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NAME:_________________________________________
DATE: _______________
AP-LAB 08/05: A Round and Round We Go
PURPOSE
E
(A) To experimentally determine the relationship between centripetal force and velocity for an object
moving in a horizontal circle.
(B) Based on measurements, approximate the velocity and tension in a string keeping a flying pig that
is flying in a conical pendulum.
BACKGROUND
When an object travels at a constant speed along a circular path, we say it is traveling in uniform circular
motion. Any object traveling in uniform circular motion is accelerated toward the center of its path by
what is called centripetal (center seeking) acceleration. The value of this acceleration can be determined
by the relationship ac 
v2
, where v is the speed and r is the radius of rotation. Since the net force on
r
an object is determined by Newton’s 2nd Law, the net force (sometimes called the centripetal force) on
the object can be found by the relation  F  ma  mac  m
v2
, and is always directed towards the
r
center of the circular path. This is how the motion of an object attached to a string moving in a near
horizontal circle can be described.
This is also what happens to an object suspended by a sting that is moving in a conical pendulum
(when the string is at an appreciable degree below horizontal). The horizontal component of its
motion is that of an object undergoing uniform circular motion, with the string applying the force that
provides the centripetal acceleration.
EQUIPMENT







Glass Pipe with her string
Rubber Washer
Flying Pig and his string
Brass masses/washers
Balance or digital scale
Ruler
Stopwatch
PROCEDURE
For parts of this lab you will be creating most of the
procedure yourself. You will be given the tasks and tips on how to incorporate some of the
apparatus available into your procedure. If you need help using any of the equipment, please
ask you teacher.
For this lab, you will be conducting experiments with a rubber stopper moving in a horizontal
circle and with a pig flying in a conical pendulum. Before going to the lab there is some work
that must be done to get yourselves prepared.
AP-Lab08/05: A Round and Round We Go, Centripetal Force and Acceleration
Mike Maloney  2007 http://mrmaloney.com
[Page 1 of 4]
NAME:_________________________________________
DATE: _______________
Part A Prelab
1) Sketch a Free Body Diagram of the situation and develop an equation relating the weight of the
hanging mass to the mass of the stopper, the radius of rotation, and speed of rotation.
Part B Prelab
1) Once it reaches equilibrium, the pig flies in constant velocity in what is called a "conical pendulum".
Draw and label a Force Diagram of the flying pig. To do this, consider a snap-hot of the pig from the
side. Show the angle the string makes with the vertical, θ, and the radius to the center of the circle
(Hint: the radius of the circle in which it flies is not the length of the string). Diagram all the forces
on the pig. Use dashed lines to show the horizontal and vertical components of the string tension.
2) Use the Force Diagram to write the Newton's Second Law equations. Derive a formula for the
centripetal acceleration of the pig in terms of the variables you used in your force diagram.
3) Now derive a formula for the theoretical speed of the pig in equilibrium based on its mass and the
other variables in your force diagram (θ, r, L, etc), and solve for v.
4) You will have to determine the angle the pig is flying at. This is very hard to measure directly. See if
you can come up with a way to experimentally determine the angle or the pig.
Part A: Rotating Stopper
1) Set up : In this experiment, a string is threaded through a glass pipe. A stopper is tied to one end of
the string, and a number of washers/weights to the other end. A clip is placed between the tube and
the washers.
2) Find the mass of the washers and the mass of the stopper.
3) Practice swinging the stopper in a horizontal circle of fixed radius in circular motion. To help keep
the radius fixed, balance the clip a fixed distance (about 1 cm) below the tube while carefully
swinging it in a near horizontal circle.
4) Measure the radius of the circle. (The length of the string from the top of the tube to the center of the
stopper.)
5) Measure the period of rotation of the stopper. One group member should swing the stopper in a
horizontal circle, with the clip balanced below tube. Another member should time the stopper
through 20 complete revolutions.
6) From the time for 20 revolutions, find the period for the stopper.
7) The weight of the washers provides the centripetal force; we will assume that they are equal to each
other. Change the number of washers and repeat the experiment until you have 5 sets of data.
