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.

Question

Aditi Chauhan · Answer

(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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