PS-3220
Experiment 1: Rotational Inertia of a Point Mass
13
013-15949A
Experiment 1: Rotational Inertia of a Point Mass
*See the PASCO Web site at www.pasco.lcom for more information
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 = MR2, 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
, 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
= I
,
,
where
is the angular acceleration, which is equal to a/r (a = linear acceleration), and
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
(see Figure 1.1). Solving for the tension in the thread gives:
After the angular acceleration of the mass (m) is measured, the torque and the linear acceleration can be obtained
for the calculation of the rotational inertia.
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)
Itotal MtotalR
2
=
I
=
rT
=
F
mg T
–
ma
=
=
T
m g a
–
=
