Inertia units conversion 4

[bpelec]

I feel as though this may have been explained before, but my searching was not successful. My apologies if I have missed the answer...

I am an electrical engineer struggling with the units of inertia.

I have a specification that states that the inertial load is 0.65 lb-in-sec^2. I can't think of inertia in those units, and so I want to convert to kg-m^2.

I have found several online calculators that can perform this conversion. Here are two:

http://www.magtrol.com/support/inertia_calc.htm

http://www.linengineering.com/LinE/contents/stepmotors/Calculator.aspx

So, all seems good, but I can't work out how on earth the conversion is happening without any additional information given the change in units.

My question is this: what is the theory behind converting an inertia from lb-in-sec^2 to kg-m^2?

Many thanks,

BPELEC.

 

[rb1957]

you can't ... inertia is a term with many meanings.

one meaning is inertial force. lbm*in*sec^-2 has the dimension of force. it is an unconventional unit, a "proper" lbf = 32.174lbm*ft*sec^-2 = 384lbm*in*sec^-2.

another in rotational mass moment of inertia, that you may be more familiar with from rotating machinery.

 

[corus]

It's probably lb force -in-sec^2 you're trying to convert which is mass x acceleration x in x sec^2 = mass x length^2

corus

 

[swearingen]

Here are the steps to go from lb-in-s^2 to kg-m^2:

1lb = 4.45N
1N = 1kg-m/s^2
so
1lb = 4.45kg-m/s^2

1in = 0.0254m

Put them together and you get:

1lb-in-s^2 = 4.45kg-m/s^2 * 0.0254m * s^2

Multiplying and cancelling dimensions, you get:

1lb-in-s^2 = 0.113kg-m^2

If you type this into the converter on your first link, you get the same answer...




If you "heard" it on the internet, it's guilty until proven innocent. - DCS

 

[rb1957]

i stand corrected ! ... and obviously really confused with the indicies !

i guess that's aprt of the problem of having both pound force and pound mass.

 

[bpelec]

Thank you for all for your help and especially to swearingen for such a clear explanation!

Kind regards,

BPELEC.

 

[eromlignod]

Pounds are force; slugs are mass.

1 lb = 1 slug-ft/s^2

Using the lbm is stricly bush-league. It is an imaginary unit that is extremely misleading...much like the kgf. I avoid their use entirely where possible.

I guess they were dreamed up for people whose talents are too modest to understand the concepts of mass and force.

Don
Kansas City

 

[rb1957]

i agree don, but they are part of the environment; and if you avoid kgfs i guess you don't buy much stuff in Canada (or Europe) ... and, yes, i know they're metric rather than SI.

 

[bpelec]

I am based in the UK and last time I checked, SI units were all metric:

http://physics.nist.gov/cuu/Units/units.html

Also, I have never come across Kgf or Kgfs before.. What is the 'f'?

Ok, just found it on Wikipedia, but I have never come across Kilogram-Force before, and I work in a mechanical engineering company despite being electrical myself...

 

[rb1957]

when you buy a bag of sugar do you get a 2kg bag or a 20N bag ?

 

[bpelec]

2kg, and I interpret that as mass... If I climb up a mountain then it's weight will be different...

 

[bpelec]

But I take your point...

 

[katmar]

I don't like the step in swearingen's explanation where he says
1N = 1kg-m/s^2

What on earth is this? I would be grateful if swearingen or anybody else can explain this one to me.

The real problem is the mixing of pounds force with pounds mass. The pound force (lbf) is the unit of force in the British Engineering System of units, and in this system the unit of mass is the slug. The pound mass (lbm) is the unit of mass in the Foot-pound-second system of units, and in this system the unit of force is the poundal. Both of these systems of units (i.e. BES and F-P-S) are consistent sets of units, but things go horribly wrong when people insist on mixing the two systems (as most Americans do unfortunately).

If you mix the two systems you have to introduce the proportionality constant, which is usually written as g[sub]c[/sub]. This has the value 32.174 ft/s[sup]2[/sup], or 386.09 inch/s[sup]2[/sup].

In the original value of 0.65 lb-in-sec^2 these are pounds force and not pounds mass. The lbf value has to be multiplied by g[sub]c[/sub], ie by 386.09 to bring it to pounds mass, and then divided by 2.205 to bring it to kg. And there are 1550 inch[sup]2[/sup] in a meter[sup]2[/sup].

Now the conversion becomes
(0.65 x 386.09) / (2.205 x 1550) = 0.0734 kg.m[sup]2[/sup]
which is the value given by the first link.

If this is not a good reason to learn to use SI units then I don't know what is.


Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[SomptingGuy]

I buy a 2kg bag, one that has the same weight as a calibrated 2kg hunk of metal.

- Steve

 

[katmar]

Whoops - apologies to swearingen. As soon as I pushed the post button I saw that the reason for 1N = 1kg-m/s^2 is simply Force = mass x acceleration. Sorry for that.

But the root cause of the problem is still using pounds force where they should be pounds mass.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[eromlignod]

Pounds *are* a unit of force in engineering. As long as you stick with pounds of force, feet in length and seconds of time, you can use all the same universal engineering formulas that you can with MKS metric units. This requires that the unit of mass be a slug. This is high-school physics, guys.

One of the problems is that a lot of catalog specs still use hybrid, old-timey units, like oz-in for torque or kilogram-force. As long as you diligently boil them down to MKS or lb-ft-s, everything works out without having to use those crazy formulas with magical conversion constants in them.

Don
Kansas City

 

[kamenges]

The customary engineering unit for mass moment of inertia in the US is a bit atypical compared to the SI units. The unit is borne out of the basic Newtonian equation:

T = J*a
where:
T - torque (system unit specific)
J - Mass moment of inertia (system unit specific)
a - rotational acceleration in radians/sec^2

This results in J = T/a.

In the English unit of torque would be in pound-inches and rotational acceleration would be in radians/sec^2. This works to a unit of:
pound-inch-sec^2/radian

Technically, a radian isn't a unit, it's a ratio (that should get a discussion going) so it is dropped from the unit definition, leaving lb-in-sec^2. As stated above, given this unit, pounds are a unit of force, not the (imaginary) unit of mass.

Keith

 

[IRstuff]

Even engineers get sloppy with units. This is from a specification we received:

The resultant load is 136 kg (300 lbs) force if slowly pushed out of the way gradually and 272 kg (600 lbs) force if suddenly applied as an impact at 8.3 m/s.

So, yes, there are people citing kgf.

TTFN

FAQ731-376

 

[swearingen]

I REFUSE to use lbm and kgf. Yes, like any other unit out there, they can be defined and used. I just think they confuse issues, however, which is why I went straight from lb (I don't put the f, I think that is understood) to the SI unit of force, Newtons.

I have tutored math and physics for many years (specifically to stay up on the basics so I can answer my kids' questions) and these questions come up time and again. I always tell my students to break them down into the base units and then there's never a problem...



If you "heard" it on the internet, it's guilty until proven innocent. - DCS

 

[drawoh]

bpelec,

The equations for inertia are written out using both force units and mass units. The resulting inertia values are not equivalent.

I suggest you systematically use mass unit equations, and use...

m = w/g

The weight in pounds is a unit of force, and it must be divided by g to get mass. Kilograms are, of course, a unit of mass, and you do not divide by g.

The alternative is to be arbitrary and unmethodical where you stick the g value in your equations, and hope for the best.

JHG