Experiment 1: rotational inertia of a point mass – PASCO PS-2120A Rotary Motion Sensor User Manual
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P S - 2 1 2 0 A
E x p e r i m e n t 1 : R o t a t i o n a l I n e r t i a o f a P o i n t M a s s
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E x p e r i m e n t G u i d e
Experiment 1: Rotational Inertia of a Point Mass
*Click the equipment item to go to the PASCO web site.
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 dis-
tance 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
= 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*
Interface
Paper clips (for masses <1 g)
I
total
M
total
R
2
=
I
=
rT
=
F
mg
T
–
ma
=
=
T
m g
a
–
=