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

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The moment of inertia constant, k, typically ranges from less than one to one, representing the average distance of mass from the axis of rotation. An example of k being greater than one could occur with a thin square pipe rotating around its long axis, measured from face to face. When all mass is concentrated at a distance r from the axis, k equals one, as seen in a bicycle wheel. The discussion raises questions about the characteristics of objects with k equal to one and the implications of k being greater than one. Understanding these values is crucial for analyzing rotational dynamics.
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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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