Inertia units for a synchronous machine

[gab_xd]

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!

 

[BvU]

why would you blatantly put [rad^2]

Anybody's guess. My guess is narrowmindedness .

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

$\$

 

[gab_xd]

Anybody's guess. My guess is narrowmindedness .

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

$\$

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

 

[anorlunda]

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.

 

[gab_xd]

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.