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I am studying from the book Classical Dynamics: A Contemporary Approach by Jose & Saletan, and at page 496, they work through an example about the moment of inertia tensor of a uniform cube (sorry about the writing on the picture, I don't have an eraser with me right now),

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where they have calculated the moment of inertia tensor with respect to the fixed point in space. What I don't understand is the reason why we calculate it with respect to a point, when the physical meaning of the moment of inertia is the opposition to the angular acceleration due to the distribution of mass with respect to the axis of rotation. What is the motive behind calculating it with respect to a point?

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  • $\begingroup$ Wikipedia: “For the same object, different axes of rotation will have different moments of inertia about those axes. … The moment of inertia tensor is a convenient way to summarize all moments of inertia of an object with one quantity. … $I_n=n \cdot I \cdot n$” $\endgroup$
    – Ghoster
    Commented Sep 1, 2023 at 19:54

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with

$$ \vec L = {\bf I} \vec\omega $$

the direction of $\vec\omega$ is not specified. It just needs to be relative to the point.

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