Lab 9 Moments of Inertia
In this lab you will measure moment of inertia of a disk and a ring. Use a small hanging
weight to accelerate a pair of masses about their axii of rotation. As the hanging mass
falls, the potential energy of the hanging mass converted to rotational kinetic energy of
the rotating body and kinetic energy of the hanging mass.
You will use a stopwatch and a ruler to make measurements of the moment of inertia in
today's lab. In your pre-lab report, use conservation of energy and kinematic equations
to show that:
!
!!"#$ = !!! ( ! ! − 1)
2ℎ
Where:
I = moment of inertia of spinning object
m = the mass of the hanging weight
r = radius where the string is attached on the spinning object
g = gravitational acceleration
h = distance weight falls
t = time it takes for weight to drop a distance h
Then you can compare it with the calculated moment of inertial of the disk/ring
1
! = !!!
2
where:
R = radius of the disk
M = mass of the disk
Since the disk is sitting on a cradle which rotates with the disk, you will need repeat the
measurement twice, once without the disk, just the cradle itself to find out the moment of
inertia of the cradle, Icradle, once with the disk (ring). This time you are measuring the
moment of inertia of the cradle and the disk(ring) Itotal.
Idisk/ring = Itotal. - Icradle
Use a ruler and the scale to determine the moment of inertia of the disk/ring. Take this to
be the true value. Record uncertainties with each of the measurement.
Set up the cradle and pulley as in the figure (will be posted soon). Choose a weight to act
as the hanging mass.
Now measure the moment of inertia of the cradle by taking the average of three timed
drops. Once you've done this, add the disk and make three more measurements. Moment
of inertia of the disk is then the difference of the second measurement and the first
measurement. This value will be greater than the calculated value via measuring the mass
1 and radius of the disk. (Why?) Try two different hanging masses and observe how does
hanging mass affect your result.
Repeat this experiment using the ring in place of the disk, measuring the moment of
inertia of the ring. If you have time, repeat once more with the disk/ring combination.
How does the measured moment of inertia compare with the sum of the moments of the
ring and disk when measured individually?
In your pre-lab report, figure out how to organize your data, and put it in a data table.
2