PASCO ME-6694 TORSION PENDULUM - Manual (Page 9)

012–06339A Torsion Pendulum
5
Experiment 1. Determining the Magnitude of the Moment of
Inertia (I) Using Two Methods
Purpose
The purpose of the experiment is compare the magnitude of the moment of inertia (I) of a disk
and cylinder calculated by (1) using a torsional spring constant (
κ ) and the period of oscillation
of the Torsion Pendulum (T) and (2) with I calculated using mass and radius measurements.
Materials and Equipment Required
• Torsion Pendulum (ME-6694) • Force Sensor (CI-6537)
• Rotary Motion Sensor (CI-6538) • Table Clamp (ME-9376B)
• Mini-Rotational Accessory (CI-6691) • Support Rod (90 cm) (ME-8738)
• Science Workshop
2.1 or higher
• mass balance
• PASCO computer interface (500 or 700) • metric ruler
• computer • sturdy, non-stretching string—18 inches
• pages 2 and 3 of the manual
Theory
The magnitude of the moment of inertia (I) of a disk can be determined with the Torsion
Pendulum using the following relationship:
where T= the time (s) for a period of oscillation of the Torsion Pendulum and κ = the torsional
spring constant of the wire.
The magnitude of the moment of inertia of a disk can also be determined by measuring the
mass (m) and radius (R) of the disk and using the relationship:
I =
T
2
π
2
κ
I =
1
2
mR
2
Therefore, in the case of a uniform disk rotating about its cylinder axis, the following relationship
can be shown:
In the case of a disk plus a cylinder (Part C of the experiment), the following relationship can
be demonstrated:
where R
1
= the inner radius of the cylinder and R
2
= the outer radius of the cylinder.
1
2
mR
2
=
T
2
π
2
κ
T
2
π
2
κ
=
1
2
mR
2
+
1
2
m(R
1
2 +
R
2
2
)