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jbriggs444

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Guessing here...

If you want to use the pound mass for moment of inertia then an appropriate unit could be pound(mass) inch

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-second

[Yeah, yeah, we all know that the U.S. customary system of units is pathetic. No need to crow over it]

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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.

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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.To repeat what @jbriggs444

Replacing in the inertia unit, we get M.L² = (F.T²/L). L² = F.L.T²; So both units are equivalent.

Visit, for instance,http://www.translatorscafe.com/cafe/EN/units-converter/moment-of-inertia/12-1/

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I meantThey are out by a factor of one g expressed in inches per second squared.

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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.

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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

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