Do this until it has made exactly
five complete oscillations
, stopping the watch on the count of
five.
Divide the total elapsed time by five and record this value on the data sheet below as your first
time trial.
Repeat step 11.) four more times and determine the average value
τ
conf
1
,measured
for the

period of the rod.
12.)
Calculate the percent difference between
τ
conf
1
,theory
and
τ
conf
1
, measured
.
System: Rod in Configuration Two
(One Cylindrical Mass in Hole Three,
A Second Cylindrical Mass in Hole Four)
Calculating the Period of the Thin Rod in Configuration Two
13.)
Take a second cylindrical mass out of the box of “stuff” on the lab table.
Find the mass
M
cy,
2
of the cylinder using the mass scale.
Record this value on the data sheet below.
14.)
Use the digital vernier caliper to measure the diameter
D
cy,
2
of the cylindrical mass.
Record
this value on the data sheet below.
15.)
When this cylindrical mass is screwed into
hole four
, it will add to the moment of inertia of
the system.
The moment of inertia added by this added is given by
I
cy,
2
=
M
cy,
2
d
4
2
+
1
/
8
(
)
D
cy ,
2
2
⎡
⎣
⎤
⎦
.
(25)
Calculate this value and record it on the data sheet.
16.)
So, the total moment of inertia of the system is given by
I
conf ,
2
=
I
rod
+
I
cy,
1
+
I
cy,
2
.
(26)
Calculate this value and record it on the data sheet.
17.)
Screw cylindrical mass two onto the thin rod at hole number four.
18.)
In order to to calculate the period in configuration two, we need to
measure and/or
calculate, respectively,
the following values and record them on the data sheet below:
r
conf
2
and
τ
conf
2
,theory
.
(Note:
To measure
r
rod ,conf
2
, first locate the center of mass by balancing
the system on the edge of the meter stick.
Remember,
r
conf
2
is the distance to the center of mass
from the axle hole.)
Measuring the Period of the Thin Rod In Configuration Two
19.)
Pull the thin rod to the side until the starting angle is approximately fifteen
degrees
; i.e.
ϕ
o
≈
15
°
.
Release the rod from rest and
start
your stopwatch and
count zero
when the rod
passes the vertical moving to the left.
When it next passes the vertical moving to the left, count one.
Do this until it has made exactly
five complete oscillations
, stopping the watch on the count of
five.
Divide the total elapsed time by five and record this value on the data sheet below as your first
time trial.
Repeat step 19.) four more times and determine the average value
τ
conf
2
,measured
for the
period of the rod.
20.)
Calculate the percent difference between
τ
conf
2
,theory
and
τ
conf
2
,measured
.

Data Sheet
System: Thin Rod
Calculating the Period of the Thin Rod
M
=
_____________ kg
d
=
_____________m
=
_____________ m
C
=
d
=
_____________
I
rod
=
_____________ kg m
2
r
rod
=
_____________ m
τ
rod, theory
=
_____________ s
Measuring the Period of the Thin Rod
Trial #
Time Values s
(
)
1
2
3
4
5
τ
rod, measured
=
_____________ s
% Difference
between
τ
rod,theory
and
τ
rod ,measured
=
_____________
HI 12
−
1

System: Thin Rod In Configuration One
Calculating the Period of the Thin Rod in Configuration One
M
cy,
1
=
_____________ kg
D
cy,
1
=
_____________m
I
cy,
1
=
_____________kg m
2
I
conf
1
=
_____________ kg m
2
r
conf
1
=
_____________ m
τ
conf
1
, theory
=
_____________ s
Measuring the Period of the Thin Rod in Configuration One