Physics 125 – Mesa College
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Your Name:
Circular Motion and
Group Name:
Centripetal Forces
Lab Day:
Objective: To understand the relationship between force, mass and acceleration for
objects moving in a uniform circle; To create and interpret graphs of these relationships;
To evaluate the validity of Newton’s Second Law for objects in uniform circular motion.
Hypothesis: An object accelerates when a net force is applied to it. We assume a net force
is present if an object accelerates while observed from an inertial reference frame.
Although an object could be moving in a circle with constant speed, the direction of motion
would continuously change and thus the object must be accelerated. Circular motion
therefore requires a net unbalanced force to act on the moving object.
Mathematical Models and Reference Values Used: Newton’s ‘Laws’ state that


acceleration of an object s the result of the net external force acting on it. ∑ F = ma . For
objects that move in a circle of constant radius with constant speed, the required
v2
centripetal force can be expressed as ∑ F(r̂) = m (−r̂) . This force is necessary for circular
R
motion. Without it the object would move along a straight line.
Equipment List: Assorted Masses and Mass Hanger, Timer, Three Springs, Ruler, Bubble
Level, String.
Setup and Procedure
The experiment requires data from two
different radii of rotation. You will achieve
the best results if you complete all portions
of the experiment that depend on a
particular radius before you rearrange the
experimental setup.
1. Measure the mass of a ‘100-gram’ mass
and the black mass (the bob) on the
electronic balance and record the results in
Data Table One. Attach the ‘100-gram’ mass
to the top of the bob by sliding it beneath
the screw collar and tightening the collar.
This mass combination will be called MR the rotating mass.
figure 1
r
2. Set the tip of the lower radius marker to approximately 17 cm as measured from the
center of the rotating arm. Measure this radius as precisely as possible and record the
result in Data Table One as R1.
3. Make sure that the upper arm is adjusted so MR hangs directly over the lower radius
marker. Remember to adjust the upper arm each time you move the lower radius marker.
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Physics 125 – Mesa College
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Check to make sure the adjustment screw is tightened so the upper arm will not slide.
4. To identify the springs used, classify them from weakest to strongest.
Spring 1 – the weakest spring (stretches the most for a given applied force)
Spring 2 – the medium spring
Spring 3 – the strongest spring (stretches the least for a given applied force)
Centripetal Acceleration as a function of Centripetal Force (part one)
1. Attach Spring 1 to MR as shown in figure 2. Ensure
that Spring 1 is parallel to the tabletop when MR is
passing directly over the lower radius marker by
rotating the apparatus. If adjustments need to be
made, please notify the instructor.
figure 2
2. Rotate the apparatus until MR is passing over the tip
of the lower radius marker. Try to maintain a constant
speed and a constant radius of rotation. Once you are
satisfied, use a timer to measure how long it takes to
complete 20 revolutions. Record this value in Data
Table One.
3. Repeat step 5 for each of the other two springs, recording the results in Data Table One.
Data Table One
Empty Bob (kg) =
100 gram mass (kg) =
Spring Rotation Radius (m)
Time for 20 rotations (s)
MR (kg) =
Average Period of
Rotation (s)
1
2
3
Q1. Use Data Table One to complete Data Table Two. Show a sample calculation of average
speed and centripetal acceleration with units then fill out the rest of the table.
Data Table Two
Spring
1
2
3
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Rotation
Radius (m)
Average Speed Centripetal Acceleration
2π R
v2
(m/s)
v=
ac = (m/s2)
T
R
Physics 125 – Mesa College
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Centripetal Acceleration as a function of Reciprocal Mass
1. Use the weakest spring for this portion of the experiment at the same rotation radius.
Since the spring is weak, it is very sensitive to small changes in speed, so extreme care
must be taken in order to obtain valid data.
2. Begin taking data with just the bob then increase the rotating mass by 50 grams. Use the
collar on the bob to secure the masses.
3. Complete 40 revolutions per data point and complete Data Table Three.
Data Table Three
Rotating Mass
Description
Mass (kg)
Reciprocal Mass
(kg-1)
Time for 40
revolutions (s)
Average Period
of Rotation (s)
Bob only
Bob + ‘50’ grams
Bob + ‘100’ grams
Bob + ‘150’ grams
Bob + ‘200’ grams
Q2. Use Data Table Three to complete Data Table Four. Show a sample calculation of
average speed and centripetal acceleration with units then fill out the rest of the table.
