[Lab Index]

Physics and Measurement

"By a comparison of the results of accurate measurements with the numerical predictions of the theory, we can gain considerable confidence that the theory is correct, and we can determine in what respects it needs to be modified. It is often possible to explain a phenomenon in several rough qualitative ways, and if we are content with that, it may be impossible to decide which theory is correct. But if a theory can be given which predicts correctly the results of measurements to four or five (or even two or three) significant figures, the theory can hardly be very far wrong. Rough agreement might be a coincidence, but close agreement is unlikely to be. Furthermore, there have been many cases in the history of science when small but significant discrepancies between theory and accurate measurements have led to the development of new and more far-reaching theories. Such slight discrepancies would not even have been detected if we had been content with a merely qualitative explanation of the phenomena." - Keith R. Symon, Mechanics, Second Edition, 1964

One of the things that scientists do is make predictions - predictions based on their hypotheses, laws, and theories. The test of a prediction is whether it works in the "real world" - do the results of experiments match the theoretical prediction? If the results don't match (and these results are confirmed by other competent scientists) then the hypothesis that generated the prediction must be modified or abandoned. The ultimate authority in science is nature - not "what it says in the book".

You may not have thought about it, but when you solve a "physics problem" in a text book you are making a theoretical prediction. When you calculate that a car should skid 20 meters in some situation, the real test of the correctness of your result is whether a real car would really skid 20 meters in that situation - not "what the book says" in the "Answer Section."

Physics is a **quantitative** science. Physicists deal in
numbers - but **not** just the numbers of the mathematician. This
is an important point that is often missed by beginning physicists.
Physicist's numbers are often (or could be)
** measurements**, not the pure numbers of the
mathematician.

Therefore, physicists measure things. Measurement is very important in physics - physicists are serious about measurement. One of the major contributions of physics to other sciences and society are the many measuring devices and techniques that physics has developed. In "everyday life," we pick up a ruler and measure something without giving it much thought. Physicists think about their measurements, and need to have a much more sophisticated understanding of the measurement process than "normal" people do.

Beginning physicists often get a very distorted view of all of
this. You may remember doing an experiment, like determining the
acceleration of gravity. The acceleration of gravity is "supposed to
be" 9.8 m/s^{2} - everybody knows that. Your "answer" came
out 10.3 m/s^{2}, so your experiment "didn't work" - you were
"in error" - perhaps you even calculated your "percent of error."
Many beginning physicists are burdened by the following
**misconceptions** (that we will try to remedy in the
pages to follow):

- Measurements are numbers, and...
- There are exact values for physical quantities (like the acceleration of gravity), and...
- Somebody (a famous physicist, perhaps) knows what these exact values are, and ...
- My values are always wrong, so that ...
- Physics experiments "don't work".

So, this unit begins with a brief introduction to the four types of numbers that an experimental physicist needs to deal with, followed by an extensive discussion of the measurement process - what precision is, why it is a concern, and how to deal with it in measurements and calculations. Then there is a discussion of accuracy, and finally, straight answers to the question "Ok, so how do I actually analyze this experiment, anyway?"

Measurement Unit Contents

- Ch 1 - Measurement - Objectives
- Numbers in Physics
- Making a Measurement
- Precision
- Limits to
Precision
- Scale Uncertainty (Scale Error)
- Approximation Uncertainty (Approximation Error)
- The "Problem of Definition"
- Random Uncertainty (Random Error)
- How do I estimate the precision of a measurement?
- Standard Deviation

- Indicating Precision of a Measurement
- Indicating Precision on a Graph - Error Bars
- Handling Precision in Calculations

- Limits to
Precision
- Accuracy

- Precision
- How to Analyze a Physics
Experiment
- A "Measuring a Value" Experiment - such as measuring the free fall acceleration "g"
- An "Are These Two Values Equal?" Experiment - such as "Is Momentum/Energy Conserved When _____ ".
- An "Is This Proportional to That Experiment" - such as "Is Distance Proportional to Time Squared?"
- "What do I do if my results are inconclusive?".

- An Uncertainty Dictionary
- Labs
- A Simple Measurement - Simply measure the width and height of a photo, then calculate its area... How easy is that?
- Target Practice - A simple activity about accuracy and precision
- Another Simple Measurement - Another way a measuring instrument influences a measurement.
- Yet Another Simple Measurement - Try some more-sophisticated analysis as a class, and explore random and systematic uncertainties.
- Measuring Common Objects - An introduction to measurement
in physics. There are 2 versions:
- This version uses only significant digits
- This version uses uncertainty intervals.

- Grandma Lewin's Hypothesis - an activity based on MIT Physics 8.01 Lecture 1
- Time of Fall Experiment - good exercise in dimensional analysis and propagation of uncertainty based on MIT Physics 8.01 Lecture 1
- Measuring Pi
- Measuring Heights Using the Law of Reflection
- Kepler's Third Law and Graphical Analysis
- Hooke's Law - force vs. stretch for a spring
- Period of SHM

- Practice Quizzes

References and Links:

- Roberts, Dana, "Errors, discrepancies, and the nature of physics", The Physics Teacher, March, 1983 - a very useful introduction; a reference that I have used for years.
- Taylor, John R. "An Introduction to Error Analysis - The Study of Uncertainties in Physical Measurements, Second Edition", University Science Books - This is a really fantastic reference! Unfortunately, I found it after I had written the first draft of this unit... (but I now notice that it is referenced by Roberts, too...)
- Error Analysis - written at the college freshman level (no calculus) by Prof. Donald E. Simanek of Lock Haven University. (added March 4, 1999)
- NIST Physics Laboratory - Lots of useful information from the National Institute of Science & Technology
- NIST Reference on Constants, Units, and Uncertainty - very informative and interesting - maybe a little technical
- Accuracy and Precision - written by a professional surveyor
- Accuracy, Precision, and Uncertainty in Measurement - a short tutorial from a chemistry perspective
- The Science of Measurement - Accuracy vs. Precision - from Hawaii
- Accuracy vs. Precision, and Error vs. Uncertainty - a tutorial with a practice quiz
- Error, Accuracy, and Precision - from the University of Colorado
- Precision and Accuracy - another chemistry perspective
- Accuracy and Precision - good discussion

[Lab Index]

last update October 13, 2008 by JL Stanbrough