Experiment 103
UNIFORM CIRCULAR MOTION
LAST NAME, F.N. M.I.: ________________________________________
Student No. __________________
Program/Year: ______________
PHY104L/Section: ____________ Group No. __________________
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Date of Performance: _________________________________________
Date of Submission: __________________________________________
GRADING RUBRICS
Grade Components
POINTS
Data Tables and Graphs
20
Sample Computations
5
Guide Questions
10
Analysis
10
Conclusion
10
Presentation
5
Group Report Grade
40
TOTAL
100
SCORE
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Instructor/Professor
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EXPERIMENT NO. 103
UNIFORM CIRCULAR MOTION
INTRODUCTION
Centripetal force is a force that tends to deflect an object moving in a straight path and
compels it to move in a circular path. Centripetal force is just a label to represent the unbalanced
force experienced by the body every time it moves in a circular fashion. Newton’s Second Law of
Motion is used to measure the magnitude of the centripetal force.
In this experiment, you shall investigate the relationship between centripetal force and
factors such as frequency and radius of circular motion. This activity is limited to horizontal
circular motion only.
OBJECTIVES:
1. To determine the relationship between centripetal force and frequency of revolution.
2. To determine the relationship between centripetal force and radius of revolution.
APPARATUS:
1 set
1 pc
1 set
rotating platform
clamp-on pulley
Standard weights
1 pc
1 pc
mass hanger
Stopwatch
EQUIPMENT CARE AND SAFETY PRECAUTION
•
Take extra care when handling the clamp-on supper pulley to avoid damages.
THEORY
From Newton’s Second Law of Motion,
Fnet = ma
Equation 1
In the case of bodies moving in a circular motion, Fnet is the centripetal force, and the
acceleration is called the centripetal acceleration ac . Newton’s 2nd Law can be written as
Fc = mac
Equation 2
The magnitude of the centripetal acceleration is given by the expression,
Dv v 2
ac =
=
Dt
r
Equation 3
where v is the tangential velocity of the body and r is the radius of revolution.
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As Dt approaches zero, the instantaneous acceleration is
Dv dv v 2
=
=
Dt ®0 Dt
dt
r
ac = lim
Equation 4
Thus, the centripetal force in terms of tangential velocity is expressed as,
Fc =
mv 2
r
Equation 5
Frequency f is the number of revolutions a body makes per unit time. It is expressed in
rev/s, s-1, or hertz Hz. Period T is the time it takes for a body to make one complete revolution.
Period is the inverse of frequency.
T=
1
f
f =
or
1
T
Equation 6
The magnitude of the tangential velocity is equal to the circumference of the circular path
divided by the period of revolution.
v=
2p r
= 2p rf
T
Equation 7
Centripetal force may be written as
m ( 2p rf )
Fc =
r
2
Fc = 4mp 2 f 2 r
Equation 8
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PROCEDURE
Part A. Determining Centripetal Force (constant mass and variable radius of rotation)
1. Weigh the rotating body using digital weighing scale and record its mass in Table 1.
2. Hang a mass over the clamp-on pulley. The weight of the total hanging mass is the centripetal
force.
3. Initially set the radius to 16 cm. You can loosen up the thumb screw on the side post and slide
it to the desired radius. Tighten the thumb screw to secure its position.
4. Adjust the spring bracket up or down to make sure that the string connecting the rotating body
is in a vertical orientation.
5. Move the bracket with the orange indicator up or down located on the center post. Mark the
position of the orange indicator using the bracket. This will be the reference point.
6. Remove the hanging mass.
7. Gently rotate the apparatus. The orange indicator must be centered in the indicator bracket to
keep the rotating object at its desired radius.
8. Use a stopwatch to record the time to complete 10 revolutions. Divide the time by 10 to get the
period of revolution. Determine the frequency.
9. Compute the centripetal force using equation 8.
10. Do 5 trials using a different radius each trial.
rotating
body
mass
hanging
mass
Figure 1. Uniform Circular Motion Apparatus
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PART B. Determining the Centripetal Force (with constant radius and variable mass)
1. For this part of the experiment, there is no need to slide the side post to different positions.
Move the side post to the desired radius.
