The figure shows an arrangement of 15 identical disks that have been glued toget

Question

The figure shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.5100 m and (total) mass M = 172.0 mg. The 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? Give your answer to four significant figures. (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?

0.00003268 kgm^2

Explanation / Answer

given that ::

length of the rod, L = 1.51 m

mass of rod, M = 172 mg = 172 x 10-6 kg

rotational inertia of the arrangement about that axis is given as ::

I = 0.00003268 kg m2

(b) If we approximated the arrangement as being a uniform rod of mass M and length L, then percentage error is given as ::

Approximating the arrangement as a straight rod gives,
I = (1/12) x (172 x 10-6 kg) x (1.51 m) = 0.000032 kg m2

% error = 100 x (1 - 0.000032 / 0.000032) = 36.2 %

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