In the spirit of Section 7.3.2, find the moments of inertia of the following fractal objects. (Be careful how the mass scales.)

(a) Take a stick of length ?, and remove the middle third. Then remove the middle third from each of the remaining two pieces. Then remove the middle third from each of the remaining four pieces, and so on, forever. Let the final object have mass m (axis through center, perpendicular to stick; see Fig.).7

(b) Take a square of side ?, and remove the ???middle??? square (1/9 of the area). Then remove the ???middle??? square from each of the remaining eight squares, and so on, forever. Let the final object have mass m (axis through center, perpendicular to plane; see Fig.).

(c) Take an equilateral triangle of side ?, and remove the ???middle??? triangle (1/4 of the area). Then remove the ???middle??? triangle from each of the remaining three triangles, and so on, forever. Let the final object have mass m (axis through center, perpendicular to plane; Fig).

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