Halliday, Resnick & Walker — Rotation: Problem 40

40 Figure 10-26 shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length $L = 1.0000 \text{ m}$ and (total) mass $M = 100.0 \text{ mg}$. The disks are uniform, and the disk arrangement can rotate about a perpendicular axis through its central disk at point $O$. (a) What is the rotational inertia of the arrangement about that axis? (b) If we approximated the arrangement as being a uniform rod of mass $M$ and length $L$, what percentage error would we make in using the formula in Table 10-2e to calculate the rotational inertia?