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First Introduced and Revisited Mathematical Concepts

Student "edition" found at {csi dot journalspace dot com}.

Maybe I shouldn't have started this blog now, not with everything that's been going on.

Catching up with what I have been doing in my general science requirement mechanics lecture class, when I started talking about uniform acceleration, I began with a comparison of the table and the graphs between constant/average velocity and acceleration, seeing they are similar when it comes to displacement vs. t for the first and v vs. t for the second.

Then I showed them where displacement vs. t for the second is different, where it’s not linear anymore but parabolic. This led to the derivation of the formulas to be used, the simplest linear one dealing with no displacement.

From there, I gave them the first equation with displacement, which includes time squared and accounts for the parabola. Next I got the other three formulas based on the first two, some of which are similar and thus easy to remember.

I gave some examples, from which they have to list the given and the required first to be able to determine which equation out of the five listed to use.

I also told them the special cases where an object starts from rest (initial velocity is zero) and when an object comes to a stop (acceleration is negative and final velocity is zero). Then we had the usual exercise, where, like the previous examples given, I had them get two quantities from one problem.

In my Electromagnetic Theory class, we finished with all the possible setups to compute for the force using a point charge and either a line of charge, a ring of charge or a disk of charge, so I next tackled changing an object’s axes to make the set up symmetrical like one of the other situations we’ve discussed.

They only took this up to two dimensions in one of their previous classes (which they could not name) so that’s were I started, with the third axis being the same in both coordinate systems. In other words, that’s where the axes rotate.

This involves getting an angle based on some of the measurements given. Sometimes using the Pythagorean theorem they also have to get new measurements for the new setup couched in the previous terms. Then, after they have gotten the x’, y’ and z’ components of the force (some of which are zero) then they have to translate it to the old system and use the initially computed angle, where the components are definitely non-zero.

Next time I will discuss coordinate translation using all three axes this time, which involves two angles.

Session 1491 decelerated here. Class dismissed.


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