Class Handouts, graphs, etc. I will try to put copies here of any images I show in class, along with special notes expanding on stuff which is only briefly explained in the text.
| Newton's Picture of Keplers Second Law | At the end of class I ran through Newton's treatment of Kepler's second law, that the line between an orbiting object and the sun sweeps out equal areas in equal time. His treatment seems at first very geometrical, but in fact this is calculus. The straight line segments he considers are approximations of the elliptical path taken, and the errors made by the straight line approxiamtions are quadratic in line length, just like the error approximations we have been talking about in Math. |
| The Cosmic Microwave Background | The first system which clearly indicated to us that quantum mechanics is important was thermal radiation from small ovens. Here, radiation from the whole universe is shown to obey the same rules. |
| Parallel Axis Theorem | The textbook only lists a limited version of what one might call the parallel axis theorem in angular momentum. Here is an extension of those ideas. |
| Ellipsoids and imaging | Newton's line of reasoning that an ellipsoid images light leaving one focus onto the other focus is not in the text book, so here it is. It comes up because ellipses are also the shapes of orbits. Because of that, the name for where the sun is in the earth's orbit, focus= fiery place, has come to be the name given to the image points in an optical system. |
| The sizes of Barnacles | I know the stuff we did in class getting a size distribution of Barnaculus bigus is not in the text books, so I wrote up some of it here. The two main points are 1: that error bars often have more to do with the natural distribution of what you are measuring than with anything you might call an error, and 2: that taking and analyzing a photograph can be a quick way to get a lot of quantitative data. |
| How Bacteria Move: Fluid mechanics of very small things. | |
| Life at Low Reynolds Number | The is a delightful article by Ed Purcell about motion of bacteria. The first half is is about how small things move. When you are small enough inertia is not important at all. You do not coast to a stop, you just stop. The second half talks about diffusion and works out what sorts of foraging strategies bacteria must follow. The whole thing is conversational in tone and you should be able to follow it and have fun doing so. Purcell won a Nobel proze in physics and is an amazing intellect, but in a special way, which shows in this paper. Talking to him you first have the impression you are talking to a reasonable person, not a genius. But then you realize it is more like talking to twenty reasonable people. There is no gap or lull, and each remark is the most useful thing that the twenty people would have thought of to say next. |
| Movies of Bacteria Swimming | This link takes you to movies made in the laboratory of Howard Berg--the fellow who taught me about the reversible stirring of glycerin. In these movies there are many examples of the sorts of things bacteria must do to move in water, including amazing films of tethered e-coli. |
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More technical references: A. Shapere and F. Wilczek Gauge Kinematics of deformable bodies, American Journal of Physics, V57 ,p 514 (1989) , A. Shapere, F. Wilczek Geometry of self propulsion at low Reynolds number, Journal of Fluid Mechanics, V198, p557 (1989) R. Montgomery Gauge theories of the falling cat, Field Institute Communications V1, p. 75 (1993) | |
| Size and Mass of everything | We made a graph in class patterned after a famous plot first made by John Wheeler. Here is a note on our version. |