Classical Mechanics Project #1

Classical Mechanics Project #1

by Haifei Zheng
November 7, 1997

On page 30 of Goldstein's textbook, he draws attention to a text by Osgood, which apparently includes "delightful" pedagogic material. Goldstein draws particular attention to Osgood's page 102. Write a short critique of the pedagogic style of Osgood's book.

Before we start the critique of the specific contents on this page or even the pedagogic style of the book, it may help to know some important information about William Fogg Osgood and the ages when he lived. Osgood was born in Boston on March 10, 1864 and died in Massachusetts in 1943. In the late 19^th century, education was more strict than today. Students were demanded to follow the instructions of their professors and had very little freedom of doing things in their own way though they might have different ideas about many issues. [Editor's note: Hey, wait a minute. Professors still have that kind of authority!] And also students at that time had solid background in Greek and Latin literature. From 1890 to 1933, Osgood taught at Harvard and his best-known book is "Lehrbuch der Funktionentheories". He wrote text books on elementary and advanced calculus too.

The book "Mechanics" was finished in 1937 when Osgood was already 73, just 6 years before he passed away. As a very experienced teacher then and a very old man, Osgood must have had a lot of ideas about what questions the readers, mostly physics majors, have concerning physics concepts and principles, so he approached them with a unique pedagogic style at the undergraduate level.
Goldstein mentions the first five chapters as being an elementary introduction to the subject that is delightfully flavored. He also specifically directed our attention to the part reproduced opposite. Osgood, while introducing the centrifugal force, mentioned the basic idea of isolating the system while solving problems in mechanics.
Osgood raised the question that some "sophists", as he called them, might want to argue with. The Sophists of ancient Greece were philosophers who had a reputation for reasoning that was clever (the modern word sophisticated comes from this root) but could sometimes be misleading also. Osgood makes clear his attitude towards these people and the questions they might raise.
Let us pay attention to the italics on page 102: monumentum aere (bronze momument). This came from the then-famous poem Exegi Monumentum Aere Perennius, the 30^th poem of Odes Book III, by the Roman poet Horace. (I have included an english translation of the poem for your reference). Osgood gave applause to the person who "first uttered" the idea of isolating the system, thereby answering one of the common confusions about centrifugal force.
Now, think of going back to the late years of the last century - students can't even appreciate physics textbooks without a sound foundation in poetry and classical languages!! It must have been even harder for international students.

Other interesting examples of Osgood's pedagogic style can be found. On page 126, Osgood gave very detailed instructions to guide students in a particular exercise:

He (the student) should wrote out the full equation derived below from these, neatly on a single line, and then write the other two under this one.

From the point of view of modern education, this is not necessary and people today will regard it as micromanagement. However, I think instructions like this were taken for granted and very common at the times when Osgood was himself a student and when he taught physics as a professor at Harvard later on. On page 185, for the explanation of the Sand Tunnel, Osgood also gave guidance to teachers:

This experiment should be shown in the course. It is not necessary to have a physical laboratory. A tunnel can be bought at the Five and Ten and string is still available, even in this age of cellophane and gummed paper.

Osgood even tried to give specific instructions on what the class should include for demonstrating the ideas in his book. It now appears a bit funny to us, because most of us might have never seen any remarks like this in our textbooks even from junior high, but it gives us some subtle ideas of what college education used to be like. Moreover, it brings peace to our heart knowing that though physics majors might have "suffered" more in that age than we do today, the professors of physics did too!

If you skim through the exercises on page 104, you may notice a couple of problems as follows:

If the earth were held in her course by steel wires attached to the surface on the side toward the sun and evenly distributed as regards a cross-section by a plane at right angles to them, show that they would have to be as close together as blades of grass. It is assumed that their other ends are guided near the earth's surface.

Show that a steel wire one end of which is made fast to the sun and which rotates in a plane with constant velocity, making one rotation in a year, could just about reach to the earth without breaking. Neglect the heat of the sun and all forces of gravitation.

They seem to be a series of problems requiring an understanding of not only the centrifugal force, but also the problems themselves. I read the first one at least 10 times and still have no idea about what it is talking about. What do you think of it?