EXPERIMENT
9B
Rotational Motion 2
Moment of inertia
Objectives
•
to familiarize yourself with the concept of moment of inertia, I, which plays the
same role in the description of the rotation of a rigid body as mass plays in the
description of linear motion
•
to investigate how changing the moment of inertia of a body affects its rotational
motion
APPARATUS
See Figure 3a.
THEORY
If we apply a single unbalanced force, F, to an object, the object will undergo a linear
acceleration, a, which is determined by the unbalanced force acting on the object and the
mass of the object. The mass is a measure of an object's inertia, or its resistance to being
accelerated.
Newton’s Second Law expresses this relationship:
F = ma
If we consider rotational motion, we find that a single unbalanced torque
τ
= (Force)(lever arm)
#
produces an angular
acceleration,
α
, which depends not only on the mass of the object
but on how that mass is distributed
.
The equation which is analogous to F = ma for an
object that is rotationally accelerating is
τ
= I
α
.
(1)
where the Greek letter tau (
τ)
represents the torque in Newton-meters,
α
is the angular
acceleration in radians/sec
2
and I
is the
moment of inertia
in kg*m
2
.
The moment of
inertia is a measure of the way the mass is distributed on the object and determines its
resistance to angular acceleration.
#
In this lab the lever arm will be the radius at which the force is applied (the radius of the axle).
This is
due to the fact that the forces will be applied tangentially, i.e., perpendicular to the radius. The general form
of this relationship is
θ
τ
sin
*
*
arm
lever
force
=
, where
θ
is the angle between the force and the
lever arm.
However, in this experiment
θ
is 90° and sin(90°) = 1.

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Every rigid object has a definite moment of inertia about any particular axis of rotation.
Here are a couple of examples of the expression for I for two special objects:
One point mass m on a weightless rod of radius r
(
I = mr
2
):
x
y
z
O
Figure 1
Two point masses on a weightless rod (
I = m
1
r
1
2
+ m
2
r
2
2
):
y
x
z
0
Figure 2