Rotational Inertia of Rectangular Cube in a Hoop

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The discussion centers on the rotational inertia of a rectangular cube within a hoop. It clarifies that the equation for a rectangular cube differs from that of a hoop or solid cylinder. The rotational inertia of a cube about an axis perpendicular to a face and through its center of mass is given as 1/6 m s^2. There is confusion regarding the term "rectangular cube," prompting a request for clarification. Understanding the rotational inertia of compound objects involves summing the inertias of individual components.
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i know that the equation for rotational inertia of a hoop is different than the equation for a solid cylinder, but what is the equation for a rectangular cube in a hoop?
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\ (|) <--is what I mean if the diagram helps at all
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I have no idea what that diagram is supposed to show, but the rotational inertia of a compound object is just the sum of the rotational inertias of each component. The rotational inertia of a cube of side s about an axis perpendicular to a face and passing through its center of mass is: 1/6 m s^2
 
What do you mean by the term 'rectangular cube'?
 

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