Name ……………………………
Date……………
APP …………………..
Physical Pendulum
Equipment
The compound pendulum you will use in this
experiment is a one meter long bar of wood which
is supported at different points along its length.
1. pendulum bar and peg
2. meter stick
3. stopwatch
h - linear distance between pivot and center of
mass
I – is the rotational inertia of the pendulum
about the axis of suspension
Principles
An experimental pendulum is suspended successively about several axes at different points along its
length and the period about each axis is observed. A graph is plotted of the period versus the distance of
the axis of suspension from one end of the pendulum.
*Radius of oscillation R0: We can think of physical pendulum as if it were a simple pendulum.
For this, we can consider the mass of the rigid body to be concentrated at a single point as in the
case of simple pendulum such that time periods of two pendulums are same.
*The radius of gyration k: the radius of a thin uniform hoop rotating about an axis through its
centre and perpendicular to its plane, which has the same moment of inertia as the original
object.
R0
T  2
g
R0 
(1)
Ig
mgh
T  2
(2)
h2  k 2
gh
(3)
Procedure
Measure lengths to the nearest 0.001 meter (the nearest mm).
1. Set up the equipment and find the center of mass. DO NOT MARK IT! Determine the period
of the physical pendulum for various holes and enter the values in the table below. Don’t forget
to include your estimates on the uncertainties with which you’ve made these measurements. To
do this, time about complete swings and repeat each measurement twice. Keep the angle small
(under 6°) and constant. Be careful not to make the amplitude of oscillation too large and
explain in the report why this precaution is necessary.
1
Name ……………………………
Date……………
APP …………………..
h: pivot length (m)
T(20 cycles)
T (one cycle)
A
+
+
+
B
+
+
+
C
+
+
+
D
+
+
+
E
+
+
+
F
+
+
+
G
+
+
+
L
+
+
+
N
+
+
+
O
+
+
+
OO
+
+
+
Z
+
+
+
Radius of oscillation*
2. Graph the recorded period obtained, T, as a function of the pivot length. Why it is not a
straight line? What is the minimum period with which this pendulum could oscillate?
3. Compare the periods of holes A and Z. Explain the difference between them.
4. Determine R0 – equation 1, I – equation 2 and k – equation 3. What do your
experimental results show? What are the major sources of error in this procedure?
I
k
A
B
C
D
E
F
G
L
N
O
OO
Z
2