Understanding Units: Multiply vs Divide

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Discussion Overview

The discussion revolves around the conceptual understanding of unit multiplication versus division in physics, particularly focusing on examples like Weber (Wb) and Newton meters (Nm). Participants explore the implications of different unit combinations and their dimensional significance in various contexts, including area and volume.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the meaning of units being multiplied versus divided, using Weber (1 Wb = 1 Vs) as an example.
  • Others explain that units like m² and m³ represent area and volume, respectively, indicating a dimensional difference that necessitates multiplication.
  • A participant illustrates the concept with a practical example of calculating floor area, emphasizing the two-dimensional nature of square meters.
  • Some argue that velocity (m/s) is a derivative of position with respect to time, while Weber is an integral of voltage with respect to time.
  • There is a request for a more generalized explanation of unit multiplication beyond specific examples like m² or Nm.
  • One participant expresses confusion about visualizing the multiplication of different units, such as Newtons and meters, compared to square meters.
  • Another participant suggests that unit multiplication is an abstract concept and emphasizes that units can be defined in terms of one another.
  • Some participants challenge each other's understanding of units, questioning why certain combinations are more difficult to conceptualize than others.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding unit multiplication and division, with some agreeing on the definitions while others remain confused or seek further clarification. Multiple competing views on how to conceptualize these units exist, and the discussion remains unresolved.

Contextual Notes

Limitations include differing interpretations of unit definitions, the abstract nature of unit multiplication, and the challenge of visualizing certain unit combinations. Some participants rely on specific examples to illustrate their points, while others seek a broader conceptual framework.

polaris90
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What does it mean to have units being multiplied rather than divided. For example 1Weber which is equal to 1Vs. Saying 1 Volt second doesn't make much sense to me. I understand if it said for example N/m. In general what does it mean to have the units being multiplied rather than divided?
 
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What does it mean if you have units like m^2 or m^3?
 
Well, if you are trying to cover your floor with tiles, and your room is 5m by 6m, you need 30m^2 of floor tiles. meter^2 is dimensionally different than meter, since it is a two-dimensional area, not a length. It has to be multiplied, not divided, because of how it scales. For example, a meter is 100 centimeters; therefore, a square meter is 100^2 square centimeters.

When you have a divided unit, for example, 1 meter per second--that's the same as 1 centimeter per centisecond, because you scaled down the numerator and denominator by a factor of ten.

1 volt second = 1 millivolt kilosecond, because milli and kilo cancel out when you multiply them. Capiche?
 
Have you had calculus?

Velocity has units of m/s. Velocity is the DERIVATIVE of position with respect to time.

Weber has units of V*s. Magnetic flux (Weber) is the INTEGRAL of voltage with respect to time.
 
polaris90 said:
What does it mean to have units being multiplied rather than divided. For example 1Weber which is equal to 1Vs. Saying 1 Volt second doesn't make much sense to me. I understand if it said for example N/m. In general what does it mean to have the units being multiplied rather than divided?

does this make a difference for you?
1 Weber = 1 Vs
1 V = 1 Weber/second
 
If you have a problem with multiplying units, one can only imagine what you would think of more abstract units such as fractional dimensions...
 
@flatmaster
The only one with a reasonable answer, that helps understand it. I did some reading an you were correct about it. However, I my question was more general and used the Weber as an example. It is clearly understood when you have units such as meters per second, which means a change of a meter per every second. Or if we said one kilogram per meter squared, which means there is an amount of an kilogram for every meter in the x direction and meter in the y direction. In a more generalized form, it says a change of a unit for every change of this other unit. But if you have units being multiplied( not such as m^2 which I mentioned above), is there a more generalized way to explain it?
 
polaris90 said:
@flatmaster
The only one with a reasonable answer, that helps understand it. I did some reading an you were correct about it. However, I my question was more general and used the Weber as an example. It is clearly understood when you have units such as meters per second, which means a change of a meter per every second. Or if we said one kilogram per meter squared, which means there is an amount of an kilogram for every meter in the x direction and meter in the y direction. In a more generalized form, it says a change of a unit for every change of this other unit. But if you have units being multiplied( not such as m^2 which I mentioned above), is there a more generalized way to explain it?

So you are asking what a unit of measurement squared is? As in km² or m²?
 
No, as I already mentioned above in the text you quoted. My question is when you have two different units such as Newton Meters, which according to my reading is equal to the amount of force of one Newton applied to an arm perpendicularly which is one meter long. I understand how to work with the units when it comes to mathematical calculations. But I would like to have a more conceptual understanding of how the units work when they are being multiplied.
 
  • #10
polaris90 said:
No, as I already mentioned above in the text you quoted. My question is when you have two different units such as Newton Meters, which according to my reading is equal to the amount of force of one Newton applied to an arm perpendicularly which is one meter long. I understand how to work with the units when it comes to mathematical calculations. But I would like to have a more conceptual understanding of how the units work when they are being multiplied.

I'm really baffled by that question. So, multiplying meter by meter to get m2 is OK, but multiplying meter by Newtons to get Nm some how is causing you conceptual difficulties. How come?
 
  • #11
polaris90 said:
@flatmaster
The only one with a reasonable answer, that helps understand it.

I think there were other good answers. 256bits' answer was pretty good. You can't have division without multiplication.
 
  • #12
dauto said:
I'm really baffled by that question. So, multiplying meter by meter to get m2 is OK, but multiplying meter by Newtons to get Nm some how is causing you conceptual difficulties. How come?
Good point, I guess it might be because I cannot simply visualize it in my head as easily as a m^2.
 
  • #13
Stop trying to visualize it then. Ultimately unit multiplication is an abstract concept. You are performing a mathematical operation on non-numerical entities. A meter is not a number, it's a distance. A second is not a number, it's an amount of time. A meter per second is not a number, it's an amount of speed. Even though none of those things are numbers, it is correct to state that a meter per second is equal to a meter divided by a second. This operation is possible by definition. A meter per second is defined as a meter divided by a second (not as a meter for every second as you stated earlier), and a Weber is defined as a Volt times a second. That's all there is to it.
 
  • #14
Is it that you have problems understanding N*m as an unit but you are OK with Newton by itself?
A force measured in Newtons does not raise conceptual problems?
If this is the case, remember that N=kg*m/s^2. Now you have a problem with N too?
And N/m which you say you "understand" is "actually" kg/s^2. How do you visualize the s^2?:smile:
 
  • #15
SteamKing said:
What does it mean if you have units like m^2 or m^3?

m^2 is the unit of area whereas, m^3 is the units of Volume. Both the units are in SI system.
 
  • #16
Hey, Gudiya... that thread is from 2 years ago. That's OK, I forget to check the date often too.
 

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