Phy 340 class notes for Fall, 1999

Aug 25 Sep 8 Oct 4 Nov 1 Phy 340 page
Aug 30 Sep 13 Oct 11 Nov 8
Sep 20 Oct 18 Nov 15
Sep 27 Oct 25 Nov 22
Nov 29

Phy 340, Week 10

25 Oct Go over some of the homework problems. In one case, show a slick way to solve a quadratic equation for small values of one of the coefficients. For another, show how to set up the integral, and then state the kind of non-obvious change of variables that you have to do to get it into the standard form.

27 Oct Do something with the homework problems, then go back to the subject of rotating coordinate systems. Derive the transformation from an inertial to a rotating system. The key step is to compute the time derivative of a vector as viewed by the inertial and the rotating observers. Once you've done this, the rest follows.

[ dQ/ dt ](inertial) = [ dQ/ dt ](rotating) + w x Q

Apply this to the position vector to relate velocities in the two systems, then apply it to the velocity vector to relate the accelerations in the two systems. When you've done this and combined what can be combined, you can finally get the transformed version of F = ma in the rotating system. It has three extra terms, called the "centrifugal force," the "Coriolis force," and another one that isn't important enough to warrant a name.

29 Oct Do the exam.
Examine the structure of the new terms created by transforming to a rotating coordinate system. Start with the centrifugal force term. Write it out in a particular coordinate system where w = wez. Evaluate it for the Earth at the equator and see how it compares to the gravitational force. Result: about 0.4%.

Next, look at the Coriolis force. It is qualitatively different from the other terms. Take the particular example of an object being fired from one place to another on the Earth's surface. Set up a local coordinate system and see what this extra term does. Write out all the equations in terms of the local x-y-z coordinate system and at first just see qualitatively what they do.

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