Lab: Centripetal Acceleration
The goal of this lab is to verify the centripetal force equation
Fc = mω 2 r,
(1)
where Fc is the magnitude of the central
force required to make an object move in
a circle, m is the mass of the object, ω is
the angular speed of the object, and r is
the radius of the circular path.
You will do this by twirling around a
rubber stopper that is attached to a string.
To ensure that tension in the string is consistent, you will not hold it directly with
your hand. Rather, you will run the string
through a tube and hang a mass from its
Figure (1)
end (see fig. 1). If you twirl the stopper at
a rate such that this hanging mass stays at
There are a few tips for this lab that
a constant height, the tension in the string
will make it less difficult.
will be equal to the gravitational force on
the hanging mass, i.e.
Hint 1: It is easier if you grip the tube
T = M g,
(2) nearer to the top. If you hold it near the
bottom you may not be able to keep it
where M is the hanging mass. The tension spinning at the same speed for the full
in the string is also the force responsible thirty seconds.
for the centripetal motion of the stopper,
so
Hint 2: Don’t try to count the revoluFc = T
(3) tions by following the stopper’s motion
in this case.
By measuring the mass and angular
speed of the stopper, and the radius at
which it is twirling you can also determine the centripetal force using eqn.
(1). Within experimental uncertainties,
the centripetal force found should be the
same for both methods.
You will not measure the angular speed
of the stopper directly. Instead, you will
count the number of revolutions the stopper makes in a 30 second time period and
use this to calculate the stopper’s angular
speed, ω. Be sure to convert your answer
for ω to radians per second before using it
in eqn. (1).
Phys 152 Lab 7 (v1.0)
all the way around with your eyes. Watch
the stopper’s motion from the side, and
just count how many times the stopper
goes by on one side or the other.
Hint 3: Don’t try to measure the radius
by dodging under the moving stopper with
a meter stick. Even if you don’t get hit,
you likely won’t get a very good measurement either. Rather, measure how much
string is hanging below the tube. From
this you can calculate the radius of the
stopper’s motion if you also measure the
total length of the string.
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Phys 152 Lab 7 (v1.0)
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# of Rev.
Sample Calculations:
trial 1
trial 2
trial 3
∆t
Table 1.
Stopper mass, kg:
ω
radius
Fc by (1)
M
Fc by (3)
% Diff.
Question:
What direction is Fc in?
Question:
d1
d2
Gravity is also acting on the stopper,
pulling it downward as it revolves.
This is shown schematically (and
somewhat exaggerated) in the above
diagram. Which of the two lengths, d1
or d2, is the correct one to use for the
radius in this experiment? Which one
did you use? What error (if any) will
this introduce in your measurement of
Fc ?
Question:
How would it affect your results if your
string stretched slightly under tension?
Is this a systematic or random source
of error?
Phys 152 Lab 7 (v1.0)
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