Why is there a time unit in some inertia units and not in others?

  • I
  • Thread starter Jmoulton
  • Start date
  • #1
2
0
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.
 

Answers and Replies

  • #2
jbriggs444
Science Advisor
Homework Helper
2019 Award
9,069
3,795
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.
Guessing here...

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
jack action
Science Advisor
Insights Author
Gold Member
1,992
2,197
To repeat what @jbriggs444 said with other words (I mean, for us who don't bother with the U.S. customary system :headbang: :oldwink:):

You could rewrite the presented units this way:
  • lbf.in.s²
  • lbm.in²
Where one is a pound-force and the other is a pound-mass.

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
Science Advisor
Homework Helper
2019 Award
9,069
3,795
  • #5
jack action
Science Advisor
Insights Author
Gold Member
1,992
2,197
They are out by a factor of one g expressed in inches per second squared.
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.
 
  • Like
Likes jbriggs444
  • #6
2
0
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.
 
  • #7
jack action
Science Advisor
Insights Author
Gold Member
1,992
2,197
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
 

Related Threads on Why is there a time unit in some inertia units and not in others?

Replies
10
Views
13K
Replies
21
Views
3K
  • Last Post
Replies
6
Views
207K
  • Last Post
Replies
3
Views
10K
Replies
6
Views
2K
Replies
8
Views
2K
Replies
1
Views
2K
Replies
5
Views
730
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
17
Views
3K
Top