Wilberforce
Pendulum Lab
Template
Table 4
Names: Jessica Vuong
Linh Huynh
Nguyen Ho
Period: 2
Date: March 13, 2007
Abstract: To determine how changing the radius between the masses on the ends of the arms of a
Wilberforce pendulum and its center affects the period of the pendulum. Another
objective was to use the pendulum to find the rotational inertia of a clamp later placed
on it.
Introduction: Use the Wilberforce Pendulum to determine the relationship between changing the
radius between masses on the pendulum and the period of the pendulum. Measure
the radii by finding the distance between the center of the mass and the center of
the steel rod, which represented the arm of the pendulum, and do ten trials where
each trial, the radius is changed. Then square each of the radii from each trial and
square each of the periods. Then, make an excel spreadsheet to graph R2 vs. T2 and
find the best fit curve. These graphs will show the relationship between radius and
period. Afterwards, you will need to use the formula of the period for a compound
pendulum: T=2*Pi*sqrt(Itotal/x), where x is the torsion constant, and the formula for
total rotational inertia of the system ( Itotal=Irod+Idisk+2Ibolts) to find I0 which equals
Irod + Idisk. After connecting a metal clamp to the pendulum, you will do one trial to
find the period of the clamp at a certain radius. Using those formulas and the data
obtained from the last trial with the metal clamp, you will be able to find the
rotational inertia of the clamp.
Diagram: Draw a picture of the pendulum and other equipment involved with this lab. It would
be good to also label measurements and masses that you found.
Procedure:
1) Set the Wilberforce Pendulum on the table. Then disassemble the pendulum into all of its
components leaving the stand intact. Just take off the wooden disk, the steel rod, and the
masses from the pendulum.
2) Measure the masses of the wooden disk, the steel rod, and the bolts that go on the end of
the pendulum. There are six bolts but since you will put two small bolts and a large bolt
on each end of the steel rod, measure the mass of the 3 bolts together because that will be
the total mass on each end of the rod. Record the masses in three significant figures and
remember to convert to meters.
3) Using the ruler, measure the length of the steel rod. Then divide that value by two to find
the radius. Record this in meters and in two significant figures.
4) Reassemble the Wilberforce pendulum and place, on each end, two small bolts and a
large bolt on the very ends of the arms. Make sure that the masses are tightly fastened.
5) Now, measure with the bolts on the ends of the arms, with one small bolt on each side of
the big bolt, measure the length of those three bolts. Then divide it by two to find the
center of mass, in units of meters and in two significant figures.
6) With the masses on the ends of the rod, have one person push one end of the steel rod in a
circle and then let go. The other person should start the stopwatch the second the other
person lets go. Count out each cycle, where each cycle represents the end you pushed
getting back to where it started, and after five cycles stop the stopwatch. Record this time
but be sure to divide by 5 later to find the period T.
7) Now, do nine more trials where each trial is done with a decreasing radius between the
center of mass of the bolts and the center of the steel rod. Each trial, move the bolts closer
to the center.
8) Now find R^2 vs. T^2 and graph them, with R^2 on the x-axis and T^2 on the y-axis. The
units of R^2 will be m^2 and the units of T^2 will be s^2.
9) Then do the analysis to find the total rotational inertia of the pendulum.
10) Now measure the mass of the metal clamp, and then place it near the top of the
pendulum.
11) Do one trial with this metal clamp near the top of the pendulum, and record the period.
Then do calculations to find the rotational inertia of the metal clamp.
Analysis: 1) Put all tables and graphs that were needed to accomplish the goal of the lab. You
must have data tables and the graphs with best-fit curve and r2 value. Include tables
for R vs. T and R2 vs. T2 and graphs for R vs. T and R2 vs. T2.
2) After finishing including the tables and graphs, show your calculations that need to
be done in order to find I0 and the rotational inertia of the metal clamp. Actually
show what formulas are being used before plugging in the numbers. Then, explain
how the tables, graphs, and your calculations altogether helped you answer the
purpose of this lab.
Conclusion: Here, you need to answer the question that was proposed in the abstract. So, state
what the rotational inertia of the metal clamp is and the relationship between radius
and period.
Sources of Error: State any possible sources of error that could have prevented your results from
being close to ideal. For instance, were bolts not tightened enough or was there
an error in measuring or timing?
* Do not forget to staple your raw data that you wrote down throughout the process of doing the
lab. This means the data that was written by hand while you were measuring masses and
conducting the trials.