Studio Physics I
Activity 12 – Introduction to Circular Motion
1. Go to your Physics I folder and double-click on the file FerrisWheel.xmbl or you can
download the files you need from the Physics I web site. After loading and clicking on “OK”
twice (continue without interface), your computer screen should look like the image below.
#3 Page Select
#1 Add Point
#2 Toggle Trails
2. Click on the icon #1 and on the icon #2 shown in the figure above. This will instruct the
software to leave a trail of markers at every location that you point the cursor to and click.
3. Center the cursor over a point on the wheel that you think you can keep track of. We suggest
that you choose a point in the lower left-hand portion of the picture. This is because these
points remain easy to see for many frames of the movie. They will not be obstructed by
anything as the frames advance. (Note that the Ferris Wheel spins in the clockwise direction
as we view it.) Click on the point on the wheel that you have chosen. The movie will
advance to the next frame and a small red dot should appear at the location you clicked on.
The spot on the wheel that you chose to keep track of should have rotated through some
angle. Click on the spot in its new location. Collect about 20 data points. Note that the first
click will not be counted due to a bug or “feature” (if you prefer) in the software.
4. Based on the trail of circles left on the movie image, does the Ferris Wheel appear to be
rotating with a relatively constant speed? Explain your reasoning.
5. Use the Page Select menu (#3 above) to switch to the analysis page for the remainder of the
activity. Your screen should look like the picture shown below.
Copyright © 1999, 2000, 2001 Cummings; Rev. 19-Feb-06 Bedrosian
6. Sketch the plots on your activity sheet of X Velocity and Y Velocity versus time. (You can
change the item plotted by clicking on the label.) Is the velocity in the x-direction constant?
Is the velocity in the y direction constant? Write down the range of values for each.
7. In addition to the x and y components of velocity that we looked at above, let’s consider the
magnitude of the velocity of the wheel, or speed. In general, how does one get the magnitude
of the velocity from Vx and Vy (the components)? (If you aren’t sure, check page 42 of the
book.) Calculate the magnitude of the velocity from the x and y components in your data
table for the first two times listed in the table. Show all your work on your activity write-up.
Do your results agree with the values of V listed in the table? (They should.)
8. Sketch a graph of the magnitude of velocity (speed) versus time. What is the approximate
value of the average speed? What is the difference between the highest and lowest values as
a percentage of the average? (This percentage is a crude indication of the uncertainty in your
measurement.) Is the speed relatively constant?
9. What is the magnitude and direction of the centripetal acceleration of a passenger on this
Ferris Wheel at the highest point? What is the magnitude and direction of the centripetal
acceleration of a passenger on this Ferris Wheel at the lowest point? To get the magnitude,
check both the “A” and “Ac” columns of the data table. Are the numbers nearly constant?
(Note all accelerations should be in units of m/s2.) The “A” column was calculated using the
magnitude of the acceleration vector from the “Ax” and “Ay” columns. The “Ac” column
was calculated using the formula v2/r. Which column would you predict to be more accurate?
(Ask your TA or instructor if you aren’t sure.) How do you know the direction of the
centripetal acceleration vector?
Copyright © 1999, 2000, 2001 Cummings; Rev. 19-Feb-06 Bedrosian
10. What forces act on a person at the top of the Ferris wheel? (Note that the person is upside
down at the top. Hence, the normal force from the seat on the person points downward. If
this seems puzzling, talk about it with others on your team, a TA, or your instructor.) What
forces act on a person at the bottom of the Ferris Wheel? What are the directions of these
forces? Draw a free-body diagram for the passenger at the highest point. Draw a free-body
diagram for the passenger at the lowest point. Show the direction of acceleration off to the
side of each of the free-body diagrams. Have your TA (or professor) check your work on
this question before proceeding.
11. Translate each of the two free body diagrams into an algebraic expression based on Newton’s
2nd Law (F = ma). Use the 6-step process we discussed in class. What numerical value will
you use in these equations for acceleration? Solve for the normal force of the seat on a
passenger in terms of the other symbols. Make sure your signs (+/–) are consistent with
the directions of the forces and acceleration.
12. If we were to measure a person’s “apparent weight” on a Ferris Wheel (or in an elevator or
anywhere else), what we would actually be measuring is the normal force exerted on the
person. What is the apparent weight of a person with mass = 68 kg or weight = 68*9.8 = 666
N when he is at the highest point on the Ferris Wheel in the video? What is the apparent
weight of the person at the lowest point?
13. If you were riding this Ferris Wheel upside down at the top, why wouldn’t you fall out of the
seat since all of the forces on you are down? Hint: The answer is not because you are
strapped into the seat.
Don’t forget the exercise on the next page!
Copyright © 1999, 2000, 2001 Cummings; Rev. 19-Feb-06 Bedrosian
Exercise
A jet aircraft is flying in a vertical circle in a maneuver called a “loop-the-loop.” At the top of the
circle, the jet’s speed is 245 m/s and the center of the circle is 1225 m directly below the jet. The
jet is flying upside down. The ratio of the normal force (N) from the seat on the pilot to the
weight of the pilot at rest on the ground (W) is commonly called the “g-force” on the pilot, a
dimensionless number. What is the g-force or N  W for this pilot? Use g = 9.8 m/s2.
14. Use the six-step process we discussed in class to analyze this problem. First, identify the
forces on the pilot. (Hint: There are two.)
15. Choose a coordinate system. We recommend you make the direction of acceleration the
positive direction to avoid problems with – signs. (What is the direction of acceleration?)
16. Draw a free-body diagram of the pilot. (Hint: The pilot is upside down. What does that
imply about the normal force?)
17. Figure out whether the forces you identified are positive or negative in your coordinate
system.
18. Write Newton’s 2nd Law (F = ma). This should come directly from your diagram.
19. Calculate acceleration based on what we learned in class. (Class notes or book page 70.)
20. Solve for N  W using algebra. Why didn’t we need to know the pilot’s mass?
21. If you were the pilot of the jet at the top of the loop (upside down), what would it feel like?
Would it feel like you were falling out of your seat or would you feel pressed into your seat?
22. Suppose the jet does the loop a second time, only this time the jet is right-side up at the top of
the loop. (This maneuver is called an outside loop.) If you were the pilot, would it feel like
you were rising out of your seat against the straps or would you feel pressed into your seat?
Pilots call this “pulling negative g’s.” Explain what they mean.
23. One more maneuver to execute, and then we can finish the exercise and land our jet. This
time, we will fly right-side up, adjusting the engine thrust and the control surfaces so that all
forces on the jet cancel except the force of gravity. The jet will follow a parabolic trajectory
that we previously studied: projectile motion. Is the force of gravity from the earth still
acting on the people inside the jet? What would the ride feel like to people inside the jet?
(Explain any seeming contradictions in your answers to the first two questions.) Why might
it be useful to fly a large cargo jet for 30 seconds or more on such a trajectory?
Copyright © 1999, 2000, 2001 Cummings; Rev. 19-Feb-06 Bedrosian