 Solution

ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2019/3/b/solution

The parallel axis through the centre is the rod's own long axis, with zero moment of inertia in the thin-rod approximation. By the parallel axis theorem, the displaced parallel axis has

I_{D} = 0 + M D^{2} = M D^{2} .

Equivalently, every mass element is the same perpendicular distance

D

from that axis, so the defining integral immediately gives this result.

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