I will add all captions to these fresh shots as the weekend continues . . .


PhySP18SS4.2.1


PhySp18SS4.2.2 Proper way to describe a vector in “people speak”.


PhySp18SS4.2.3 Map View, like I am looking down on the problem from above.


PhySp18SS4.2.4 Profile view, like I am looking at the problem from the side.


PhySp18SS4.2.5 . . .


PhySp18SS4.2.6 Headtotail method or sometimes called “tiptotail” method. Best way to visualize the interactions of the vectors in your problem.


PhySp18SS4.2.7 . . .


PhySp18SS4.2.8 adding vectors is kind of weird


PhySp18SS4.2.9 Remember, the resultant always starts at the first tail (the beginning) and ends at the last head (the ending).


PhySp18SS4.2.10 . . .


PhySp18SS4.2.11 Line of Action is a virtual extension of the vector to infinity (or off your page, whichever one comes first ; ) It is useful when you are trying to redraw a vector and you want to keep the orientation the same (railroad track method). It also comes in REAL handy when you are doing torque problems.


PhySp18SS4.2.12 Using LOAs to help you construct a head to tail


PhySp18SS4.2.13 Instead of calling the resultant here, I should have labeled ∑F.


PhySp18SS4.2.14 . . .


PhySp18SS4.2.15 You can multiply a vector by a scalar. All that does is make it longer or shorter. It does NOT affect the orientation (angle).


PhySp18SS4.2.16 . . .


PhySp18SS4.2.17 Head to tail of adjustred lengths


PhySp18SS4.2.18 . . .


PhySp18SS4.2.19 Adding six force vectors together to produce a resultant (∑F). It is the tan colored arrow. If you end up with a resultant force vector then the object that the six forces are acting on will not only move, it will accelerate (speed up or slow down). If you were to add those six vectors together and the sixth arrows tip ended up touching the first arrows tail, then there would be NO resultant vector an therefore, no acceleration. This is called EQUILIBRIUM. If you go one step further and make the object stationary, the situation is called “static”.


PhySp18SS4.2.20 Here are those same vectors from the previous screen shot, but now they are arranged in a Free Body Diagram (FBD). If you look back and forth, you will see that all the vectors are the same, except that here, they all emanate from the center of mass of the object. This is how you have to draw the vectors if you are adding them using the component method.


PhySp18SS4.2.21 Head to tail vs. FBD method.


PhySp18SS4.2.22 Here is an example of a FBD. We will get good at these later.


PhySp18SS4.2.23: You should be at the “dog tilting head” stage of understanding right now for dot products and scalar products. They will slowly begin to dominate your thinking about the universe. I can’t believe I get the privilege of being the first to introduce them to you.


PhySp18SS4.2.24 . . .


PhySp18SS4.2.25 . . .


PhySp18SS4.2.26 . . .


PhySp18SS4.2.27 Well, this is way beyond where we are, but up until about mid April we can get away with calling everything a dot (center of mass) like in the figure on the left, but once we start talking about cross products we are going to have to start thinking about objects as “extended objects” because WHERE a force hits a body will matter since now the object can ROTATE. Anyway . . . forget I said anything. That’s acomin.


PhySp18SS4.2.28 Another example of cross product causing torque which causes rotation.


PhySp18SS4.2.29 cross products causing a water molecule to rotate inside your food inside your microwave oven.


PhySp18SS4.2.30 Kind of a cool puzzle for adding vectors. Various combos.


PhySp18SS4.2.31 .. .


PhySp18SS4.2.32 Adding and subtracting vectors sometimes have the same rules as you learned b ack in grade school


PhySp18SS4.2.33 You can add, subtract, multiply (dot or cross product), but you can NOT divide a vector by a vector.


PhySp18SS4.2.34 Ahhh . . . three dimensional vectors.


PhySp18SS4.2.35 3D dimensional vectors


PhySp18SS4.2.36 Unit vectors turn scalars into vectors by giving them up,down,left,right,out, in direction.


PhySp18SS4.2.37 turning a vector into its components.


PhySp18SS4.2.38


PhySp18SS4.2.39 The girl who made this poster went off to dominate West Point . . . just like she dominated vectors.


PhySp18SS4.2.40 . . .


PhySp18SS4.2.41 Component method


PhySp18SS4.2.42 All the rest of these are examples of component method.


PhySp18SS4.2.45


PhySp18SS4.2.46


PhySp18SS4.2.47


PhySp18SS4.2.48


PhySp18SS4.2.49


PhySp18SS4.2.50


PhySp18SS4.2.51
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