Rev 5/03
Experiment 7: Uniform Circular Motion
Purpose
(1) to study uniform circular motion
(2) to study centripetal force
Apparatus
centripetal force apparatus, a timer, a ruler, slotted weights, equal-arm balance
Fig. 1. Centripetal Force Apparatus:
Static Test
Fig. 2. Centripetal Force Apparatus:
in Operation
Theoretical Summary
Centripetal Force
In this experiment, you will spin a bob around a rotating shaft in uniform circular motion.
An object in uniform circular motion moves in a circle at a constant speed by a force
directed towards the center of the circle (a centripetal force). The formula for centripetal force
Fc is
m = mass of the rotating object
Fc = m v2
where
r
v = speed of the object
r = radius of the circle
We can find an equation for the velocity
v=∆x
∆t
by calculating the distance and time for one revolution. The distance is the circumference of the
circle 2r and the time is the period of revolution T. So:
v = 2r
T
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Experiment 7
By substituting this for v in the equation for centripetal force, we arrive at formula (1):
(1)
Fc = 4 π2 • m • r
T2
Static Test of the Centripetal Force
Consider the bob hanging from the crossarm with the stretched spring and a cord with
suspended weights attached to it as in Figure 1. The horizontal forces on the bob are provided by
the spring and the tension in the spring due to the suspended weights. If the bob is not moving,
we know that the net force is zero and the two horizontal forces are equal. The force exerted by
the spring equals the force of gravity on the weights.
This gives us another technique for finding the centripetal force. The centripetal force in
our experiment is provided by the spring that holds the bob to the rotating shaft. The force of a
spring depends on the force constant of the individual spring and the distance it is stretched. If
we stretch the spring the same distance it is stretched during the rotation, the force exerted by the
spring will be the same as the centripetal force.
Procedure Part Ia. Static test of the steel spring.
(a) Detach the bob and record its mass Mbob. Clamp the pointer rod in some
intermediate position of your choice. Measure the distance from the middle of the
rotating shaft to the pointer rod to one millimeter accuracy, and record it as r1.
(b) Hang the bob exactly above the tip of pointer, by making two adjustments:
(i) move the crossarm horizontally (use its clamp)
(ii) raise or lower the bob by changing the length of string (by wrapping
it around its cleat).
As accurately as your eye can see, the tip of the bob and the pointer should be
within two millimeters of each other.
(c) Attach the steel spring and the cord to the bob. Pass the cord over the pulley and
load the hanger so that the bob is again exactly above the tip of the pointer (see
Figure 1). Record the total hanging mass as Mhanging1.
Remember: This static test allows you to measure the force exerted by the steel
spring on the bob.
Procedure Part Ib. Uniform Circular Motion. Basic Runs.
(d) Remove the hanger and secure its cord by winding it around the bob. Practice
rotating the knurled section of the shaft with your fingers as shown in Figure 2
until you are able to maintain uniform circular motion, with the bob passing exactly
over the pointer at every revolution as best you can. You can place a cardboard
screen behind the bob for easier viewing if you wish.
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Experiment 7
(e) Determine the time TN it takes to complete N revolutions. Make three runs, with
N=50, 70, and 90 revolutions. Record TN for every run. ( You will need to continue
rotating with your fingers as you check the time.)
Suggestion: Check the value of T = TN / N from all three runs, to verify that
they are consistent.
Procedure Part II. Changing the Radius.
(f) Repeat the steps (a) through (e) with two markedly different positions of the
pointer. Label your new values by r2 and Mhanging2, and r3 and Mhanging3.
Important: Do not forget to adjust the cross-arm each time!
Procedure Part III. Changing the Mass.
(g) Add 50 to 100 grams to the mass of the bob using slotted weights. Record the
new mass as Mbob′. Repeat steps (a) through (e), recording the hanging mass in the
static test as Mhanging′. (Use your last pointer position r3 for this part.)
Lab Report
Part I.
(1) Calculate the average value of T = TN / N from your three runs. Using formula (1)
calculate Fc in newtons, rounding-off its value to three significant digits.
(2) From the static test, Using your value , calculate the tension in the cord
Mhanging1  g = Fstatic. Display the % difference δ between Fc and
Fstatic, that is
δ = Fc – Fstatic
Fstatic
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x 100%
Experiment 7
Part II.
(3) Calculate the following using data from Parts I and II and fill out Table A:
TABLE A: CHANGING THE RADIUS
Source of Data:
r
(meters)
<T>
(sec)
Fc
(Newtons)
Fstatic
(Newtons)
δ
(%)
Part I
Part II
Part III.
(4) Calculate the following using data from Parts II and III and fill out Table B:
TABLE B: CHANGING THE MASS
Source:
Mbob
(kg)
r
(meters)
<T>
(sec)
Fc
(Newtons)
Fstatic
(Newtons)
δ
(%)
Part II
Part III
(5) Question #1: Explain, using algebra, why both values of Fstatic should theoretically
be equal in Table B while this is not true for the two values of Fstatic in Table A.
(6) Question #2: To find Fc by Formula (1) you had to measure:
(i) masses. (ii) distances. (iii) time-intervals.
With the apparatus you have used, and with the range of values you dealt
with, estimate the expected %-uncertainties in each of these three kinds of
measurements. Give objective reasons for your estimates.
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