Name
Partners Name
Class and section number
Date
Title
Objective:
Restate the objective in your own words.
Materials and Instrumentation:
What is measured (the physical quantity related to purpose of the experiment)
Under what condition (what quantities are kept constant; what quantities are measured?)
What was used to make the measurement? What is its precision?
If needed, provide a labeled sketch of the set up.
Data:
Include all measured quantities with their units and sig. fig. or uncertainty of measurement
Include a copy of the data table. The table of data is not required if the data is collected using the logger pro (too many data points). The table of data can be handwritten, or a computer printout.
Label everything!
Calculations and Analysis:
Include all calculation steps related to physical quantities as well as the error analysis in this section.
Include any graphs.
Results:
Report the results of the experiment including their uncertainty of measurement in an appropriate format.
Discussion and Conclusion:
Why did we do this experiment? (Essentially what are we testing?)
How did you accomplish the objective? (Mention how what you did relates to the concepts being tested)
Do your results support the concepts tested? If not, briefly mention why not.
What were potential sources of error? (Human error is not accepted)
Also answer questions stated in the lab manual Online Angular Momentum Lab
Objective
The object of this experiment is to observe and analyze one-dimensional rotational collisions
between a disk and a bar rotating about a common axis. You will test the law of conservation
of angular momentum and determine whether or not rotational kinetic energy is conserved
during the collision.
Theory
Angular momentum is a useful quantity for analyzing the motion of objects over time because
it is a conserved quantity:
~L = I~ (1)
To understand this, consider the time derivative of angular momentum:
d~L
dt
= I
d~
dt
(2)
Recognizing that the term d~
dt
on the right side of this expression is the angular acceleration
~ = d
dt
, and using Newtons 3rd law for rotational motion ~ = I~ we can say that:
d~L
dt
= ~ (3)
This implies that if no outside torques act on a system, the angular momentum of the system
will not change in time. If there are no external torques, what would be the slope of equation
(1)?
Think to yourself
Imagine you want to devise your own procedure for comparing the angular momentum of a
set of objects before and after a collision. You have a rotation sensor, calipers and rulers,
1
a scale, and two flat disks of different size. Think of a procedure for how these objects can
be used to measure conservation of angular momentum. There is no right way to do this.
Write a brief description of your proposed procedure. Angular momentum is only conserved
if no external torques act on the systemhow could you avoid introducing unwanted external
torques?
Experiment
Someone conducted an experiment measuring angular momentum during a collision using
a thin disk and a thin rectangular-shaped bar of aluminum. They also used a rotation
sensor which measured angular velocity (radians/second) as a function of time. The disk
was placed flat on a rotation sensor. The rotation sensor has a thin axle going straight
through the center, and each object has a hole drilled through the center so that the disk
and bar can be centered on the rotation sensor. The disk was spun for some time before the
bar was dropped onto the center of the disk.
Here are the measurements that were taken for each object:
Disk mass: 464 g
Disk radius: 0.063 m
Bar mass: 182 g
Bar length: 0.29 m
Bar width: 0.05 m
2
Assume the scale has an uncertainty of 1g and the ruler has an uncertainty of 1mm.
1. What is the moment of inertia just before the collision? What is the moment of inertia
just after the collision? The moment of inertia for a uniform disk of mass m and
radius r rotating about its center of mass is Idisk =
1
2
mR2. The moment of inertia for
a uniform bar of mass m length L and width w rotating about its center of mass is
Ibar =
1
12
m(L2 + w2)
Analysis
1. Download the data set from this experiment by going to the following link:
https://tinyurl.com/AngularMomentumData.
Using whatever tools you prefer (LoggerPro, Excel, Google Sheets, etc.) plot the
angular velocity as a function of time.
2. When one stationary object is dropped onto another the collision is not instantaneous
it takes some time for the stationary object to spin up and the rotating object to slow
down until they are moving at a common angular velocity. Just by looking at the
graph, when does the collision start and end? How do you know?
3. Generate a procedure for comparing the angular momentum before and after the col-
lision. Write a brief description of your procedure.
4. What are the sources of uncertainty in your measured values for the angular mo-
mentum? Are you able to show that momentum is conserved within this uncertainty
range?
5. Because there is friction between the objects as they collide we expect energy to not
be conserved. In addition to comparing the angular momentum before and after the
collision, determine the total rotational kinetic energy (KErot =
1
2
I2) of the system
before and after the collision. What percentage of the kinetic energy was lost in the
collision?
Report
In addition to the standard elements of a well written lab report described in the introduction
to this manual, your report must include:
3
https://tinyurl.com/AngularMomentumData
1. A detailed description of your procedure for the analysis
2. A graph of angular momentum before and after the collision and kinetic energy before
and after the collision
3. A conclusion in which you address the following:
(a) Whether or not angular momentum was conserved.
(b) Whether or not the energy of the system was conserved.
4
