PS-3220
Experiment 2: Rotational Inertia of Disk and Ring
17
013-15949A
Experiment 2: Rotational Inertia of Disk and Ring
*See the PASCO Web site at www.pasco.lcom for more information
Purpose
The purpose of this experiment is to experimentally find the rotational inertia of a ring and a disk and verify that
these values correspond to the calculated theoretical values.
Theory
Theoretically, the rotational inertia, I, of a ring about its center of mass is given by:
where
M
is the mass of the ring,
R
is the inner radius of the ring, and
R
is the outer
radius of the ring. See Figure 2.1.
The rotational inertia of a disk about its center of mass is given by:
where
M
is the mass of the disk and
R
is the radius of the disk. See Figure 2.2. To find
the rotational inertia experimentally, a known torque is applied to the object and the
resulting angular acceleration is measured, Since
= I
,
where
is the angular acceleration, which is equal to
a/r
(
a
= acceleration), and
is the
torque caused by the weight hanging from the thread that is wrapped about the 3-step
Pulley on the Rotary Motion Sensor. The torque is given by:
where
r
is the radius of the pulley step about which the thread is wound, and
T
is the tension in the thread when the
apparatus is rotating.
Applying Newton’s Second Law for the hanging mass,
m
, gives:
See Figure 2.3. Solving for the tension in the thread gives:
Once the angular acceleration is measured, the radius and the linear acceleration,
a
, can be obtained for the
calculation of the torque.
Equipment Required*
Equipment Required*
Wireless Rotary Motion Sensor (PS-3220
Base and Support Rod (ME-9355)
PASCO Data Collection Software
Mass and Hanger Set (ME-8979)1
Rotational Inertia Accessory Kit (ME-3420)
Triple Beam Balance (SE-8723)
Calipers (SF-8711)
Paper clips (for masses <1g)
Figure 2.1: Ring
about
center of mass
R1
R2
I
1
2
---
M R
1
2
R
2
2
+
=
I
1
2
---
MR
2
=
Figure 2.2: Disk about
center of mass
R
I
---
=
rT
=
F
mg T
–
ma
=
=
T
m g a
–
=
