AP Laboratory Investigation – The Physical Pendulum.
Name(s): _________________________________
Materials: wooden bars, wooden disks, hoops, bowling ball, irregularly shaped wooden
objects, lead weights, stopwatches, meter sticks, oscillation supports, and string.
Purpose: To investigate simple harmonic motion, center of mass, and moments of inertia
properties.
Procedure and data analysis: Case 1: The bowling ball
Measure the period of the bowling ball pendulum. Measure the time for at least 15-20
oscillations and then divide the result by the corresponding number of oscillations.
Repeat at least three times to obtain an average value for the period.
Te, bowling ball (experimental) = _____________
A. Think of this pendulum as if it were a simple pendulum. Explain exactly what you
measured and report the value(s). Calculate the theoretical period value based on its
physical dimensions/measurements and the simple pendulum formula. Report the %
difference when compared to the experimental value obtained earlier.
Tt1 (theoretical) = _________________ ; % difference = _______________
B. Think of this pendulum as a physical pendulum: a uniform sphere at the end of a
massless string. Measure the physical dimensions needed to calculate the moment of
inertia and the new theoretical period value (and the % difference). Hint: you may need to
apply the parallel axis theorem here.
I1 (moment of inertia) = ___________; Tt2 = ________________; % diff. = ___________
C. (Bonus) Think of this pendulum as a physical pendulum composed of a uniform
sphere and a uniform chain/bar whose mass is not negligible any longer. Measure the
physical dimensions needed to calculate the moment of inertia and the new theoretical
period value (and the % difference). Hint: you will need not only the parallel axis
theorem but also the center of mass formula here.
I2 (moment of inertia) = ____________ ; Tt3 = _______________; % diff. = __________
Your lab report should contain a discussion which clearly outlines the details of finding
these moments of inertia and your thoughts on the values of the percent difference values
obtained in each case. Are these percent values getting smaller? Should they get smaller?
Why?
If time permits, shorten the chain length by about 30-40% (please let me know if you are
that far and I will safely do it for you) and repeat your measurements and calculations for
the bowling ball.
Case 2: Bar attached to a string
Measure the period of the bar pendulum. Measure the time for at least 15-20 oscillations
and then divide the result by the corresponding number of oscillations. Repeat at least
three times to obtain an average value for the period.
Te (experimental) = _____________
A. Think of this pendulum as if it were a simple pendulum. Explain exactly what you
measured and report the value(s). Calculate the theoretical period value based on its
physical dimensions/measurements and the simple pendulum formula. Report the %
difference when compared to the experimental value obtained earlier.
Tt1 (theoretical) = _________________ ; % difference = _______________
B. Think of this pendulum as a physical pendulum: a uniform bar at the end of a massless
string. Measure (or obtain from your teacher) the physical dimensions needed to calculate
the moment of inertia and the new theoretical period value (and the % difference). Hint:
you may need to apply the parallel axis theorem here.
I1 (moment of inertia) = ___________; Tt2 = ________________; % diff. = ___________
Again, you will discuss your results in this section as part of your lab report.
Case 3: Hoop and disk
Measure the period of the hoop and disk pendula. Measure the time for at least 15-20
oscillations and then divide the result by the corresponding number of oscillations.
Repeat at least three times to obtain an average value for the period.
Te,hoop (experimental) = _____________
Te, disk (experimental) = _____________
A. Think of this pendulum as if it were a simple pendulum. Explain exactly what you
measured and report the value(s). Based on these values, calculate the theoretical period
value based on its physical dimensions/measurements and the simple pendulum formula.
Report the % difference when compared to the experimental value obtained earlier.
Tt,hoop (theoretical) = _________________ ; % difference = _______________
Tt,disk (theoretical) = _________________ ; % difference = _______________
B. Think of these pendulums as physical pendulums: a hoop and a disk. Measure (or
obtain from your teacher) the needed physical dimensions needed to obtain the moment
of inertia and the new theoretical period value (and the % difference). Hint: you may
need to apply the parallel axis theorem here.
Ihoop (moment of inertia) = ___________; Tt, hoop = _____________; % diff. = ______
Idisk (moment of inertia) = ___________; Tt, disk = _____________; % diff. = __________
Again, you will discuss your results in this section as part of your lab report.
Case 4: Irregular shaped wooden object (bonus/puzzle)
A. Design a way to experimentally determine the center of mass for the irregularly
shaped wooded object provided. In your lab report, fully explain your procedure. Label
this point on the object using some masking tape (please do not write on the object itself).
B. With the center of mass identified, set the object in small oscillations around at least
three small holes and carefully record all period values.
C. Design a way to obtain the moment of inertia of this object with respect to its own
center of mass. Find the value. Design a way to verify that the value you have obtained is
close to the real value. Fully explain your procedure in the lab report.
Case 5: Aquarium (bonus/puzzle)
You have just bumped into an aquarium
like in the picture (halfway full) and
disturbed its surface like the sketch
shows. Is the resulting motion SHM? If
you think it is, prove it and find its
period of oscillation. Assume you know
all the aquarium dimensions and the
disturbance is small.