Sphere vs Cube: Rotational Inertia

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A sphere has less rotational inertia compared to a cube when both have the same mass and the cube's side length equals the sphere's diameter. The rotational inertia of a solid sphere about its center is calculated as (2/5)mr², while the cube's inertia is (1/6)ml² for rotation about an axis through its center. Given the dimensions specified, the cube's larger moment of inertia results from its shape and distribution of mass. The discussion emphasizes the importance of understanding the theory behind moment of inertia calculations. Overall, the cube exhibits greater rotational inertia than the sphere under the given conditions.
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Which would have more rotational inertia? A sphere or cube?
Suppose they have the same mass, the side of the cube has the same length as the diameter of the sphere, the cube's rotation axis is perpendicular to two of its faces. Which one would have more rotational inertia about an axis through the center of mass?
 
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What about the explanation/theory?
 

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