®
Model No. CI-6538
Rotary Motion Sensor
17
Experiment 1: Rotational Inertia of a
Point Mass
Purpose
The purpose of this experiment is to find the rotational inertia of a point mass
experimentally and to verify that this value corresponds to the calculated
theoretical value.
Theory
Theoretically, the rotational inertia,
I
, of a point mass is given by
I = MR
2
,
where
M
is the mass, and
R
is the distance the mass is from the axis of
rotation. Since this experiment uses two masses equidistant from the center
of rotation, the total rotational inertia will be
where M
total
= M
1
+ M
2
, the total mass of both point masses.
To find the rotational inertia experimentally, a known torque is applied to the
object and the resulting angular acceleration is measured. Since
τ
= I
α
,
where
α
is the angular acceleration, which is equal to
a/r
(
a
= linear
acceleration)
,
and
τ
is the torque caused by the weight hanging from the
thread that is wrapped around the 3-step Pulley.
where
r
is the radius of the chosen pulley 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
Equipment Required
ScienceWorkshop
®
750 Interface (CI-
6450 or CI-7599)
Rotary Motion Sensor (CI-6538)
Mini-Rotational Accessory (CI-6691)
Mass and Hangar Set (ME-9348)
Base and Support Rod (ME-9355)
Triple Beam Balance (SE-8723)
Paper clips (for masses <1 g)
Calipers
I
total
M
total
R
2
=
I
τ α
⁄
=
τ
rT
=
Σ
F
mg
T
–
ma
=
=