Otterbein University Department of Physics
Physics Laboratory 1500-6
EXPERIMENT 1500-6
CENTRIPETAL ACCELERATION
NAME:
INTRODUCTION
In this experiment you are to find the mass of a rotating object by using Newton's 2nd Law,
F = m a. Since the unknown mass will be moving in uniform circular motion, F is the
centripetal force that pulls the mass towards the center of rotation. This force is supplied
by the spring, see figure. The centripetal acceleration is the constant acceleration toward
the center, which changes the direction of the velocity of the mass and keeps it moving in a
circle. The magnitude of the centripetal force, |F| = F, can be found experimentally by
stretching the spring when it’s not rotating, by pulling on it with a string. By putting
weights on a hanger connected to the string, you can find the force that the spring provides
when stretched.
The centripetal acceleration can be found from the relationship, |a| = a = v2/R, where v is
the linear speed of the rotating object and R is the radius of the circle. R can be measured
directly, and v can be found by measuring the number of revolutions in a given time. For a
single revolution, v = 2πr/T, where T is the period of revolution. The unknown mass is then
determined from m = F/a.
THE EXPERIMENT
The objective of the experiment is to measure the mass of the rotating object by
performing three measurements each at three different radii. You will need to find the
radius of the circular motion of the mass, the centripetal force provided by the spring, and
the velocity of the mass as it moves. Follow the procedure below.
1. Set the pointer to the position on the base closest to the center (i.e. minimum radius).
2. Measure the distance from the center of the vertical axle to the pointer. Record this
value in Table 1.
3. Release the rotating mass from the spring. Adjust the horizontal beam so that the
rotating mass hangs directly over the pointer. When finished, tighten the thumbscrew
on top to hold it in place. Reattach the spring.
4. Have one member of the group carefully start to spin the mass. The objective is to
spin it exactly fast enough so that the mass lines up right above the pointer on every
revolution. It will be necessary to continually give the rod little pushes with your
fingers (on the knurled surface) to keep it at the proper speed.
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Otterbein University Department of Physics
Physics Laboratory 1500-6
5. Once the mass is up to speed, use a stopwatch to time how long it takes for the mass
to go through 80 revolutions. Do this three times and record your times in Table 1.
Find the average of these times.
6. Swing the rotating mass so that it is over the pointer. On the side opposite the spring,
attach a string (with a paper clip) to the mass. Hang the string over the pulley. Add
weights to the string until the rotating mass once again is centered over the pointer.
Record the hanging weight necessary to align the tip of the mass with the pointer in
Table 1.
7. Move the pointer to the middle of its range. Repeat steps 2-6.
8. Move the pointer to its most distant setting. Repeat steps 2-6.
Counterweight
Rotating
mass
Pulley
for hanging
mass
Spring
Pointer
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Otterbein University Department of Physics
Physics Laboratory 1500-6
Table 1
Trial
r (m)
T1 (s)
T2 (s)
T3 (s)
Tavg (s)
Hanging
mass (kg)
Near
Middle
Far
CALCULATIONS
A note of precaution: there are two masses in this experiment, the hanging mass and the
(unknown) rotating mass. Do not confuse them in your calculations!
1. The precision of the data you have taken suggests that you retain three significant
figures in your calculations. Using the number of revolutions, the average time and the
radius, calculate the linear speed of the rotating mass for the three trials. Use the space
below to show your work, and record your values in Table 2.
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Otterbein University Department of Physics
Physics Laboratory 1500-6
2. Find the centripetal acceleration undergone by the rotating mass for each trial. Use the
space below for work and record your results in Table 2.
3. For each trial, find the force of the spring and record it in Table 2.
4. For each trial, calculate the value of the unknown mass. Show your work below and
record your answer in Table 2.
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Otterbein University Department of Physics
Physics Laboratory 1500-6
Table 2
Trial
r (m)
ac (m/s2)
v (m/s)
Fc (N)
Unknown
mass
m (kg)
Near
Middle
Far
ANALYSIS
From the three results in Table 2, what is your value of the unknown mass, and your
estimate of the uncertainty? Briefly describe how you found your estimate.
Let’s try a different way of calculating the best guess on the mass. Make a plot of force
versus acceleration from the values of ac and Fc of Table 2. Find the slope of the line by
the method learned in the very first lab, constraining the line to go through a=0, F=0 (since
there is obviously no acceleration or force if the bar isn’t rotating). Label and attach the
graph.
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Otterbein University Department of Physics
Physics Laboratory 1500-6
Use the graph to find another estimate of the mass. Describe how below.
Finally, unhook your rotating mass and weigh it. How close did you get?
What could be done to improve the accuracy of this experiment?
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