Conventional calculations of the inertia tensor in undergraduate physics course are usually done for highly symmetrical bodies. Students might therefore get the impression that the moment of inertia about any axis through the center of mass is the same only for bodies with the highest degree of symmetry relative to this point, e.g., for spheres. A simple, seemingly counterintuitive example is presented, showing that the moment of inertia of a non-regular body, here an assembly of material points, can be the same about any axis passing through its center of mass.

1.
Charles
Kittel
,
Walter D.
Knight
,
Malvin A.
Ruderman
,
Carl A.
Helmholz
, and
Burton J.
Moyer
,
Mechanics
, 2nd ed. (
McGraw-Hill Book Company
,
New York
,
1973
).
2.
John R.
Taylor
,
Classical Mechanics
, 2004th ed. (
University Science Books
,
Sausalito, California
,
2004
).
3.
P. K.
Aravind
, “
Gravitational collapse and moment of inertia of regular polyhedral configurations
,”
Am. J. Phys.
59
,
647
652
(
1991
).
4.
P. K.
Aravind
, “
A comment on the moment of inertia of symmetrical solids
,”
Am. J. Phys.
60
,
754
755
(
1992
).
5.
Frédéric
Perrier
, “
Moments of inertia of Archimedean solids
,” <http://www.ipgp.fr/sites/default/files/archimedeani_200115.pdf> (accessed on March 13,
2021
).
6.
Symmetry–Isotropic moments of inertia, Physics Stack Exchange. <https://physics.stackexchange.com/questions/514554/isotropic-moments-of-inertia> (accessed on March 5,
2021
).
7.
Lev D.
Landau
and
Evgeny M.
Lifshitz
,
Mechanics
, 3rd. ed. (
Butterworth-Heinemann
,
Amsterdam
,
1976
), Vol.
1
.
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