Example of moment of inertia constant K, greater than one?

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SUMMARY

The moment of inertia constant, k, in the equation I = kmr^2, typically ranges from 0 to 1, representing the average distance of mass from the axis of rotation. An example of k being greater than one occurs when measuring the radius of a thin square pipe from face to face, rather than from corner to corner. In contrast, k equals one when all mass is uniformly distributed at a distance r from the axis, such as in a bicycle wheel where mass is concentrated at the rim. Understanding these variations in k is crucial for analyzing rotational dynamics.

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  • Understanding of rotational dynamics and moment of inertia
  • Familiarity with the equation I = kmr^2
  • Knowledge of mass distribution in rigid bodies
  • Basic concepts of geometry related to shapes and axes
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Regarding the moment of inertia constant, k, as in I = kmr^2, k is often a fraction less than one, and sometimes is equal to one. http://en.wikipedia.org/wiki/List_of_moments_of_inertia

Is there an example of k being greater than one?
 
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The "k" is, in some sense, a measure of the average distance of the mass of an object from its axis of rotation. If all of the mass of the object is within radius r from the axis of rotation then the figure for k is guaranteed to be less than or equal to one.

The value of 1 is obtained when all of the mass is exactly at distance r from the axis of rotation. This would apply for something like a bicycle wheel where the mass is concentrated at the rim.

If you considered a thin square pipe rotating its long axis and if you measured its radius r from face to face (rather than from corner to corner) then I suppose that could give you a figure for k that is greater than one.
 
What does an object with k = 1 look like? What would it mean for k > 1?
 

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