units

Postby mr-mitch » Mon Sep 14, 2009 3:10 pm UTC

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.

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Re: Units

Postby eSOANEM » Mon Sep 14, 2009 4:47 pm UTC

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.
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Re: Units

Postby gmalivuk » Mon Sep 14, 2009 6:15 pm UTC

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.
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Re: Units

Postby Zamfir » Mon Sep 14, 2009 6:32 pm UTC

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").

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Re: Units

Postby Carnildo » Tue Sep 15, 2009 3:07 am UTC

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.

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Re: Units

Postby PM 2Ring » Tue Sep 15, 2009 6:24 am UTC

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. :)

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Re: Units

Postby Tass » Tue Sep 15, 2009 1:48 pm UTC

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

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Re: Units

Postby PM 2Ring » Tue Sep 15, 2009 3:54 pm UTC

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

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