NSU PHYSICS
A Laboratory on Rolling Motion
Introduction:
Review Chapter 10 in Serway & Jewett, Principles of Physics , 4th ed or Chapters 7 & 8
in Serway/Faughn, College Physics, 7th ed. Look particularly at the sections concerning rolling
energy and motion. Write down the equations that define the rotational kinetic energy and the
translational kinetic energy
Krot = _______________________.
Ktrans = _______________________.
Also, write down the relationship between the velocity of the center of mass and angular
velocity for rolling motion as well as the relationship between the acceleration of the center of
mass and the angular acceleration for rolling motion:
vcm = _______________________.
acm = ______________________.
Equipment Needed:
. Microsoft Windows Compatible Computer
. World In Motion 4.0
Data Collection Procedure:
Starting the program
1) Click on “Start\Programs\World-in-Motion 4.0\Video Analysis”.
2) Click on “Open video file”.
3) Double click on “NSU Videos”.
4) Double click on “E2225.AVI”
(Note: This is a set of 10 successive pictures (or frames) of a bicycle wheel rolling down
an incline. Each frame differs from the previous frame by .067 of a second)
Recording the position of the center of the wheel and the outside edge of the wheel
1) Click on the center of the wheel as each picture is presented. You can move forward frame
by frame by clicking on the “Step>>” button on the right side. There will be 10 values. Then
click on the “data set 1” button to activate the second data set.
2) Click on the outside edge of the wheel marked with the tape as each picture is presented.
You can move forward frame by frame by clicking on the “Step>>” button on the right side.
3) Now click on “Video Scale” and “New Origin”. Then click on the lowest mark for the center
of the wheel. The results of the video marking should look like this:
Graphing and Analyzing the Data
1) Click on “Graphs” on the bottom right hand side of the screen.
2) Select Option 4 under Data Analysis Choices. Click “Next”.
3) Under the direction of motion, click on “X and Y direction” for the C.M. and the point. Then
click on Y is “vertical” and then “Next”.
4) The graphs we wish to plot are “Position versus Time”, and “Angle versus Time”. Click on
the box to the left of these two options and then click “next”. Print out the title page, and
these graphs.
5) Now, on the right side in the middle, click on “Graph>>” to bring of the “position versus
time” graph for data set 1 (the center of the wheel).
Analysis of Position vs Time graph for the center of the wheel motion
What is the shape of this graph? ___________.
We will use the graphical analysis program to fit the angle vs time graph. In order to do
this, move to the data table in World in Motion and press the bar labeled “click here to copy all
data to the clipboard”. Minimize the World in Motion Program and then start up Graphical
Analysis. Load the file “rotkin1.dat”. Click on the first box of the data table and select “Paste
Data” from the “Edit” menu. Click on the Graph, and select “Automatic Curve Fit” from the
“Analyze” menu. Select the “Quadratic function” from the menu, click “ok”, and click “ok –
keep fit”. Print out the resulting graph with the fit displayed. Record the fit constants below:
A = Ro,cm = _______________ m.
B = vo,cm = _______________ m/s.
C = acm/2 = ______________ m/s2. Î acm = 2C = _____________ m/s2
Analysis of Angle vs Time graph
View the “angle vs time” graph. What is the shape of this graph? ___________.
We will use the graphical analysis program to fit the angle vs time graph. In order to do
this, move to the data table in World in motion and press the bar labeled “click here to copy all
data to the clipboard”. Minimize the World in Motion Program and then start up Graphical
Analysis. Load the file “rotkin2.dat”. Click on the first box of the data table and select “Paste
Data” from the “Edit” menu. Click on the Graph, and select “Automatic Curve Fit” from the
“Analyze” menu. Select the “Quadratic function” from the menu, click “ok”, and click “ok –
keep fit”. Print out the resulting graph with the fit displayed. Record the fit constants below:
A = θo = _______________ rad.
B = ωo = _______________ rad/s.
C = α/2 = ______________ rad/s2. Î α = 2C = _____________ rad/s2
From the first graph screen, record the radius of the motion and then using the fit constants
above calculate the acceleration and initial velocity of the center of the wheel:
Radius (r) = ___________ m.
acm = αr = _____________ m/s2.
vo,cm = ωr = _________________ m/s.
How do these two calculations compare to the direct measurements above? Compute
percent differences for both the tangential acceleration and initial tangential velocity:
% difference for acm = ____________________.
% difference for vo,cm = ____________________.
Minimize Graphical Analysis and return to World in Motion. Click on the “data analysis”
button. Deselect the “position vs time” and “angle vs time” options and then select “energy vs
time”, “velocity vs time”, and “angular velocity vs time”. Click the “Next” button. Print out
these graphs.
Another Calculation of the angular acceleration and initial angular velocity of the rolling wheel
Go to the graph marked “Angular velocity versus Time”. Measure the slope of the line.
You can do this by left clicking on the left side of the line and right clicking on the right side of
the line. At the bottom of the graph is a box marked “Slope is angular acceleration”. The value
in this box is the angular acceleration and is in rad/s2.
α = _____________ rad/s2.
The intercept is the initial angular velocity ωo:
ωo = _______________ rad/s
How do these values compare with the values obtained from the Graphical Analysis fit of “angle
vs time”?
Another calculation of the acceleration and initial velocity of the center of the wheel
Go to the graph marked “Velocity versus Time” for data set 1. Measure the slope and
intercept of the blue line at the top marked “V”. You can do this by left clicking on the left side
of the line and right clicking on the right side of the line. The slope is the acceleration of the
center of the wheel in m/s2 and the intercept is the initial velocity in m/s
acm = _____________ m/s2.
vo,cm = _____________ m/s.
How do these values compare with the values obtained from the Graphical Analysis fit of
“Position vs time”?
Energy Analysis
Go to the graph marked “Energy vs Time”. On this graph, KE is the translational kinetic
energy, RE is the rotational kinetic energy, PE is the gravitational potential energy, and TE is the
total mechanical energy (the sum of the these three).
Is the Total Mechanical Energy Conserved? How can you tell from the graph?
Lets do a specific Energy Calculation using data that we have obtained.
Potential Energy at 0.067 to 0.533 seconds:
Using the “Data Set 1 position versus time” data along with the mass, m, of the wheel,
calculate these potential energies:
PE (at 0.067 seconds) = mgy0.067 = ____________ J.
PE (at 0.533 seconds) = mgy0.533 = ____________ J.
Calculation of the Translational Kinetic Energy at 0.067 to 0.533 seconds:
Using the Data Set 1 velocity versus time” data along with the mass, m, of the wheel,
calculate these Kinetic Energies:
KE (at 0.067 seconds) = ½ m v0.0672 = ___________ J.
KE (at 0.533 seconds) = ½ m v0.5332 = ___________ J.
Calculation of the Rotational Kinetic Energy at 0.067 to 0.533 seconds:
Using the angular velocity versus time” data along with the Rotational Inertia, I, of the
wheel, calculate these Kinetic Energies:
RE (at 0.067 seconds) = ½ I ω0.0672 = ___________ J.
RE (at 0.533 seconds) = ½ I ω0.5332 = ___________ J.
Compute the Sum of PE, KE, and RE at 0.067 and 0.533 seconds:
PE + KE + RE (at 0.067 seconds) = ____________ J.
PE + KE + RE (at 0.533 seconds) = ____________ J.
How do these values compare? Was any energy lost? How much?
Conclusion:
Write a one-paragraph conclusion that summarizes the results of this laboratory
experience.