Notes to chapter 3. Newtonian Mechanics and Causality.

Biographies.

• Galileo Galilei. (1564-1642) Sometimes Galileo is called the "father of the experimental method".
• François Viète (1540-1603). In his book In artem analyticam isagoge Viète introduced symbols (letters) to represent mathematical unknowns.
• Rene Descartes. (1596-1650) Most of his physics is mercifully forgotten, but his Analytical Geometry serves as a powerful tool even today.
• Sir Isaac Newton. (1642-1727) Newton produced the first comprehensive mathematical model linking the mechanical laws of terrestrial and celestial phenomena.
• Sir Isaac Newton. (1642-1727) With picture.
• Gottfried Wilhelm von Leibniz. (1646-1716) Here's another Leibniz biography.
• Francois-Marie Voltaire (1694-1778) Here's another Voltaire biography.
• Pierre de Maupertuis (1698-1759)

The mind reading puzzle may be found at this link, the National Institute of Health website.

The lab experiment on the pendulum. Here's the answers to the questions in that experiment. Ignore the material on logarithmic graphs, since you were not asked to do that.

A discussion of the fallacy of the method of differences, a defective data analysis method often seen in physics lab manuals when constant acceleration data is to be anlyzed. Valid alternative methods are suggested.

Now that the assignment deadline is past, here's my comments on the "Looking out at the universe" picture.

I considered putting here some notes on one and two dimensional equations of motion, including vectors and Galileo's superposition principle. But before re-inventing the wheel, I checked the www to see whether anyone already had such material online. I found these:

• Galileo describes motion. An interesting document on Galileo's development of the equations of motion for constant acceleration. Also includes a spreadsheet analysis of actual student data.
• Vector kinematics A series of lessons at the high school level. Chapter 1 and 2 take a vector approach to Galileo's equations. Later chapters help explain Newton's mechanics, which will be useful for the second half of our textbook chatper 3.

There's lots of web documents on this subject that take a calculus approach, and go beyond the simple case of constant acceleration, but I don't list them here. If interested, do a search with keywords "vector kinematics".

As you read these documents be aware that various symbols may be used for displacement: x, v, s, and d are common. Over the years I've used them all, but you might prefer to avoid "s" since it is easily mistaken for "speed". Let's state the kinemtaic equations here using "d" for displacement.

To aid your review, I have prepared some notes paralleling my presentation in class:

• Kinematics, Galileo's laws.
• Mechanics, including Newton's laws and some comments about energy and momentum.
• The mechanical universe. Newton and Leibniz have opposing views about the way the universe operates.

For a laboratory resource, you ought to look at this document on errors.

Here's a short document on scientific method, summarizing some comments I made in class this past week.

Uses and Misuses of Logic is an essay I wrote back in 1997. It touches on many of the topics we will deal with throughout this course:

• Facts, hypotheses, laws, and theory.
• The roles of induction and deduction.
• The so-called search for "truth". Absoslute and proximate truths.
• The question "What distinguishes science from other types of human inquiry?"
• What characterizes scientific revolutions?
• What is "reality", really?
• The relation between mathematics and physics.

This material might be called a summary of the important ideas of this course and the questions we hope to slowly answer as the semester unfolds. It needs to be reorganized, and may even need another title, but it's got a lot of important stuff in it and I strongly recommend that you read it.

—Donald E. Simanek, Feb, 2005