Centripetal Acceleration
College Physics Lab I
PH 141
Uniform Motion in a Circle
Purpose: To demonstrate the relationship between centripetal force and angular velocity for an
object moving in a circular path at constant speed.
Discussion: The object moving in a horizontal circular path is a rubber stopper (or two) with a
mass m of approximately 30 g, and the centripetal force is provided by the tension in the string.
Assuming there is no friction between the string and the glass tube, the tension is determined by
the weight Mg hanging down through the glass tube. Note that when the object is in motion, the
string is not truly horizontal, it is some angle θ below the horizontal. Therefore, the actual radius
of the circular motion is Lcos θ, where L is the distance from the top of the glass tube to the
center of the object. The component of the tension towards the center is Mgcos θ. The
application of Newton's second law to this motion states,
g cos
cos
(1)
where ω is the angular velocity in rad/s. Canceling the cos θ,
g
(2)
A note about SAFETY: Start and stop the rubber stopper carefully!
Make sure that m and M are securely attached to the string!
Procedure:
1. We want to show the relationship between Mg and ω, by varying M and ω while we
keep L constant at roughly 1 m. Note that if we make a graph of Mg vs. ω2, we should
obtain a straight line with a slope of mL.
2. Measure m and L. You can keep L constant during the experiment by attaching a piece
of tape to the string just below the glass tube. As you swing the stopper you can adjust ω
so that the tape remains in the correct position.
3. It will be up to you to obtain acceptable data by choosing particular values of M, and
determining the corresponding ω's. If the object completes n revolutions in time t, then
Centripetal Acceleration
2
(3)
(in rad/s). Careful timing will be critical. Of course you should use something like n=20
(or more) in order to reduce the relative timing error due to your reaction time. When
counting revolutions, make sure that you really do count n, not (n - 1). Repeat as often as
necessary to insure that your t's are fairly reliable. Note that as you increase M,
ω increases. If ω increases to the point that each revolution requires roughly 0.6 s (or
less), you may find that correct timing and counting become nearly impossible. In that
case you should try smaller M's. You should plan in advance so that you have 6-8 data
points, that your largest M is approximately twice your smallest M (or more), and that
your largest ω is not so large that accuracy is sacrificed.
4. Make a graph of Mg (N) vs. ω2 (rad2/s2). If possible find the slope of the best straight
line through data. Divide your slope by L. This result should be close to m (in kg).
Calculate the % error. Don't be surprised if it is not very close, even if you have a fairly
straight line. Our main purpose was to demonstrate the linear relationship between Mg
and ω2.