Problem — Science fiction: invariant moment of inertia

Problem

Imagine a universe in which the moment of inertia depends only on mass and not on spatial distribution. Discuss which familiar rotational phenomena would disappear.

Solution

If $I$ depended only on mass, all objects of equal mass would have the same moment of inertia, regardless of shape. The consequences:

• a solid sphere and a hollow one would roll down a slope in the same time: the “race” between bodies of different shapes would disappear;
• skaters and divers could no longer accelerate by changing body geometry: pulling in the arms would not change $I$, and hence not $\omega$ either;
• conservation of $L = I\omega$ would lose its spectacular effects, because $I$ would be a rigid constant like mass.

$\ev{\text{a dynamically impoverished universe, without the shape effects of rotation}}$

Links

Topics: Rotational dynamics Concepts: Moment of inertia · Conservation of angular momentum Skills: Analysis of limiting cases and science fiction