Class Notes for Fall, 2000

Week of	Aug 23	Sep 6	Oct 2	Nov 6	Phy 205 page
	Aug 28	Sep 11	Oct 9	Nov 13
		Sep 18	Oct 16	Nov 20	Notes for Fall, 1999
		Sep 25	Oct 23	Nov 27
			Oct 30

Phy 205, Week 1

Aug 23 A general introduction to the course, emphasizing that there are a fairly small number of ideas on which everything else is based. This makes it a simpler subject than for example, biology. That doesn't mean it's easier, just less complex.

It is often hard to discern where the simplicity lies, and where the basic ideas in a textbook such as ours are. I will try to show what the basic ideas are and which of the text's material is of marginal importance.

Standard definitions of units. The metric prefixes, or at least the common ones. Next, try to get an idea of the various size scales that occur in nature, all the way from 10²⁶ meters or so for the most distant object seen down to 10^-15 meters for the size of a nucleus. There are probably still smaller objects, but that's all a bit uncertain.

Aug 25 Dimensional analysis. Use the example of a pendulum to show how to get a lot of information about a mechanical system simply by requiring that the dimensions make sense.

A mass swinging back and forth on the end of a string has a period defined as the time it takes to go through a full cycle and start over. Later in the course I will solve this in detail and show how to get the whole solution. For now, I want to examine what the result could possible depend on. Various possibilities include
(1) the length of the string
(2) the mass on the end
(3) the gravitational field
(4) the maximum angle
(5) air resistance
(6) friction at the pivot
Maybe others.

Whatever the formula is to describe the period, it is a time. That means that whatever combinations of mass and length and other things go into it, they must come out as time. A combination of quantities of the form M^aL^bg^c is not obviously a time. Is there any combination of powers, a, b, c, that will make this come out to have sensible units?

I worked out the details in class and found that only if a=0, and b=1/2, and c=-1/2 does this work. This predicts that if I change the mass on the end of the string, the period won't change. And it didn't! It also predicts that if I change the length of the string, the period will change in a way that is proportional to the square root of the length. Again, this worked when I tried it.