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:

- Measure the mass and length of a meter stick
- Measure the center of mass of the meter stick, and the distance from that center of mass to a set of holes
- Suspend the meters stick from 5 of the holes, and measure its period for each (2 trials of 20 swings each)
- 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 - 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**?

- Does your value of

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.