According to Table 8.2, the moment of inertia for a rod that rotates about an axis perpendicular to the rod and passing through one end is I = ML²/3; if the axis passes through the center of the rod, then I = ML²/12. Give a physical explanation for this difference in terms of the way the mass of the rod is distributed with respect to the axis in the two cases.

Table 8.2

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TABLE 8.2 Moment of Inertia for Some Common Objects Object Shape Object Shape Нoop Rod pivoted at center I = mR? I = fmL? Solid sphere Pulley/cylinder/disc I = žmR? I = +mR? R R. Wheel or hollow cylinder Spherical shell I = }m(Rima + Rhin) Rmin I = žmR? Solid square plate with axis perpendicular to plate Rod pivoted at one end I = }mL? 1- ĮmL?