Physics

Physics

Problem

A uniform thin rod of length 1.0 m1.0\,\text{m} and mass 4.0 kg4.0\,\text{kg} is mounted to rotate about an axis perpendicular to the rod and located 0.25 m0.25\,\text{m} from the rod’s center. Engineers plan to relocate the axis to pass through the center of the rod. By approximately what percentage will the rod’s rotational inertia decrease after the relocation? a) 17\% b) 43\% c) 33\% d) 57\%
Intuitive explanation

The key is recognizing that rotational inertia depends critically on where the axis is located—specifically, how far mass is distributed from that axis. Use the parallel axis theorem to find II about each axis: the current axis is offset from the center, so it has a larger moment of inertia than an axis through the center. Calculate both values and compare their ratio to find the percentage change.

Intuitive explanation

The key is recognizing that rotational inertia depends critically on where the axis is located—specifically, how far mass is distributed from that axis. Use the parallel axis theorem to find II about each axis: the current axis is offset from the center, so it has a larger moment of inertia than an axis through the center. Calculate both values and compare their ratio to find the percentage change.

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