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Physics 2010
Laboratory 4: Rotational Dynamics
NAME ___________________________
Section Day (circle): M
Tu
W
Th
F
Section Time:
8a
10a
12p
2p
4p
TA Name:
________________________
This lab will cover the concepts of moment of inertia and rotational kinetic energy.
These concepts
play the same roles in rotational motion as mass and kinetic energy do for straightline motion.
Instructions:
Make safety a priority.
This experiment uses fairly heavy rolling objects. There is a risk
of toe injury as well as damage to equipment.
Background Information
1.
Moment of Inertia
The
moment of inertia
,
I
, (also called
moment
and
rotational inertia
) of a body is a measure of how
much a body resists changing its rate of rotation about some axis.
Similar to mass in linear motion, the
larger a body’s moment,
I,
the more work it takes to increase the body’s rotation rate.
The moment of inertia is always defined with reference to a particular axis of rotation
─
often a
symmetry axis, but it can be any axis, even one that is outside the body. The moment of inertia of a
body about a particular axis is defined as:
(1)
The moment of inertia of a point mass
m
orbiting at radius
r
about an axis, is
I =
mr
2
(2)
If many point masses make up the body, equation 1 can be rewritten as
I = I
1
+ I
2
+ … + I
i
=
m
1
r
1
2
+ m
2
r
2
2
+ … + m
i
r
i
2
(3)
where
r
i
is the distance of mass
m
i
from the axis of rotation. If the body is a continuous object of some
arbitrary shape, then performing the sum requires techniques of calculus. In this course, we tell you the
answer for various shapes. For a disk of mass M and radius R (see Fig. 1), the moment of inertia
through the center of symmetry is
I
disc
=
½
MR
2
.
(4)
Notice that the thickness of the disk doesn't enter into the
expression for I
disc
, so the expression for I is the same for a
solid cylinder as it is for a flat disk.
A cylinder is just a very
thick disk.
Figure 1.
Solid disk with axis of symmetry,
uniform mass and density.
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The expression in equation I
disc
=
½
MR
2
is only true for a
uniform
disk or cylinder. If the object is a
hoop or a thinwalled cylinder, a different formula is used. The moment of inertia of a hoop or thin
walled cylinder is I
hoop
= MR
2
.
Because all the mass is at the same radius from the axis, making it
more resistant to changes in its rate of rotation.
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 Spring '06
 DUBSON
 Physics, Energy, Inertia, Kinetic Energy, Mass, Moment Of Inertia, Rigid Body

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