The compatibility of the Newtonian formulation of mechanical energy and the transformation equations of Galilean relativity is demonstrated for three simple examples of motion treated in most introductory physics courses (free fall, a frictionless inclined plane, and a mass/spring system). Only elementary concepts and mathematics, accessible to students at that level, are used. Emphasis is on pedagogy and concepts related to the transformation properties of potential energy.

1.
Common introductory physics texts include various editions of: D. C. Giancoli (Pearson, Prentice Hall); P. A. Tipler (W. H. Freeman); R. Wolfson (Pearson, Addison-Wesley); H. D. Young and R. A. Freedman (Pearson, Addison-Wesley); and R. A. Serway and J. W. Jewett (Brooks/Cole).
2.
B. J.
Tefft
and
J. A.
Tefft
, “
Galilean relativity and the work-kinetic energy theorem
,”
Phys. Teach.
45
,
218
220
(
April
2007
).
3.
R. A.
Diaz
,
W. J.
Herrera
, and
D. A.
Manjarrés
, “
Work and energy in inertial and noninertial reference frames
,”
Am. J. Phys.
77
,
270
273
(
March
2009
).
4.
F. C.
Santos
,
V.
Soares
, and
A. C.
Tort
, “
A note on the conservation of mechanical energy and the Galilean principle of relativity
,”
Eur. J. Phys.
31
,
827
834
(
June
2010
).
5.
Saeed
Ghanbari
, “
Mechanical energy change in inertial reference frames
,”
Phys. Teach.
54
,
360
363
(
Sept.
2016
).
6.
This is a valid approximation, since Earth’s mass, 5.97×1024 kg, is very much larger than that of terrestrial objects falling from heights much less than Earth’s radius, 6.38×106 m.
7.
Lev
Vygotsky
,
Wikipedia
, https://en.wikipedia.org/wiki/Lev_Vygotsky.
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