Lab Activity Phy223
Rotational Mechanics, Part II: Swinging Stick
Names:
Swinging Stick
Introduction
In this activity you will find the minimum period of a swinging stick (a roughly 8-foot-long piece of
1x2 nominal lumber) both theoretically and experimentally and compare the results.
Procedure and Instructions for Report
A. Abstract
Give a brief description of what you did. What is the purpose of this lab?
B. Finding the experimental values for xmin and Tmin
Your goal is to find the period T of oscillation as a function of x, the distance between the axis of
rotation (pin) and the center of mass (cm). You will then use your data to experimentally find the
distance xmin , for which the period T has its minimum value Tmin .
Experimental Setup:
Procedure and Data:
1. Use every hole, starting with the first hole from the center of mass, as the axis of rotation.
2. For each hole: take two or three trials to measure the period T. Make sure to keep the
amplitude low (less than 10⁰). Keep friction to a minimum. Record all data in an Excel
spreadsheet (i.e. all values for T, their average, and the distance x) and include it in your report.
Rotational Mechanics, Part II: Swinging Stick
Lab Activity Phy223
Analysis:
1. Create a graph showing the period T as a function of x, the distance between the axis of
rotation and the center of mass.
2. Use your graph to find your experimental result for
the corresponding period
xmin (the distance with a minimum T) and
Tmin .
C. Finding the theoretical values for xmin and Tmin
The swinging stick is an example for a physical pendulum. The physical pendulum is covered in
section 14.6 of your textbook. You will probably need your textbook to work through the
following steps.
1. Draw an extended FBD for the swinging stick at a point half-way through an oscillation
(maximum amplitude). Important hint: you can draw the FBD with the stick at the left-ofequilibrium position shown in the figure above or in the right-of-equilibrium position as shown in
figure 14.21 of your textbook. Note that the angle  is measured counterclockwise from the
equilibrium position. This means that  is negative in the figure above or positive in figure 14.21.
2. Use the parallel axis theorem to create an equation for the moment of inertia for your stick
as a function of x (the distance the axis of rotation is away from the center of mass).
3. Write out the equation for
  I about the axis of rotation (not the center of mass)
using information from #1 and #2 above. What force is exerting the torque to speed up and
slow down the stick? Is I the moment of inertia about the center of mass or not?
4. Solve the differential equation you obtained in step 3. Use section 14.6 in your textbook for
guidance. You will get an equation for the angular frequency  as a function of x.
5. Rewrite this equation to determine a function for the period T (i.e. express  in terms of T and
solve for T).
6. Use calculus to predict the position
minimum period
xmin for the minimum period and the value for the
Tmin . In Excel, create a graph of T vs. x, and include it in your report.
D. Conclusions
1. Compare - using a graph overlay - your theoretical function for the period to your experimental
function.
2. Compare your theoretical and empirical values for
difference
xmin,theory  xmin,exp eriment
xmin,theory
xmin and Tmin . Determine the percent
. Discuss your results.
3. Give possible sources of error and discuss their significance.
4. Discuss the physical meaning of the minimum of the period. That is, what’s happening
physically that reduces the period and then increases it again? Hint: in your equation for T vs. x,
what is the physical meaning of the numerator and denominator?