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.

Simran Bhatia , 10 Years ago

Grade 11