| Week of | Aug 22 | Sep 5 | Oct 1 | Nov 5
| Phy 205 page |
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| Sep 17 | Oct 15 | Nov 19 | |||
| Sep 24 | Oct 22 | Nov 26 | |||
| Oct 29 | Notes for Fall, 2000 |
22 Aug After a few general remarks, plunge into vectors. How is a vector distinguished from a scalar? The latter (scalar) is a number -- with or without units. A vector also has direction.
The simplest example of a vector is the displacement vector; distance and direction combine to form a vector. The distance from Miami to Tampa is about 300 miles, but if that is all you know then getting to Tampa will be a challenge.
Show how vector addition is defined. For the example of the displacement vector, addition is nothing more than doing one journey followed by another. The picture of the vectors is formed by drawing arrows to represent the legs of the trip and putting them tip-to-tail. You have another way to picture vector addition by putting the arrows tail-to-tail and constructing a parallelogram. The sum better be the same whichever way you choose to draw the picture. Work out an example with a demonstration.
Brief description of vector subtraction as undoing addition.
24 Aug Multiply a vector by a scalar and you change its length and maybe its units too. If the scalar is negative it reverses direction. This is not an arbitrary choice; it's the only way you can make it work and come out sensibly.
Subtraction of vectors again, emphasizing the geometric way of doing it.
You can look at vector subtraction in more than one way:
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Components: Pick a couple of special vectors, called basis vectors. They are taken to be perpendicular to each other and to have unit magnitude. This doesn't mean a length of one foot or one meter; it means one with no dimensions. This notation for them is i and j.
Note: most browsers don't have hats over the i and the j, so I can't do that and I'll have to use boldface type instead.
Show how to write a given vector in terms of these basis vectors. One vector is written as the sum
The components are the numbers that multiply the basis vectors -- they aren't vectors themselves. I did a couple of examples of adding vectors using components and taking magnitudes of vectors using components and the Pythagorean Theorem.
Next an experiment to add three forces formed by lead fishing weights. The forces had to be arranged to add to zero in order to prevent a balance from tipping over. To set it up I did some trigonometry to figure out where to put the weights.
