Rank the moments of inertia of this objectabout the axes indicated. Two identica

Question

Rank the moments of inertia of this objectabout the axes indicated. Two identical uniform solid spheres are attached by a solid uniformthin rod, as shown in the figure. The rod lies on a line connectingthe centers of mass of the two spheres. The axes A, B, C, and D arein the plane of the page (which also contains the centers of massof the spheres and the rod), while axes E and F (represented byblack dots) are perpendicular to the page. Rank the moments of inertia of this objectabout the axes indicated. Rank from largest to smallest. Torank items as equivalent, overlap them.

Explanation / Answer

Let d be the distance between the dotted lines IA = 2 * M * (2 d)2 = 8 Md2 IB = M * [d2 + (3 d)2] = 10d2 IC = M * (4 d)2 = 16 d2 This not completly accurate but the ordering will still be thesame The moment of inertia of a sphere is 2/5 M d2 By the parallel axis theorem IA = 2 M d2 [ 2 / 5 + 22] = 44 / 5 M d2 IB = 2 * 2/5 M d2 + Md2 [ 1 + 32] = 54 / 5 M d2 IC = 2 * 2/5 M d2 + Md2 * 42 = 84 / 5 M d2 IC = 2 * 2/5 M d2 + Md2 * 42 = 84 / 5 M d2

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