Symmetry and invariance play a fundamental role in modern physics and related disciplines, and students entering a STEM field need practice with symmetry-based arguments as part of the preparation for their future careers. We refer to symmetry-based solutions as those that either make use of the existing geometric symmetry in a problem to simplify calculations or include transformations with the purpose of creating a simpler equivalent problem. We begin by giving some examples of symmetry-based solutions involving Gauss’s law, where such techniques are already widely used. Then we will propose additional problems where solutions based on symmetry and invariance are appropriate, but not yet in common use to our knowledge.
References
1.
R.
Feynman
, R.
Leighton
, and M.
Sands
, The Feynman Lectures on Physics
, Vol. 1
(Addison-Wesley, Reading
, MA
, 1963
), Chaps. 11 and 52.;R.
Feynman
, “Symmetry in physical laws
,” Phys. Teach.
4
, 161
(April
, 1966
).2.
J.
Sztrajman
and A.
Sztrajman
, “An easy way to one-dimensional elastic collisions
,” Phys. Teach.
55
, 164
–165
(March
2017
);Deb
Funk
, “Elastic collisions with two moving objects made simple
,” Phys. Teach.
44
, 80
–81
(Feb.
2006
);H.
Hui
, “More on one-dimensional collisions
,” Phys. Teach.
40
, 72
(Feb.
2002
);C. T.
Tindal
, “An intuitive approach to collisions
,” Phys. Teach.
36
, 344
–346
(Sept.
1998
);L.
Millet
, “The one-dimensional elastic collision equation: vf = 2vc – vi
,” Phys. Teach.
36
, 186
(March
1998
).3.
See, for example,
H.
Young
and R.
Freedman
, University Physics
, 14th ed. (Pearson
, Boston
, 2016
).4.
The authors wish to thank one of the anonymous reviewers for suggesting this transformation.
5.
C.
Dias
and L.
Goncalves
, “The concept of negative mass and its application to helium-balloon type dynamics
,” Am. J. Phys.
82
, 997
(Oct.
2014
).6.
A.
Bartlett
, “‘Apparent weight’: A concept that is confusing and unnecessary
,” Phys. Teach.
48
, 522
(Nov.
2010
).7.
E.
Kapotis
and G.
Kalkanis
, “Einstein’s elevator in class: A self construction by students for the study of the equivalence principle
,” Phys. Teach.
54
, 404
(Oct.
2016
).© 2019 American Association of Physics Teachers.
2019
American Association of Physics Teachers
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.