This formula is the most "brute force" approach to calculating the moment of inertia. A new axis of rotation ends up with a different formula, even if the physical shape of the object remains the same. The consequence of this formula is that the same object gets a different moment of inertia value, depending on how it is rotating. You do this for all of the particles that make up the rotating object and then add those values together, and that gives the moment of inertia. Basically, for any rotating object, the moment of inertia can be calculated by taking the distance of each particle from the axis of rotation ( r in the equation), squaring that value (that's the r 2 term), and multiplying it times the mass of that particle. The general formula represents the most basic conceptual understanding of the moment of inertia. The general formula for deriving the moment of inertia.
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