Moments of inertia (MOIs) are usually derived via substantial integration and may intimidate undergraduates without prior backgrounds in calculus. This paper presents an intuitive geometric operation, termed “squashing,” that transforms an object into an equivalent one with a reduced dimension, whose MOI is simpler to determine. The combination of squashing and other methods (e.g., scaling arguments, the perpendicular-axis and parallel-axis theorems) enables the computation of complex MOIs with minimal integration.

1.
Joseph A.
Rizcallah
, “
Moment of inertia by differentiation
,”
Phys. Teach.
53
,
482
484
(
Nov.
2015
).
2.
W. L.
Andersen
, “
Noncalculus treatment of steady-state rolling of a thin disk on a horizontal surface
,”
Phys. Teach.
45
,
430
433
(
Oct.
2007
).
3.
Seok-Cheol
Hong
and
Seok-In
Hong
, “
Moments of inertia of disks and spheres without integration
,”
Phys. Teach.
51
,
139
140
(
March
2013
).
4.
David
Morin
,
Introduction to Classical Mechanics: With Problems and Solutions
, 1st ed. (
Cambridge University Press
,
Cambridge
,
2008
), pp.
314
316
.
5.
Bernard
Ricardo
, “
Using scaling to compute moments of inertia of symmetric objects
,”
Eur. J. Phys.
36
(
5
),
055003
(June
2015
).
6.
Robert
Rabino
, “
Moments of inertia by scaling arguments: How to avoid messy integrals
,”
Am. J. Phys.
53
,
501
502
(
May
1985
).
7.
Benjamin
Oostra
, “
Moment of inertia without integrals
,”
Phys. Teach.
44
,
283
285
(
May
2006
).
8.
J.
Littlewood
and
J.
Hebborn
,
Mechanics
5
, 1st ed. (
Heinemann
,
Oxford
,
2001
), pp.
56
57
.
AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.