A ball on a flat rotating turntable executes circular orbits analogous to those of a charged particle in a uniform magnetic field. Stable circular orbits are also possible on rotating conical turntables and are analogous to those of a charged particle in an axial magnetic field superimposed on a radial electric field. The existence and stability of these orbits is derived and discussed. Further, parallels are drawn between the mechanical and electromagnetic cases, with particular attention to the magnetic vector potential. Finally, an experimental confirmation is reported and discussed.

1.
S.
Earnshaw
,
Dynamics, or an Elementary Treatise on Motion
, 3rd ed. (
Deighton
,
Cambridge
,
1844
).
2.
J. A.
Burns
, “
Ball rolling on a turntable: analog for charged particle dynamics
,”
Am. J. Phys.
49
,
56
58
(
1981
).
3.
K.
Weltner
, “
Stable circular orbits of freely moving balls on rotating discs
,”
Am. J. Phys.
47
,
984
986
(
1979
).
4.
R. H.
Romer
, “
Motion of a sphere on a tilted turntable
,”
Am. J. Phys.
49
,
985
986
(
1981
).
5.
G. H.
Vineyard
, “
Simulation of trajectories of charged particles in magnetic fields
,”
J. Appl. Phys.
23
,
35
39
(
1952
).
6.
E.
Eriksen
and
K.
Voyenli
, “
Quasi-electrodynamic effects in the motion of a sphere that rolls on a rotating disc
,”
Eur. J. Phys.
12
,
135
141
(
1991
).
7.
K.
Weltner
, “
Movement of spheres on rotating discs: A new method to measure coefficients of rolling friction by the central drift
,”
Mech. Res. Commun.
10
,
223
232
(
1983
).
8.
A. V.
Borisov
,
I. S.
Mamaev
, and
I. A.
Bizyaev
The jacobi integral in nonholonomic mechanics
,”
Regular Chaotic Dyn.
20
,
383
400
(
2015
).
9.
H. O.
Newboult
,
Analytical Method in Dynamics
(
Clarendon
,
Oxford
,
1946
).
10.
W.
Weckesser
, “
A ball rolling on a freely spinning turntable
,”
Am. J. Phys.
65
,
736
738
(
1997
).
11.
M. D.
Semon
and
J. R.
Taylor
, “
Thoughts on the magnetic vector potential
,”
Am. J. Phys.
64
,
1361
1369
(
1996
).
12.
MATLAB 8.5 Release
2015a
, The MathWorks, Inc., Natick, MA.
13.
R.
Broucke
, “
Notes on the central force rn
,”
Astrophys. Space. Sci.
72
,
33
35
(
1980
).
14.
D.
Brown
, “
Computer Program Tracker: Video Analysis and Modeling Tool, Version 4.93 (2009)
,” <http://physlets.org/tracker/>.
15.
K.
Weltner
, “
Central drift of freely moving balls on rotating disks: A new method to measure coefficients of rolling friction
,”
Am. J. Phys.
55
,
937
942
(
1987
).
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.