Class Notes
These notes are NOT intended to be a complete record of what has been covered in class. Students are responsible for all material discussed in class and in the assigned readings, not just what appears here. I will try (but not always succeed) to be brief here. I will focus on material not adequately discussed in the text.
Last year I wrote notes for each class. Those will follow fairly closely this year's topics, so you may wish to peruse them at this link.
Mon, 3/31

Today I mentioned an observation about elastic collisions in one dimension that is not in the textbook. We previously deduced in class, and it is derived in the textbook, that the velocities relative to the center of mass flip sign in such a collision. To easily use this fact  it is helpful to note that  this sign-flipping condition,

v_1f - v_cm = -(v_1i - v_cm),

implies that  

v_1f = 2 v_cm - v_1i,

and similarly for m_2.
Thur,  2/20

Today in class I went over the problem of the mass on the ledge with the pulley, to illustrate the general method for all these problems. The most common problem students have in doing these problems is trying to guess the answer. This is a bad idea, since it is almost impossible. Instead, just "put one foot in front of the other" and go step by step. Here are the steps:

Problem solving recipe:

0. Choose what objects you are going to apply F=ma to.

1. Draw a free body diagram for each of these objects.

2. Choose the positive directions for each coordinate and write out F=ma (with more than one component if the motion is in more than one dimension) for each object. If numbers are given in the problem (like the mass in kilograms), define a sybol representing that quantity and use the symbol, not the number.

2b. If there is an unstretchable string or some such thing then you need to impose constraints on the motion that relate one displacement to another. For example in the ledge problem we solved, a_2 = (1/2) a_1.

3. Check that the number of equations is greater than or equal to the number of unknowns.

4. Solve for the unknowns.

5. Check that the dimensions are correct and the limits of your solutions make sense (eg as one mass goes to zero or infinity, or when gravity is turned off, or when an angle goes to zero or pi/2...).

6. Plug in the numbers, if any.
Mon, 2/10:

monkey & hunter demo, racing balls demo

Tue, 2/11:

-    Demos shown: (see lecture demo link (also on course homepage)).
     C3-04 INERTIA - LEAD BRICK AND HAND
     C3-12 PENCIL AND PLYWOOD
    
- pencil & plywood demo reminded us of the hazards of space debris colliding with the shuttle or space station.
- discussed mass vs. weight
- normal force exerted by a scale: what the scale reads, weight at rest, weight on an accelerating elevator
- free body diagrams

-Newton's laws:
I. Force-free motion is unaccelerated*.
II. F= ma
III. If bodies A & B exert pairwise forces, then F_AB = - F_BA.

 In more explicit detail, I & II can be stated:
I. [There exists a set of reference frames, called "inertial", such that]
force-free motion is unaccelerated.

II. [There exists a parameter m, called the "mass", such that the acceleration of a body is given by]
a= F/m, where the total force F is the vector sum of the individual forces acting on the body.

- mass is not reducible to length and time so it is another kind of quantity, with "dimensions of mass". The SI unit is 1 kg.
- dimensions and units for force.

- *Problem: unaccelerated relative to WHAT??!  If there were an absolute rest frame we could say relative to THAT. Newton took this route in stating his laws, i.e. he relied on the hypothesis that there is indeed an absolute rest frame. However Galileo already had observed that in fact one cannot distinguish the physics in two frames moving at constant velocity with respect to each other. (He gave the example of experiments in the hold of a ship that was gliding smoothly across a calm sea.) With no absolute rest frame, we must instead observe that while there is no single absolute rest frame, there is an absolute family of frames, all moving uniformly relative to each other, in which force free motion is unaccelerated. These are called inertial reference frames.