Moment of inertia is rotational mass — how hard something is to spin. Pick a shape, move the axis, and watch the parallel-axis theorem add its md² term.
Moment of InertiaLive
rotational mass & the parallel-axis theorem
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Moment of inertia is rotational mass: how hard it is to spin an object. Mass farther from the axis counts more (∝ r²). The parallel-axis theorem adds md² when the axis moves off the center of mass.
Reading this result: The axis runs through the center of mass, so there is no parallel-axis penalty — this is the smallest moment of inertia this body can have.
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How it works
Moment of inertia I = ∫r²dm depends on how mass is distributed relative to the rotation axis; standard shapes give I = c·mR² with c from 0.4 (sphere) to 1 (ring). The parallel-axis theorem, I = I_cm + md², handles rotation about any axis parallel to the one through the center of mass. Educational tool.
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The solver uses established numerical methods, but results are for research and educational purposes and should be validated against experiment or professional review before you rely on them.