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Mass moment of inertia calculations

Mass moment of inertia calculations

Mass moment of inertia calculations

(OP)
I have a fundamental question about calculating the mass moment of inertia.  Using the US units and then the Metric units.  But then can one use the common units conversion programs, like UCONEER for an appropriate conversion back and forth?

Take an example of a solid shaft, 840kg weight, 280mm dia.
Using the formulas that are common, (hyperphysics.phy-astr.gsu.edu), I = 0.5 * m * r^2
I obtain 0.839 kgm^2 for the metric and use a gc of 9.81.
Next the US, the result is 6.05 lbft^2 using a gc of 32.2.

The convertors have a mass moment section, but the conversions are not consistent with the above.  Should one expect to be able to convert? Or are my units at any step not consistent?  I said this is fundamental, but I am not comfortable with my two methods.  Thanks.

Dave Harhay
Bronx, Taylor-Wilson
North Canton, OH

RE: Mass moment of inertia calculations

It is a standard unit conversion
  kg/lb*(m/ft)^2*english=metric

If the conversion program gives a different answer you have other issues with your analysis or the program.

RE: Mass moment of inertia calculations

yes, convertors probably use "proper" imperial units like slugs ...

but you can convert m to ft and kg(mass) to lb(mass), so ...

RE: Mass moment of inertia calculations

dharhay,

   The problem with switching between English units and metric is the use of lbm and kgf.  I strongly recommend using the SI system equations and treating pounds as a unit of weight.

   m = w/g

   Otherwise, you will be constantly trying to remember whether or not and where to put g in your equation.

               JHG

RE: Mass moment of inertia calculations

Yes, thank goodness I no longer have to perform calculations in English (US) units. You shouldn't be dividing the 840kg by 9.81 because it's already a mass (although people call it a weight).
Cheers,
John

RE: Mass moment of inertia calculations

OP says kgf (ie weight) so dividing by g makes sense.

i get the same results (FWIW)

RE: Mass moment of inertia calculations

0.5*840kg*(280mm/2)^2 = 8.232kg*m^2
converts to 195.3483lb*ft^2

"kg weight" is by definition a kg.  Otherwise, weight in metric would be expressed as newtons, as befitting a force.  Likewise a 1 pound weight is a 1 pound mass, which is equivalent to kg/2.2046 .

In both cases, it's not the unit system that's the problem, it's the fact that people use weights and masses interchangeably.

TTFN

FAQ731-376: Eng-Tips.com Forum Policies

RE: Mass moment of inertia calculations

Quote:

In both cases, it's not the unit system that's the problem, it's the fact that people use weights and masses interchangeably.
Amen to that.

=====================================
(2B)+(2B)'  ?

RE: Mass moment of inertia calculations

Disclaimer: I am the author of Uconeer I would like to explain why my program gives the correct answer to this conversion.

gc is only required if you are mixing units.  If you are using consistent sets of units, then if you measure your mass in pounds you should use poundals for force.  And if you use pounds force as your unit of force then you should use slugs for your mass.  But engineers like to use pounds mass and pounds force in the same formula so gc is introduced purely as a units conversion factor.

In SI units there is no such concept as gc.

In the formula you have given for mass moment of inertia there is no force involved, so there is no need for gc at all.

In your example
mass = 840 kg (1852 lb  NB these are pounds mass)
radius = 0.14 m (0.4593 ft)
MoI = 840 x 0.142/2 = 8.232 kg.m2
    = 1852 x 0.45932/2 = 195.3 lb.ft2

And Uconeer gives this same conversion

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Mass moment of inertia calculations

the OP clearly states "weight is 840kg" and seems (IMHO) to be clearly aware that in his mass moment of inertia he's dealing with kg as a mass measure, hence 0.5*(840/9.81)*0.14^2 = 0.839kgm^2 and similarly 0.5*(840*2.2/32.2)*(0.14*39.37/12)^2

no ??

RE: Mass moment of inertia calculations

In my experience it is much more likely that when someone says "weight is 840 kg" they mean "mass is 840 kg" rather than meaning "the force it exerts under the influence of the earth's gravity is 840 kg.force".

A steel shaft of 280 mm diameter would have a mass of about 500 kg/m of linear length.  If the mass is 840 kg the length of the shaft is about 1700 mm.  If the force the shaft exerts under the influence of gravity is 840 kg.force then the shaft is about 170 mm long, i.e. shorter than its diameter and unlikely in my opinion.

Nevertheless, we have beaten all the permutations to death and the OP should now easily resolve his problem.