Data Table Four
Rotating Mass
Description
Bob only
Bob + ‘50’ grams
Bob + ‘100’ grams
Bob + ‘150’ grams
Bob + ‘200’ grams
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Rotation
Radius (m)
Average Speed
2π R
(m/s)
v=
T
Centripetal
Acceleration
v2
ac = (m/s2)
R
Physics 125 – Mesa College
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Spring Calibration to determine Centripetal Force
In order to have some known quantities with which
to compare the rotation data it is necessary to
determine how much force is needed to stretch the
springs to a given length.
figure 3
1. Detach the spring and verify that the bob hangs
directly over the lower radial indicator. Make sure
the upper radial arm is well secured then reattach
the spring.
2. Use a length of string to connect a mass hanger
and the bob as shown in figure 3.
3. Add mass to the hanger until the bob is once
again positioned directly over the lower radial indicator. Remove the mass hanger and use
the electronic balance to measure the mass. Record the result in Data Table Five.
4. Repeat step 3 for the other two springs.
Data Table Five
Spring
Rotation
Radius (m)
Hanger & Mass (kg)
1
2
3
Q3. If the bob is in equilibrium then the tension in the string must equal the force exerted
by the spring on the bob. In the space below show a sample calculation for the tension in
the string, with units. Use the data you have taken to fill out Data Table Six.
Data Table Six
Spring
Rotation
Radius (m)
Spring force (N)
1
2
3
5. Now adjust the lower radial indicator to ~20 cm. Loosen the adjustment screw and
reposition the upper radial arm until the bob hangs directly over the top of the lower
radial indicator. Retighten the adjustment screw. Measure the distance as accurately as
possible and record it in Data Tables Seven and Eight.
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6. Obtain spring calibration data for each spring at this new position.
Data Table Seven
Spring
Rotation
Radius (m)
Hanger & Mass (kg)
1
2
3
Data Table Eight
Spring
Rotation
Radius (m)
Spring force (N)
1
2
3
Centripetal Acceleration as a function of Centripetal Force (part two)
To avoid having to reposition the upper and lower radial indicators multiple times, we split
the first portion of the experiment into two parts. Now you will obtain rotation data at the
new (~20 cm) rotation radius.
1. Attach Spring 1 to MR. Ensure that Spring 1 is parallel to the tabletop when MR is passing
directly over the lower radius marker by rotating the apparatus. If adjustments need to be
made, please notify the instructor.
2. Rotate the apparatus until MR is passing over the tip of the lower radius marker. Try to
maintain a constant speed and a constant radius of rotation. Once you are satisfied, use a
timer to measure how long it takes to complete 20 revolutions. Record this value in Data
Table Nine.
3. Repeat step 5 for each of the other two springs, recording the results in Data Table One.
Data Table Nine
Empty Bob (kg) =
100 gram mass (kg) =
Spring Rotation Radius (m)
Time for 20 rotations (s)
1
2
3
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MR (kg) =
Average Period of
Rotation (s)
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Q4. Use Data Table Nine to complete Data Table Ten. Show a sample calculation of average
speed and centripetal acceleration with units then fill out the rest of the table.
Data Table Ten
Spring
Rotation
Radius (m)
Average Speed Centripetal Acceleration
2π R
v2
(m/s)
v=
ac = (m/s2)
T
R
1
2
3
Graphical Analysis
Centripetal Acceleration as a function of Centripetal Force
Q5. Using a Cartesian coordinate system construct a graph of the acceleration of the
rotating mass as a function of the centripetal force applied to it - using Data Tables Two,
Ten and Six and Eight. Draw a best-fit line then calculate the slope on the graph, with
units. Transfer your result to Data Table Eleven.
Q6. Use the slope value from Q5 to write the equation of the line suggested by your graph.
Ignore any intercept, so your function should have the form y(x) = mx .
Centripetal Acceleration as a function of Reciprocal Mass
Q7. Using a Cartesian coordinate system construct a graph of the centripetal acceleration
of the bob as a function of the rotating reciprocal mass, using Data Tables Three and Four.
Draw a best-fit line then calculate the slope on the graph, with units. Transfer your result
to Data Table Eleven.
Q8. Use the slope value from Q11 to write the equation of the line suggested by your
graph. Ignore any intercept, so your function should have the form y(x) = mx .
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Data Table Eleven
Quantity
Value
Units
Q5 slope
Rotating Mass (MR)
Q8 slope
Centripetal Force
Q9. Use the Q5 slope value to determine the inertial mass of the rotating mass. The inertial
mass is a measure of ‘resistance to acceleration’.
Q10. Calculate the percent difference between the two ways you determined the rotating
mass (the graph and the electronic balance). Show all work with units.
Q11. Use the Q8 slope value to determine the centripetal force acting on the rotating
mass.
Q12. Calculate the percent difference between the two ways you determined the
centripetal force acting on the rotating mass (the graph and the spring calibration
calculation for spring 1 in Data Table Six). Show all work with units.
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