Lab 13: Angular Momentum
Objective:
To observe the change in angular momentum by testing the law of conservation of angular
momentum and to determine if rotational energy is conserved after altering certain variables of
the experiment. We were also tasked with creating our own experiment that would allow us to
observe these changes.
Scientific Instruments:
● Ruler: The ruler allowed us to measure the length and the width of our objects. This was
an accurate measurement tool which measured to the closest inch.
● Dial Caliper: The dial caliper allows us to measure the diameter of our disk, so we can
use the measurements for future equations. This was an accurate measurement that
measured to the closest millimeter.
● Scale: The scale was used to weigh our disk and bar so we can use these weights to plug
into equations. This was an accurate measurement tool that measures to the closest .01
gram.
● Rotary Motion Sensor: This instrument measured the angle, velocity, and acceleration of
our experiment, which we got our data from to convert into our graphs.
● LabQuest: Measurement device that was connected to the rotary motion sensor which
allows us to record the angular velocity and acceleration. This tool was extremely
accurate.
● LoggerPro: The software that was connected to LabQuest and the computer which
allowed us to plot our data onto a graph. This software is extremely accurate and
produces good graphs.
Procedure:
1. Weigh the disk and bar using the scale, measure the length and width of the bar and
radius of disk.
2. Turn on LabQuest, connect LabQuest to rotation sensor, connect LabQuest to computer,
make sure LabQuest is reading an angle, zero it out.
3. Place the uniform disk on the stationary rotation sensor, start spinning the uniform disk
and let it spin for a second, start the run on LabQuest, gently place the bar on the axis of
rotation after 4 seconds and allow the run to finish.
4. Observe data/graph that has transferred onto Logger Pro, write down the velocity at 2
seconds (as this will be your initial angular velocity) and write down the velocity at 9
seconds (as this will be your final angular velocity).
5. Use data to calculate the initial and final values for angular momentum and kinetic
energy.
Data:
Radius of Disk: 0.0635 m
Length of Bar: 0.305 m
Width of Bar: 0.051 m
Mass of Disk: 0.47069 kg
Mass of Bar: 0.12780 kg
ω initial = 29.11 rad/s
ω final = 13.22 rad/s
Inertia of Disk = .5 (m)(R^2)
= .5 (0.47069 kg)((0.0635 m)^2)
= 0.000949 kg(m^2)
Inertia of Bar = 1/12 (m)( (L)^2 + (w)^2 )
= 1/12 (0.12780 kg)( (0.305 m)^2 + (0.051 m)^2 )
= 0.00102 kg(m^2)
Initial Angular Momentum = (Inertia of Disk)(ω initial) + (Inertia of Bar)(ω initial)
= (0.000949 kg(m^2))(29.11 rad/s) + 0
= 0.0276 N(m)
Final Angular Momentum = (Inertia of Disk + Inertia of Bar)(ω final)
= ( 0.000949 kg(m^2) + 0.00102 kg(m^2) )(13.22 rad/s)
= 0.026 N(m)
Initial KErot = .5 (Inertia of Disk)(initial ω^2)
= .5 (0.000949 kg(m^2))( (29.11 rad/s)^2 )
= .402 J
Final KErot = .5 (Inertia of Disk + Inertia of Bar)(final ω^2)
= .5 ( 0.000949 kg(m^2) + 0.00102 kg(m^2) ) ( (13.22 rad/s)^2 )
= 0.172 J
Net External Torque = Initial Angular Momentum - Final Angular Momentum
= 0.0276 N(m) - 0.026 N(m)
= 0.0016 N(m)
Analysis:
For this procedure, the sources of uncertainty in our measured values for angular momentum
have to do with the execution of the procedure. For example, it was difficult to drop the bar
directly onto the axis of rotation/center of the disk. This form of human error is a source of
uncertainty in the procedure as dropping the bar perfectly is extremely difficult. In our data
section, we calculated the initial and final angular momentum of the system in our experiment.
We found that the initial and angular momentum differed by 0.0016 N(m) which is a percent
error of approximately 5.80% between the two angular momentums. We calculated the initial
and final angular momentum in our data section above. It’s clear that angular momentum was not
conserved in our experiment. Thus, we were not able to show that angular momentum is
conserved within the uncertainty range.
Percent Error of Angular Momentum = | [ (Initial Angular Momentum - Final Angular
Momentum) / (Initial Angular Momentum) ] x 100 |
= | [ (0.0276 N(m) - 0.026 N(m)) / (0.0276 N(m)) ] x 100 |
= 5.80%
In our procedure, approximately 57.2% of the kinetic energy was lost in the collision. We
calculated the initial and final kinetic energy in our data section above.
KE Lost = | [ (Initial KE - Final KE)/ (Initial KE) ] x 100 |
= | [ (.402 J - 0.172 J) / (.402 J) ] x 100 |
= 57.2% of the Kinetic Energy was lost.
Graph:
Conclusions:
In our experiment, we calculated the initial and final angular momentum of the system using the
data that we collected during the procedure. We determined that the angular momentum was not
entirely conserved. However, the initial and final angular momentum were not far from each
other, the initial angular momentum being 0.0276 N(m) and the final angular momentum being
0.026 N(m). The overall percent error in angular momentum was approximately 5.80%. The
angular momentum is being conserved when the bar is put on the disk, which also makes the bar
turn, taking in the angular momentum. However, the final angular momentum would decrease
due to an external torque, when the bar is first put onto the spinning disk with initial angular
momentum. Furthermore, it is the external torque due to friction that results in a loss of angular
momentum in our experiment. We calculated that the external torque due to friction was 0.0016
N(m) which caused the angular momentum to decrease. This friction most likely occurred with
the rubbing of the disk with the Rotary Motion Sensor and once we placed the bar on top of the
disk.
After calculating everything, we determined that the energy of the system was not conserved in
this experiment. In fact, we found that approximately 57.2% of the kinetic energy of the system
was lost. This loss of kinetic energy is a result of the friction that occurred in our procedure.
Since the friction created an external torque, we see that the energy of the system decreased. This
friction might have been caused by the contact that the disk is constantly making with the Rotary
Motion Sensor and the rubbing of the disk and bar.