Katmar Software
Engineering & Risk Analysis Software
http://katmarsoftware.com

RE: Mass moment of inertia calculations

"In my experience it is much more likely that when someone says "weight is 840 kg" they mean "mass is 840 kg" rather than meaning "the force it exerts under the influence of the earth's gravity is 840 kg.force".

That's funny. The opposite is my experience. Guess it depends on your age. All I know is that a chunk of 840kg weighs 840kg on earth. Calling it a mass of 840kg doesn't shed any more light on the matter ( no pun). It still weighs 840 Kg. The only reason we use the g conversion to mass is the need to get forces in dynamic situations involving accelerations different from g.

 

RE: Mass moment of inertia calculations

Someone who "weighs" 70 kg, has a mass of 70 kg.  It can't be any other way.  Dividing kg by g makes no physical sense whatsoever, since weight is mass*g.  All normal weight scales are normalized to mass, i.e., a weight of 150 lb means there was a mass of 150 lb, or 68 kg on the scale.

 

TTFN

FAQ731-376: Eng-Tips.com Forum Policies

RE: Mass moment of inertia calculations

i assume that when someone says they weigh 70kg that they've omitted the "f", ie 70kgf, and 1kgf = 1kg(m)*9.81m/sec^2.

if something weighs 70N, then it's mass is 70kg  

RE: Mass moment of inertia calculations

(OP)
Thanks for your responses.  One thing I want to say is that I am not disputing the accuracy of Uconeer.  And I have weights for the various components.

 

Dave Harhay
Bronx, Taylor-Wilson
North Canton, OH

RE: Mass moment of inertia calculations

Quote:

if something weighs 70N, then it's mass is 70kg  
That doesn't sound right to me.

=====================================
(2B)+(2B)'  ?

RE: Mass moment of inertia calculations

"post in haste, regret at leisure" or something like ....

the other posters are right ... weight in kgf = mass in kg
1 kgf = 1kg*g = 9.8N

not as i and the OP calc'd

sigh

RE: Mass moment of inertia calculations

rb1957,

   My point, above, is that if you are not consistent in your units, you are going to be confused with your equations.

   Banish kilograms force and pounds mass.  Use the gravitational constant to convert weight units into mass.  If you have a mass of 70kg, you have a weight of 154lb, or 687N.   

               JHG

RE: Mass moment of inertia calculations

Quote:


   My point, above, is that if you are not consistent in your units, you are going to be confused with your equations.   Banish kilograms force and pounds mass.  Use the gravitational constant to convert weight units into mass.  If you have a mass of 70kg, you have a weight of 154lb, or 687N.   

I totally agree.  It may be different in Imperial units for historical reasons, but when using SI, use SI.  That means the unit of force, including weight, is the Newton.  Using kgf for weight just causes confusion, as this thread demonstrates very well.  Using units like kgf/cm^2 for stress is just crazy.

 

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Mass moment of inertia calculations

All I can add is that y'all should lobby for a mathtool that does units, like Mathcad or SMath.  Mathcad has lb, lbf, kg, and kgf all defined and inline convertible, i.e., lbf = lb*g = 4.4482N.  No fuss, no muss.  The only time I have problems with units, now, is usually just entry errors, which is pretty rare.

Seriously, though, had the OP and others been using either program, this thread would have never been necessary.  Had the OP done his original calculation in Mathcad, the units inconsistency would have popped right out, and his unit conversions would have been trivial and painless.

I've got Katmar's program as well (Thanks, Katmar), but it doesn't do general and sequential calculations.  The day it does, Katmar could probably make a killing (hint, hint...).

TTFN

FAQ731-376: Eng-Tips.com Forum Policies

RE: Mass moment of inertia calculations

Go to
http://www.onlineconversion.com/auto_convert.pl
and type into the box:
convert 1 kg*m^2 to lbm*ft^2

The result will be:
1 kg*m^2 = 23.73036 lbm*ft^2
which is consistent with results reported by IRstuff and Katmar

There is nothing inherently wrong with using lbm as a unit of mass (although I would choose SI given a choice, it's not the only way).  Errors can happen in any system of units if you don't apply it properly.   And when solving the originally posted problem of this thread, there is no difference if you treat kg as weight or mass in the original post - it describes the same shaft as first mentioned by IRstuff.

