Name
Period
Date
Rotational Inertia of Point Masses
Purpose
To create graphical and mathematical representations of the relationship between
the rotational inertia (I), the total mass (m), and the distance the masses are from the
axis of rotation (r) for a system of particles consisting of two point masses.

Open Data Studio file Angular Acceleration.

Drape the string over the Super Pulley such that the string is in the groove of the
pulley and the Mass Hanger hangs freely. The clamp-on Super Pulley must be
adjusted at an angle, so that the thread runs in a line tangent to the point where it
leaves the 3-step Pulley and straight down the middle of the groove on the
clamp-on Super Pulley.

Be sure to wrap the string around the largest pulley of the rotary motion sensor
which has a radius of r = 0.024 m.

The mass hanger is 5.0 g = 0.005 kg.

If the data shows a negative rotation, wrap the string in the other direction.
Part 1: The Rotational Inertia of the Rod

Take the masses off of the rod and place a 0.020 kg mass on the mass hanger.
Data

Angular Acceleration rad
Hanging Mass
(kg)
Trial 1
s2
Trial 2

Trial 3
0.025
Evaluation of Data
Experimental Rotational Inertia from the pre-lab:
I
rmg   r 

where m = hanging mass = 0.025 kg
and
r = radius of the pulley = 0.024 m
Average
Angular Acceleration
rad 2
s


Rotational Inertia of the rod
kgm2


Part 2: The Rotational Inertia of the rotating point masses (I)
vs. the total Mass of the point masses (m) with constant
distance from the axis of rotation.


Mass the two brass masses together with their screws and record.
Place the masses back onto the rod at the ends of the rod. Measure the
distance to the masses from the axis of rotation and record. This perpendicular
distance must be measured from the center of the rod (the axis of rotation) to the
center of mass of the point masses.
Distance to the masses =
m
Place a 0.050 kg mass onto the mass hanger for a total hanging mass of 0.055 kg
for Parts 2 & 3.
Add the same mass to each end to keep the device balanced.
The total mass is the sum of the two masses with screws and all added masses.



Data
Mass of both
masses with
screws
(kg)
0

Angular Acceleration rad

Added
Masses
(kg)
Total
Mass
(kg)
Trial 1
Trial 2
Trial 3
0
0
2 x 0.050
2 x 0.100
2 x 0.120
2 x 0.150
0
---
---
---
Evaluation of Data
I system 
Experimental Rotational Inertia of the system:
s2
rm g   r 

where m = hanging mass = 0.055 kg
and
r = radius of the pulley = 0.024 m
I masses  I system  I rod
Rotational Inertia of the point masses:
Average
Angular Acceleration
rad 2
s
---



Rotational Inertia of the
system
kgm2
Rotational Inertia of the
point masses
kgm2
Rotational Inertia of the rod
0




Use LoggerPro to graph the Rotational Inertia of the point masses vs. the Total Mass.
Part 3: The Rotational Inertia of the point masses (I) vs. the
Distance to the masses from the axis of rotation (r) with
constant total mass.

Mass the two brass masses together with their screws and record as the
Constant total mass =
kg +
kg =
kg
Mass 1
Mass 2
Total Mass

Place the masses back onto the rod at equidistant positions. The masses must
always be equidistant from the axis of rotation.
There are no added masses in Part 3!
The perpendicular distance must be measured from the center of the rod (the
axis of rotation) to the center of mass of the point masses.
Place a 0.050 kg mass onto the mass hanger for a total hanging mass of 0.055 kg
for Parts 2 & 3.



Data

Distance to the masses from the
axis of rotation (r)
(m)
0
0.070
0.100
0.130
0.160
0.180
Angular Acceleration rad
Trial 1
---
Trial 2
---
Evaluation of Data
Experimental Rotational Inertia of the system:
I system 

s2
Trial 3
---
rm g   r 

where m = hanging mass = 0.055 kg
and
r = radius of the pulley = 0.024 m
I masses  I system  I rod
Rotational Inertia of the point masses:
Average
Angular
Acceleration
rad 2
s
---



Rotational
Inertia of the
system
kgm2
Rotational
Inertia of the
point masses
kgm2
0
0




Use LoggerPro to graph the Rotational Inertia of the point masses vs. the
Distance to the Masses from the Axis of Rotation.