| Week of | Aug 25
| Sep 8
| Oct 4
| Nov 1
| Phy 205 page |
| Aug 30 | Sep 13 | Oct 11 | Nov 8 | ||
| Sep 20 | Oct 18 | Nov 15 | Notes for Fall, 1998 | ||
| Sep 27 | Oct 25 | Nov 22 | |||
| Nov 29 |
11 Oct The center of mass. How can you define the "average" position of two objects? Is the halfway point between them? That's one possible definition, but not the most useful, certainly not for our purposes.
An analog: in the two sections of this class, if you know the average exam grade for one section and for the other, is the overall average grade one-half the sum of these? No, because the two classes have very different numbers of people in them.
To see what has to be done for mechanics, start from F = ma for one particle, and apply it successively to two particles. This is a brief recapitulation of the derivation done last Friday, in which you are forced into the use of the center of mass as the "average" position of the two masses.
Apply it to the Earth-Moon system to see where the center of mass of the two is. Result: it's underground, about three quarters of the way toward the surface from the center.
Demo: For two objects tied together and thrown up in the air, the center of mass should follow a parabolic trajectory, even if the individual masses have a more complicated motion.
13 Oct Discuss a few of the coming homework problems. Especially in reference to the worksheets done this week in the discussion section, go back and say what Newton's first and second laws REALLY are. The first is actually a definition of an inertial system:
1. Definition: An "inertial system" ("inertial coordinate system," "inertial frame," "inertial reference system") is one in which IF there is no total force on a mass THEN its acceleration equals zero.
2. IF you are in an inertial system, THEN F = ma (or more generally = dp/ dt).
The sun is going around the Earth once a day while the Earth stands still. This is a perfectly defensible statement; it's just that the Earth is not an inertial system, so that F is NOT equal to ma. If you want to work in a non-inertial system, you have to face the fact that Newton's equations will have to be modified. This is exactly what's done by meteorologists and oceanographers. Newton's equations are patched up by adding terms called "centrifugal force" and "Coriolis force" so that the answers come out right. We are not going to do this, so in this course, I'll use only inertial frames and these extra "forces" will never appear.
Derive conservation of momentum in a way very much like what I did for getting the equation for center of mass. Apply it to a simple example done in a demonstration.
