PASCO ME-8950A COMPLETE ROTATIONAL SYSTEM - Manual (Page 41)

012-05293F Complete Rotational System
37
Experiment 6: Rotational Inertia of Disk Off-Axis
(Fixed/Rotating)
EQUIPMENT REQUIRED
- DataStudio Program - Calipers
- PASCO Interface (See Note) - Mass and Hanger Set
- Rotational Inertia Accessory (ME-8953) - Paper Clips (for masses < 1 g)
- Photogate/Pulley System - Balance
Purpose
The purpose of this experiment is to find the rotational inertia of a disk about an axis parallel
to the center of mass axis.
Theory
Theoretically, the rotational inertia, I, of a disk about a perpendicular axis through its center
of mass is given by:
where M is the mass of the disk and R is the radius of the disk. The rotational inertia of a disk
about an axis parallel to the center of mass axis is given by:
where d is the distance between the two axes.
In one part of this experiment, the disk is mounted on its ball bearing side which allows the
disk to freely rotate relative to the track. So as the track is rotated, the disk does not rotate
relative to its center of mass. Since the disk is not rotating about its center of mass, it acts as a
point mass rather than an extended object and its rotational inertia reduces from:
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 and τ is the torque caused by the
weight hanging from the thread which is wrapped around the three step pulley on the shaft of
the apparatus.
where r is the radius of the step pulley about which the thread is wound and T is the tension in
the thread when the apparatus is rotating.
I
cm
1
2
---MR
2
=
I I
cm
Md
2
+ =
I I
cm
Md
2
to I + Md
2
= =
I
τ
α
--- =
τ
rT =
Note: If you are
using a PASPORT
interface, you will
also need a Digital
Adapter (PS-2159)