We analyze a simple pendulum by measuring the period and the maximum speed of the bob. Both quantities are measured to high precision using a laser diode and an infrared photodetector located at the bottom of the pendulum. Expressing the period in terms of the maximum speed enables students to examine the large angle dependence of the period, and provides a method to calibrate the speed and do a detailed analysis of the effect of air friction on a sphere. We find that the force due to air friction is well described by a linear and quadratic term in the speed. We investigate the dependence of each term on the sphere’s diameter for Reynolds numbers from 250 to 104.

1.
We found over 300 articles in this journal and over 150 articles in The Physics Teacher which discussed some aspect of pendula. The ones we have listed include measurements of vmax and/or damping.
2.
R. A.
Nelson
and
M. G.
Olsson
, “
The pendulum-rich physics from a simple system
,”
Am. J. Phys.
54
,
112
121
(
1986
).
3.
P. T.
Squire
, “
Pendulum damping
,”
Am. J. Phys.
54
,
984
991
(
1986
).
4.
V. K.
Gupta
,
G.
Shanker
, and
N. K.
Sharma
, “
Experiment on fluid drag and viscosity with an oscillating sphere
,”
Am. J. Phys.
54
,
619
622
(
1986
).
5.
The laser diode we used was purchased from Z-Bolt, ⟨www.z-bolt.com⟩, part number APC-5. We put the laser module in a metal sleeve to facilitate heat transfer.
6.
S. T.
Thornton
and
J. B.
Marion
,
Classical Dynamics of Particles and Systems
(
Brooks/Cole
, New York,
2004
), 5th ed.
7.
We used the spreadsheet Excel because it is commonly used in the student laboratory.
8.
D.
Halliday
and
R.
Resnick
,
Fundamentals of Physics
(
Wiley
, New York,
1988
), 3rd ed.
9.
J. R.
Taylor
,
Classical Mechanics
(
University Science Books
, Sausalito, CA,
2005
).
10.
R. A.
Serway
and
J. W.
Jewett
 Jr.
,
Principles of Physics
(
Harcourt Brace Javanovich
, San Diego,
2002
).
11.
The uncertainty in the parameters of the fit was determined using the graphing program PSI-Plot, ⟨www.polysoftware.com⟩.
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.