Circular Relationships

The ancients were interested in the harmony of the universe. They dedicated themselves to the study of the shapes of nature. In particular, the Greeks analyzed the circle extensively. Circle size is best categorized using a measurement called the diameter.

Question: Why is the diameter the best measurement to categorize a circle?

The outer perimeter of the circle, or circumference, can also be a useful measurement to categorize a circle. Both of these measurements present special difficulties when concerned with measuring accurately.

Question: Why is it difficult to measure diameter accurately?

Question: Why is it difficult to measure circumference accurately?

Let’s do what the Greeks did and measure the diameter and circumference of several different circles. For convenience, we will be using coins.

Procedure Part 1: Devise a way to accurately measure the diameter of a circle using the measurement tools at your lab station. Record your procedure in your lab notebook.

Question: What are the strengths of your procedure?

Question: What limitations are present in your procedure?

Procedure Part 2: Devise a way to accurately measure the circumference of the coin using the measurement tools at your lab station.

Question: What are the strengths of your procedure?

Question: What limitations are present in your procedure?

Collect data for the various coins. You may also want to measure other circular objects should time present itself.

Analyzing Your Data

  1. Make sure that your measurements of circumference and diameter have the same units. (You may need to convert units depending on your measurement procedure).
  2. Using graph paper and being careful of a choice of scales for each axis, plot a point for each coin with diameter on the x-axis and circumference on the y-axis.
  3. Draw a straight line of best-fit on the graph and find the slope.

Concluding Questions

  1. Why is it appropriate to draw a straight-line fit on this graph?
  2. What is the physical meaning of this slope?
  3. In this lab you were restricted to the equipment on your table. What other equipment would have been helpful in this lab?
  4. Were the limitations of your procedure significant? Explain your reasoning.