Inertia units for a synchronous machine

In summary, angles do not have dimensions, and so asking for units in terms of kg m2/rad2 is problematic.
  • #1
gab_xd
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0
TL;DR Summary
Are [kg m^2] and [kg m^2 /rad^2] equivalent?
Hello everyone,

I'm sorry if this is not the right sub-forum to post this, but this doubt has been haunting me for a while.

I've got some rotatory machine -let's say, generic synchronous machine-. Turns out there are typical values for [kg m^2] (inertia) in the 2-10 range; the software I'm using asks for inertia values considering [kg m^2 / rad^2] units. Are these equivalent? A quick Google search tells me that they are, but I'm still confused as to why would you blatantly put [rad^2] in there without consequences.

Thanks in advance!
 
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  • #2
gab_xd said:
why would you blatantly put [rad^2]
Anybody's guess. My guess is narrowmindedness :wink: .

For ##\tau = I\alpha## that would lead to kg m2/rad and for ##E={1\over 2} I\alpha^2 ## you'd get your kg m2/rad2.

You could try to find an example in your software documentation to check that kg m2 is adequate.
(And if you find a counter-example, please post here !)Disclaimer: not an expert, just a physicist -- and the thread remained unanswered for three days, which is atypical for PF :smile:

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  • #3
BvU said:
Anybody's guess. My guess is narrowmindedness :wink: .

For ##\tau = I\alpha## that would lead to kg m2/rad and for ##E={1\over 2} I\alpha^2 ## you'd get your kg m2/rad2.

You could try to find an example in your software documentation to check that kg m2 is adequate.
(And if you find a counter-example, please post here !)Disclaimer: not an expert, just a physicist -- and the thread remained unanswered for three days, which is atypical for PF :smile:

##\ ##
Hi BvU,

Thanks for your answer! I thought the question remained unanswered because "it was too basic" :(
During the weekend, I tried getting the units out myself but didn't get to anything conclusive; I will try to find some examples in the software documentation, and will let you know as soon as I can.

I just hope the person that listed the units as ##kg m2## didn't use RPM as his angular frequency unit. :p
 
  • #4
Part of the problem is that angles are a ratio, and thus have no dimension of their own. That's controversial. The link below is a PF Insights article on that subject. The comment thread on the article is 105 posts long.

https://www.physicsforums.com/insights/can-angles-assigned-dimension/

If an angle has no dimensions, "[kg m^2] and [kg m^2 /rad^2] equivalent" is true.
 
  • #5
Thanks Anorlunda!

Now that I think about it, it's not the first time I have had problems with angle's dimensions. I'll read that post as soon as I can; took a quick look and it surely looks like a rabbit hole.
 

FAQ: Inertia units for a synchronous machine

What are inertia units for a synchronous machine?

Inertia units refer to the measurement of the rotational mass of a synchronous machine. It is typically measured in kilogram-meters squared (kgm2) or pound-feet squared (lbft2).

Why is it important to measure inertia units for a synchronous machine?

Inertia units are important because they determine the ability of a synchronous machine to maintain a stable speed and respond to changes in load. Higher inertia units indicate a greater ability to maintain stability.

How are inertia units calculated for a synchronous machine?

Inertia units are calculated by multiplying the square of the rotor diameter by the density of the rotor material. This value is then divided by the number of poles in the machine.

What is the typical range of inertia units for a synchronous machine?

The typical range of inertia units for a synchronous machine is between 0.01 and 10 kgm2 or lbft2. The exact value will depend on the size and design of the machine.

How do inertia units affect the performance of a synchronous machine?

Inertia units directly affect the dynamic response and stability of a synchronous machine. Higher inertia units result in slower speed changes and better stability, while lower inertia units result in faster speed changes and potentially less stability.

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