PASCO CI-6538 Rotary Motion Sensor - Manual (Page 18)

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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 = Iα,
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 =
ΣF
mg T – ma = =