For similar solid bodies made from constant density, how does the Moment of Inertia about a particular axis vary with linear dimensions?

This is from an school textbook.

I have covered all of MI and don't find it particularly troubling but I am not sure what this question is asking. What is meant by linear dimensions in this context?

Is it to do with proportionality?

  • 2
    $\begingroup$ I think they are asking about how moments of inertia scale. Imagine doubling the size of the body, leaving its shape and density the same. By how much do the moments of inertia increase? It's quite instructive... it tells you why you don't want to be close to unprotected rotating machine parts of even medium size. $\endgroup$
    – CuriousOne
    Jan 2, 2015 at 10:32

1 Answer 1


There is a rotational dimension around the axis ($\theta$ in radians e.g.) and a linear dimension away from the axis (the radial direction). And one more linear dimension along the axis, which is not relevant for moment of inertia.

They are simply asking, what is the relationship between moment of inertia and distance from the axis (in the radial direction).

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    $\begingroup$ I think I've got it. Because mass is proportional to volume/length^3, then the moment of inertia is proportional to length^5. Is that right? $\endgroup$ Jan 2, 2015 at 11:55
  • $\begingroup$ @GridleyQuayle What is volume/length^3? I'm not sure where you are going, but I believe the question simply asks for the relationship between moment of inertia $I$ and radial distance $r$. Do you know the standard formula for moment of inertia, then this should be solved $\endgroup$
    – Steeven
    Jan 16, 2016 at 9:51

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