8) For your last two sets of data, change the radius by moving the clip. Repeat the experiment for those
two setups with the new radius and record your results.
Part B: The Flying Pig
1) Measure the mass of the pig and the length of the string the pig is attached to. For the string length
include half the width of the pig (you want the length to its center of mass).
2) Now start the pig flying. Once the pig is up and flying in a circle of constant radius, measure the
radius of the circle and the angle θ as accurately as you can. Express your answer in meters.
3) Measure the speed of the pig. To do this, time 10 rotations of the pig and determine the Period for
one rotation. Then determine the speed based on the radius and period.
4) Using your equation from your prelab, calculate the theoretical speed of the pig based on your
measurements. Compare this speed to the measured speed by calculating a percent error.
AP-Lab08/05: A Round and Round We Go, Centripetal Force and Acceleration
Mike Maloney  2007 http://mrmaloney.com
[Page 2 of 4]
NAME:_________________________________________
DATE: _______________
ANALYSIS ( PUT NUMERICAL ANSWERS IN THE ACCOMPANYING DATA TABLE )
Part A: Rotating Stopper
1) Draw and label a free body diagram for the setup. Assume the stopper is being rotated horizontally.
2) Create an F equation for the stopper that relates the tension in the string (weight of the washers) to
the speed of the stopper.
3) For each of your trials find the period of the stopper and its angular velocity in rad/sec.
4) Determine the tangential velocity of the stopper.
5) Create a graph of the centripetal force (washer weight) vs. the velocity for your first five (5) sets of data
and fit an appropriate equation to the data.
6) Create a graph of the centripetal force (washer weight) vs. the velocity squared for your first five (5)
sets of data and fit an appropriate equation to the data.
7) Using the F equation from question 2, your weight data and the mass of your stopper, determine the
theoretical tangential speed of your stopper and enter it in the data table.
8) Compare your theoretical centripetal force (washer weight) to you experimental one by calculating a
% error.
Part B: Pigs Really Can Fly!
1) If the string were longer, how would it change the flight of the pig? Do the Newton's 2nd law
equations shed any light on this? Why or why not?
2) If the pig flew at a greater angle, would it change any of your measurements? Explain.
3) Would using a more massive pig have changed your results in anyway? What considerations might
there be if you increased the mass of the pig by an appreciable amount?
Concluding Questions
1) Based on our graphs, what type of relationship exists between velocity and centripetal force? Explain.
2) Is it possible to swing something in a completely horizontal circle? Explain.
3) Why might your theoretical and experimental values for centripetal force or speed be different?
4) In the last two sets of data, you changed the radius of the stopper. How did this change affect the
speed of the stopper and the centripetal force? Is this what you expected? Explain.
AP-Lab08/05: A Round and Round We Go, Centripetal Force and Acceleration
Mike Maloney  2007 http://mrmaloney.com
[Page 3 of 4]
NAME:_________________________________________
DATE: _______________
DATA TABLE
Part A: Rotating Stopper
Mass of stopper: ______________ kg
Trial
Number of
Washers
Mass of 50 washers: _______________ kg
Weight of
Washers
(N)
Radius
(m)
Time for 20
revolutions
(sec)
Average mass of 1 washer: ______________ kg
Angular
Speed
(rad/sec)
Period
(sec)
Tangential
Speed
(m/s)
1
2
3
4
5
6
7
F c vs. v fit equation: ____________________________________________ F c vs. v2 fit equation: ________________________________________
Trial
Expected F c (weight of
washers) [N]
Measured F c based on
speed [N]
Percent Error
1
2
3
4
5
6
7
Part B: Flying Pig
String Length (m):
Period (sec):
Radius (m):
Experimental Speed (m/s):
Angle  (deg):
Theoretical Speed (m/s):
Pig Mass/Weight (kg/N):
/
% Error
angle  equation:
AP-Lab08/05: A Round and Round We Go, Centripetal Force and Acceleration
Mike Maloney  2007 http://mrmaloney.com
[Page 4 of 4]