Mass moment of inertia calculations 1

[dharhay]

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

 

[CastMetal]

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.

 

[rb1957]

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

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

 

[drawoh]

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

 

[JohnGP]

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

 

[rb1957]

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

i get the same results (FWIW)

 

[IRstuff]

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

 

[electricpete]

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)' ?

 

[katmar]

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

 

[rb1957]

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 ??

 

[katmar]

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

 

[zekeman]

"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.

 

[IRstuff]

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

 

[rb1957]

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

 

[dharhay]

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

 

[electricpete]

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

That doesn't sound right to me.

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

 

[rb1957]

"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

 

[drawoh]

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

 

[IDS]

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/

 

[IRstuff]

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