Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

# The Physical Pendulum

You all know how an ideal pendulum works: it swings back and forth with a period which depends only on its length:

```                                     L
period  T  =  2 * pi * sqrt [ --- ]
g
```

Ideal pendula are abstract creations; any real pendulum breaks the ideal requirements of

• massless string
• infinitely compact mass

As your lab manual for this week describes, it is possible to derive a relationship between the period of a physical pendulum and several of its properties:

```                        2                  2
2         4 pi      2        4 pi  I
T  d  =  [ ---- ] * d    +  [ ------- ]
g                  m g

```

Your job this week:

1. Measure the mass and length of a meter stick
2. Measure the center of mass of the meter stick, and the distance from that center of mass to a set of holes
3. Suspend the meters stick from 5 of the holes, and measure its period for each (2 trials of 20 swings each)
4. Make a graph from which you can determine g, the local value of gravitational acceleration, and I, the moment of inertia of the meterstick around its center of mass
5. Answer the questions:
• Does your value of g agree within the uncertainties with the standard value?
• Does your value of I agree within the uncertainties with the theoretical value (based on size and shape)?
• Which of the measurements you make introduces the largest component of the uncertainty in the value of g?

#### What do I have to submit?

You may NOT use a computer for any purpose in this week's exercise. Paper, pencil, ruler, calculator -- no more.

Once again, I want to try to give you a chance to finish all your work by the end of the lab period. Therefore, I expect:

• A neat table of all your measurements, including headings and all appropriate units and uncertainties
• A table which lists
• Each type of measurement you make this week
• The tool you used to make it
• The percentage uncertainty in your measurements using this tool
• Calculation of the moment of inertia of the meterstick around its center of mass, based on its size and shape. Include uncertainty.
• A graph showing a plot of (T^2 * d), with units of (seconds^2 * meters), versus (d^2), with units of (meters^2).
• Calculation of g, based on the slope of the graph. Include uncertainty.
• Calculation of I, based on the horizontal intercept of the graph. Include uncertainty.
• Answer to the question: Is your value of g equal to the standard value, within the uncertainty?
• Answer to the question: Are the two values of moment of inertia equal, within the uncertainty?
• Answer to the question: Which of the measurements you make introduces the largest component of the uncertainty in the value of g?

I will deduct a full letter grade from any report which includes the phrase "human error."

Last modified Apr 4, 2001 by MWR.

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.