PASCO ME-8950A COMPLETE ROTATIONAL SYSTEM - Manual (Page 19)

012-05293F Complete Rotational System
15
rotating
platform
hanging
mass
mg
T
a
"A" base
Experiment 2: Rotational Inertia of a Point Mass
EQUIPMENT NEEDED
- DataStudio Software
- PASCO Interface (see Note)
- Mass and Hanger Set
- Paper clips (for masses < 1 g) - Photogate/Pulley System
- Balance - Calipers
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, R is
the distance the mass is from the axis of rotation.
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 step pulley below the rotating platform, and
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.
Applying Newton’s Second Law for the hanging mass, m, gives (see Figure 2.1).
Solving for the tension in the thread gives:
I
τ
α
--- =
τ rT =
ΣF mg T – ma = =
T m g a – ( ) =
Figure 2.1: Rotational Apparatus and Free-Body Diagram
Note: If you are
using a PASPORT
interface, you will
also need a Digital
Adapter (PS-2159)