- #1
Jmoulton
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Why are some inertia units lb-in-s^2 and others lb-in^2. what the difference? The first one is from a gear box spec and the second is from a motor rotor.
Why is there a time unit in some inertia units and not in others?
Note that if you have a system with components with different units of inertia, you have to convert them to the same unit before adding them up. So yes, you would need to multiply the units with lbf.in.s² by 386.0885865302 to get the system inertia in lbm.in².
- #2
jbriggs444
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Guessing here...Jmoulton said:
If you want to use the pound mass for moment of inertia then an appropriate unit could be pound(mass) inch2.
If you want to use the pound force for moment of inertia then you have to first convert it to a unit of mass. For instance, the mass which would be accelerated at a rate of one inch per second squared by a force of one pound force. That unit of mass is also known as a "slinch". (A slug is what you get when you use feet instead of inches. A slinch is what you get when you use inches).
One pound force is one slinch-inch-second2. If you express moment of inertia in slinch-inch2 then that is the same as one pound(force)-inch-second2
[Yeah, yeah, we all know that the U.S. customary system of units is pathetic. No need to crow over it]
- #3
- 3,105
- 7,668
To repeat what @jbriggs444 said with other words (I mean, for us who don't bother with the U.S. customary system 
):
You could rewrite the presented units this way:
If you do a dimension analysis, the unit for inertia should be M.L² (Mass X Length²).
But from F= ma (or m = F/a), we know that a mass could be defined as F.T²/L (Force X Time² / Length).
Replacing in the inertia unit, we get M.L² = (F.T²/L). L² = F.L.T²; So both units are equivalent.
):You could rewrite the presented units this way:
- lbf.in.s²
- lbm.in²
If you do a dimension analysis, the unit for inertia should be M.L² (Mass X Length²).
But from F= ma (or m = F/a), we know that a mass could be defined as F.T²/L (Force X Time² / Length).
Replacing in the inertia unit, we get M.L² = (F.T²/L). L² = F.L.T²; So both units are equivalent.
- #4
jbriggs444
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I agree that both units have the proper dimensionality to measure a moment of inertia. But I do not agree that the two units are the same. They are out by a factor of one g expressed in inches per second squared.jack action said:
Visit, for instance,http://www.translatorscafe.com/cafe/EN/units-converter/moment-of-inertia/12-1/
- #5
- 3,105
- 7,668
I meant equivalent in the sense that they represent the same dimension (like bar and Pascal for units of pressure for example), but not necessarily by the same factor. Sorry for the confusion.jbriggs444 said:
- #6
Jmoulton
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Ok this is a little more clear but if I may follow up with this. I went to this site mentioned above:
http://www.translatorscafe.com/cafe/EN/units-converter/moment-of-inertia/12-1/
and 1 pound-force inch second² = 386.0885865302 pound inch². So if I have a control system with several components I just add the inertia's together but they have to be the same units so all the pound-force inch second² components need to be multiplied by 386.09 in order to get a system inertia. This is all I need to do to get the system inertia, correct? Thanks in advance for your help.
http://www.translatorscafe.com/cafe/EN/units-converter/moment-of-inertia/12-1/
and 1 pound-force inch second² = 386.0885865302 pound inch². So if I have a control system with several components I just add the inertia's together but they have to be the same units so all the pound-force inch second² components need to be multiplied by 386.09 in order to get a system inertia. This is all I need to do to get the system inertia, correct? Thanks in advance for your help.
- #7
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- 7,668
Yes, 386.0885865302 is the conversion factor to establish the relation between those 2 units.
Since weight = mass X g, therefore lbf = lbm X g, where g = 386.0885865302 in/s². Thus:
1 lbf.in.s²
= 1 X lbf X in X s²
= 1 X (lbm X 386.0885865302 X in / s²) X in X s²
= 386.0885865302 X lbm X in²
= 386.0885865302 lbm.in²
Since weight = mass X g, therefore lbf = lbm X g, where g = 386.0885865302 in/s². Thus:
1 lbf.in.s²
= 1 X lbf X in X s²
= 1 X (lbm X 386.0885865302 X in / s²) X in X s²
= 386.0885865302 X lbm X in²
= 386.0885865302 lbm.in²
1. What is the significance of a time unit in inertia units?
The inclusion of a time unit in some inertia units is essential to accurately measure and describe the physical properties of objects. Inertia is the tendency of an object to resist changes in its state of motion, and it depends on the mass of the object and the time it takes to accelerate. Therefore, a time unit is necessary to quantify the rate of acceleration and determine the inertia of an object.
2. Why do some inertia units not have a time unit?
Some inertia units, such as kilograms (kg), do not have a time unit because they are based on the International System of Units (SI), which uses fundamental units of length, mass, and time. In these units, the concept of inertia is indirectly included in the mass unit, as it is a measure of the amount of matter in an object.
3. How does the absence of a time unit affect the measurement of inertia?
The absence of a time unit in certain inertia units can make it challenging to accurately measure the inertia of an object. This is because the rate of acceleration, which is a crucial factor in determining inertia, cannot be directly quantified without a time unit. As a result, other methods, such as using force or momentum, may be used to calculate inertia in these units.
4. Why do some fields of science use different inertia units?
Different fields of science may use different inertia units depending on the context in which they are studying objects. For example, in astrophysics, where objects have large masses and are subject to extreme gravitational forces, units such as solar mass (M☉) or Earth mass (M⊕) may be used to describe inertia. In contrast, in everyday life, units such as grams (g) or pounds (lbs) may be used to measure inertia.
5. How does the use of different inertia units affect scientific research?
The use of different inertia units does not significantly impact scientific research, as there are conversion factors that allow for easy conversion between units. However, using the most appropriate units for a particular field or context can make calculations and comparisons more convenient and meaningful. Additionally, the inclusion or exclusion of a time unit in inertia units can affect the accuracy and precision of measurements in scientific research.
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