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In this problem, we use the result of the previous problem for the rotational inertia of a disk to compute the rotational inertia of a uniform solid sphere of mass M and radius R about an axis through its center. Consider an element dill of the sphere in the form of a disk of thickness dz at a height z above the center (see Fig). (a) Expressed as a fraction of the total mass M, what is the mass dill of the element? (b) Considering the element as a disk, what is its rotational inertia dI? (c) Integrate the result of (b) over the entire sphere to find the rotational inertia of the sphere.
(a) Equate mass per unit volume of the disk and the solid sphere,(b) The rotational inertia of the disk with mass dm and radius r is:(c) Integrate the rotational inertia of the disk under the limit z = - R to z = - R
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