I have always been taught to use lbm and lbf rather than "lb" to distinguish the two units from each other.  (It is usually clear from context, but it is also logical that we should distinguish the two units which describe fundamentally different attributes)  Since kgf seems widespread in certain circles, perhaps we should use kgm when referring to mass?!?  (Just kidding... there is no doubt what a kg is in SI)

=====================================
(2B)+(2B)'  ?

RE: Mass moment of inertia calculations

And by the way, go to the grocery store deli section and place your order in units of slugs... see what kind of response you get winky smile

lbm will be around for a long time. Deal with it.

=====================================
(2B)+(2B)'  ?

RE: Mass moment of inertia calculations

Actually I was not intending to provoke a unit debate or philisophical discussion of the difference between mass and weight.  Just asking for patience and tolerance of other approaches.

=====================================
(2B)+(2B)'  ?

RE: Mass moment of inertia calculations

Quote (electricpete):


And by the way, go to the grocery store deli section and place your order in units of slugs... see what kind of response you get ...

   I never ask my butcher to work out the mass moment of inertia of stuff.  Butchers are armed.  Probably, it is best to not make fun of them.

   When I took dynamics in college, we learned two set of equations, one for English units, and one for SI.  Mass was measured in pounds and kilograms.  When I got to do real work, I learned that there is more than one metric system.  We have kilograms force and centimeters.

   I want to use one set of equations.  I treat pounds as force (weight) and kilograms as mass, and everything works out.  You don't even have to use slugs.  You can just bury w/g in your equations.   

               JHG

RE: Mass moment of inertia calculations

Quote:

I never ask my butcher to work out the mass moment of inertia of stuff.  Butchers are armed.  Probably, it is best to not make fun of them.
LOL. Good one.

=====================================
(2B)+(2B)'  ?

RE: Mass moment of inertia calculations

D,

That's the beauty of using Mathcad or SMath.  There is only ONE equation.  You can put in any unit that's defined, kg, lb, m, ft, or even furlong.  So, something like 0.5 * 854 kg * (1 furlong)^2 = 1.728x10^7 kg-m^2.  It's absolutely sweet for problems of this nature; no conversions, hidden or otherwise.

TTFN

FAQ731-376: Eng-Tips.com Forum Policies

RE: Mass moment of inertia calculations

Quote:

So, something like 0.5 * 854 kg * (1 furlong)^2 = 1.728x10^7 kg-m^2.  It's absolutely sweet for problems of this nature; no conversions, hidden or otherwise.  

I don't understand your point there.  That seems to have a hidden conversion from furlong^2 to m^2 built in.  Shouldn't the result be 1.728x10^5 anyway?

My preference is to work entirely in consistent units, but if you need to convert units, do a sanity check on the sanity check.

And if checking someone else's work and you see a constant quoted to more than 3 or 4 significant figures check that carefully, because it has probably been converted from a different set of units, and it is probably out by a factor of about 10 (or even on one occaision 64).

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Mass moment of inertia calculations

Quote:

Shouldn't the result be 1.728x10^5 anyway?

Oops, didn't take my own advice.

I got my archaic units mixed up; I was thinking chains, not furlongs.  1.728x10^7 is correct.


But isn't the Smoot the preferred unit for these situations?

Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
 

RE: Mass moment of inertia calculations

So close enough to 6x10^6 kg-Smoot^2 then.

RE: Mass moment of inertia calculations

5.967*10^6 Smoot^2-kg more precisely winky smile (It's also a built-in unit in Mathcad)

Well, obviously, everyone prefers to use consistent units, but we're not always in control of our customers, are we?  I often get specifications that use knots for airspeed, feet for altitude, and kilometers for range.

My point, of course, is that you can try to do the conversion each time yourself, and hope that you've done it correctly, each time, or, you can have tool that does the conversion the instant you enter the unit into the equation.  And while Mathcad is hardly bulletproof, it's still way more consistent than the typical human, and will reliably convert furlongs into Mathcad's internal unit system, which is SI, and store the unit quantity normalized to 201.168 m, which is 1/8 mi, which is 2.126x10^-14 lightyears.  Any error in the numbers will not be from the conversion, per se, but from my transcription to this posting.

If Excel, or even the Windows calculator, had the same units capability, dimensional analysis would be a snap, and transcription errors would almost be nonexistent.

TTFN

FAQ731-376: Eng-Tips.com Forum Policies

RE: Mass moment of inertia calculations

In an ideal world, we all use the same standardised set of units (SI = The International System of Units?)


and: my teacher used to hammer on the fact that "Weight is a force" and thus is expressed in Newton.

And I love that Uconeer program, which has proven to be very helpful more than often.

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