name____________________ period _______ lab partners___________________________________
In uniform circular motion an object moves in a circle at a constant speed v. While the speed is constant, the direction of the velocity vector for the object continually changes. Thus the object experiences what is called centripetal acceleration a c
. The magnitude of this acceleration depends on the speed v, and the radius of the circular path according to the equation a c
= v
2
/ r. Its direction is radially inward toward the center of the circle. In this activity, you will investigate centripetal acceleration on a phonograph record player turntable.
You will use a Low-g Accelerometer attached to the turntable to determine the relationship between centripetal acceleration, the radius of the circular path, and the rotational frequency (RPMs).
For a rotating solid disk--like the record player turntable you'll use in this lab--while the whole disk turns together as given by its rotational frequency (in revolutions per minute or second), the speed v of a particular point on the disk depends on its distance r from the center. At the very center--where r=0--speed v = 0.
At the rim--where r is greatest-- speed v is greatest. At points in between, speed v steadily increases with r.
In making one revolution, a particular point will travel a distance equal to the circumference of its circular path = 2 π r. Dividing that by the time T needed for the point to go once around gives the speed v. That is, v
= 2 π r / T. Plugging this into the equation for centripetal acceleration, a c
= v
2
/ r, gives a c
= (2 π r / T)
2
/ r or a c
= (2 π / T)
2
r. For a rotational frequency of 33.33 revolutions per minute--where T=1.80 sec--(2 π / T)
2
= 12.18. For a rotational frequency of 45 revolutions per minute--where T=1.33 sec--(2 π / T)
2
= 22.21.
Putting in these values, we have the following two equations: a c
= 12.18 r (for 33.33 revolutions per minute)
where r is in meters and a c
will be in m / sec
2 a c
= 22.21 r (for 45 revolutions per minute)
where r is in meters and a c
will be in m / sec
2
We thus expect the centripetal acceleration a c
to increase directly with the distance r of the point from the center. Notice that for points the same distance r out from the center of the rotating turntable, our equations predict the centripetal acceleration a c will be (22.21 / 12.18) = 1.82 times greater when 45 RPM is used compared to when 33.33 RPM is used.
 1) Verify centripetal acceleration a c
is generally biggest in the direction radially inward toward the center of the rotating turntable, and smallest (ideally zero) at right angles (tangentially) to that direction.
 2) Verify the extent to which the experimental data for the uniform circular motion of points on the rotating turntable support the predictions based on the equation a c
= v
2
/ r -- in particular a) that centripetal acceleration a c
will increase with distance r from the center, and b) for points the same distance r away from the center, centripetal acceleration a c
will be 1.82 times greater when the turntable spins at 45 RPM than when it spins at 33.33 RPM.
computer
Vernier computer interface
Logger Pro
Vernier Low-g Accelerometer masking tape metric ruler turntable with 33 1/3, 45 RPM settings level
When you start this lab, Logger Pro will be running and the Low-g Accelerometer connected to channel 1 on the interface. The mode where the instantaneous acceleration (in m / sec 2 ) measured by the accelerometer is continually displayed will be used to gather data. To assure that the readings it provides are meaningful, your job will be to 1) periodically click the special Zeroing key (look for ф symbol) to zero the accelerometer--

doing this when it is resting horizontally on the turntable or lab bench top, and 2) take precautions (suggested by your instructor) to make sure that the accelerometer's cable does not become tangled and put an unwanted pull on the accelerometer leading to erroneous readings.
Part I.
1) Set the turntable rotational frequency for 33.33 RPM. Position the accelerometer at the rim, arrow pointed in, and measure the distance from its center to the center of the turntable spindle. Turn on the turntable, allow
1/4 turn for it to reach full speed, and record the average of the first three readings the accelerometer / data acquisition system provides. (If those readings are not relatively consistent, repeat until they are--consult the instructor as necessary.) Record in Data Table I.
2) Move the accelerometer in toward the center 0.5 cm. Repeat step 1). After recording the average acceleration, continue to move the accelerometer in 0.5 cm toward the center in repeating step 1). Do this until you altogether have 6 to 10 data points.
3) Return the accelerometer to its position at the rim, but this time orient it so the arrow is pointed at right angles (tangentially) to the inward to the center direction. Record your data in Data Table I -- last line.
Part II
Set the turntable rotational frequency for 45 RPM and repeat steps 1) and 2) in Part I. Record your data in
Data Table II.
Data Table I
For 33 RPM, accelerometer arrow pointed radially in toward center: r, cm a c , m/sec 2
For 33 RPM, accelerometer arrow pointed at right angles to radially inward (tangentially) r, cm = a c , m/sec 2 =
Data Table II
For 45 RPM, accelerometer arrow pointed radially in toward center: r, cm a c , m/sec 2
Data Handling / Questions (Construct plots in 2. & 4. below on single graph, use different colors to distinguish pts.)
1. Does your data generally support the expectation that centripetal acceleration is the biggest in the radially inward toward the center direction and smallest (or zero) perpendicular to this? Explain.
2. Using the data in Data Table I (with arrow pointing in), plot a c
(in m / sec
2
) vertically vs. distance from center r (horizontally) paper. Draw a best fit line through the points and find the slope. Show your work
3. Compare the slope from your graph with the slope expected from a c
= 12.18 r by computing % error.
4. Using the data in Data Table II, plot a c
(in m / sec
2
) vertically vs. distance from center r (horizontally) paper. Draw a best fit line through the points and find the slope. Show your work.
5. Compare the slope from your graph with the slope expected from a c
= 22.21 r by computing % error.
6. Make a ratio of the two slopes of your best fit lines and compare this value with 1.82 per the prediction in objective #2b. In reporting the results of your check on this objective, compute % error.