2. Weigh the rotating body using digital weighing scale and record its mass.
3. Hang a mass over the clamp-on pulley. The weight of the total hanging mass is the centripetal
force.
4. Adjust the spring bracket up or down to make sure that the string connecting the rotating body
is in a vertical orientation.
5. Move the bracket with the orange indicator up or down located on the center post. Mark the
position of the orange indicator using the bracket. This will be the reference point.
6. Remove the hanging mass.
7. Gently rotate the apparatus. The orange indicator must be centered in the indicator bracket to
keep the rotating object at its desired radius.
8. Use a stopwatch to record the time to complete 10 revolutions. Divide the time by 10 to get the
period of revolution. Determine the frequency.
9. Compute the centripetal force using Equation 8.
10. Do 3 trials using a different mass each trial.
Part C. Determination of mass of rotating body (with variable force)
1. Weigh the rotating body using digital weighing scale and record its mass.
2. Hang a mass over the clamp-on pulley. The weight of the total hanging mass is the centripetal
force.
3. Set the radius. You can loosen up the thumb screw on the side post and slide it to the desired
radius. Tighten the thumb screw to secure it position. Keep the radius constant.
4. Adjust the spring bracket up or down to make sure that the string connecting the rotating body
is in a vertical orientation.
5. Move the bracket with the orange indicator up or down located on the center post. Mark the
position of the orange indicator using the bracket. This will be the reference point.
6. Remove the hanging mass.
7. Gently rotate the apparatus. The orange indicator must be centered in the indicator bracket to
keep the rotating object at its desired radius.
8. Use a stopwatch to record the time to complete 10 revolutions. Divide the time by 10 to get the
period of revolution. Determine the frequency.
9. Compute the centripetal force using equation 8.
10. Do 3 trials using a different hanging mass each trial.
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GUIDE QUESTIONS
1. When the radius and mass are held constant, how will the centripetal force vary when the
frequency is increased? (3 points)
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2. Why is it important to keep the rotating platform horizontal? (3 points)
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3. If the body is moving in a vertical circle instead, how does it affect the centripetal force?
(2 points)
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4. Give at least two sources of error in this experiment. (2 points)
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DATA SHEET
NAME
PROGRAM/YEAR
STUDENT No.
PHY104L/SECTION
Group No.
Date:
Seat No.
TABLE 1. Determining Centripetal Force (constant mass, variable radius)
total hanging mass = _______________ g
mass of rotating body m = _______________ g
centripetal force (accepted value):
Fc = _______________ dynes
TRIAL
radius, r
period, T
frequency, f
centripetal force, Fc
(experimental value)
1
cm
s
Hz
dynes
2
cm
s
Hz
dynes
3
cm
s
Hz
dynes
4
cm
s
Hz
dynes
5
cm
s
Hz
dynes
Average Centripetal Force
dynes
Percent Difference
%
APPROVED BY:
INSTRUCTOR
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DATE
TABLE 2. Determining Centripetal Force (constant radius, variable mass of rotating body)
total hanging mass = _______________ g
radius r = _______________ cm
centripetal force (accepted value):
Fc = _______________ dynes
TRIAL
period, T
mass of
rotating body,
m
frequency, f
centripetal force, Fc
(experimental value)
1
g
s
Hz
dynes
2
g
s
Hz
dynes
3
g
s
Hz
dynes
Average Centripetal Force
dynes
Percent Difference
%
TABLE 3. Determining the Mass of the Rotating Body (constant radius, variable force)
mass of rotating body (accepted value):
radius r = _______________ cm
TRIAL
centripetal force, Fc
m = _______________ g
period, T
frequency, f
mass of rotating body, m
(experimental value)
1
dynes
s
Hz
g
2
dynes
s
Hz
g
3
dynes
s
Hz
g
Average Mass
g
Percent Difference
%
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SAMPLE COMPUTATIONS:
Part A: Centripetal Force (Trial 1 only), and Percentage Difference
Part B: Centripetal Force (Trial 1 only), and Percentage Difference
Part C: Mass of Body (Trial 1 only), and Percentage Difference
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ANALYSIS:
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CONCLUSION:
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