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Finding Pi Circle lab

What does π (pi) represent?

Digits of pi

Circles: Math is fun

How does one measure pi?

When a circle’s diameter is 1, its circumference is π.

The distance half way around the edge of the circle
will be 3.14159265…   Pi

When a circle’s radius is 1—called a unit circle—its circumference is 2π.

 

Pi is related to an angular measurement called a radian.

In calculus based physics, radians are far more useful and natural to use than degrees.

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Objectives: 

-determine the relationship between the circumference of a circle and its diameter.

– learn how to use Logger Pro (Graphical analysis software).

– understand that data must be carefully collected, analyzed and interpreted.

Materials:  Various circular objects, string, meter stick (and do not use a calculator!)

Procedure:

  1. Measure the diameter of one of the circular objects.
    Record the number in your data table
    (Watch the meter stick precision: Measurements should be recorded to millimeters, zeros are important too.)

  2. Use the string to measure the circumference of the circular object.
    Then measure the string with the meter stick, and record the value in the data table
  3. Continue until you have filled in your entire data table.
    (2 points guarantees a straight line, you need at least 8 data points for most labs)

  4. Clean up any string, return it to the designated area, make sure all data is recorded.

  5. Create a graph of Circumference (y axis) and Diameter (x axis) using LoggerPro.
  6. Find the slope of the line using Graphical Analysis.
    .
  7. Interpret the slope qualitatively: tell me what the slope represents. This should be written on the face of the graph, in a text box.
  8. Perform a percent error calculation: 

  (Accepted – experimental) x 100%

Accepted

9. Write the equation of the line with: name of the quantities and units on the x and y axis.

 

Result:

Actual student data

Actual student data

 

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