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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.
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

Simran Bhatia , 9 Years ago
Grade 11
anser 1 Answers
Aditi Chauhan

Last Activity: 9 Years ago

(a) Equate mass per unit volume of the disk and the solid sphere,
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(b) The rotational inertia of the disk with mass dm and radius r is:

236-2162_1.PNG
(c) Integrate the rotational inertia of the disk under the limit z = - R to z = - R
236-2308_1.PNG

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