Basics: Vectors and Vector Addition

**pre-reqs:** trig

Think of the following two things. Temperature and wind speed. These are two different things that you could measure, but there is one big difference. Wind speed has two parts to it – how fast and which direction. Temperature is just one thing (no direction). Temperature is an example of a scalar quantity (just one piece of information). Wind speed is an example of a vector quantity – multiple pieces of information. Here are some other examples:

**Scalar:** mass, money, density, volume, resistance
**Vector:** velocity (most physicist reserve the word “speed” to mean just the magnitude), acceleration, force, momentum, displacement, electric field

Ok, I get it – but who cares? Well, if you are taking an introductory physics course, you should care. Here is a question I like to ask to start the discussion of vectors:

If I move 3 feet and then 2 feet, how far am I from where I started?

The answer is that there is no answer. I commonly get the quick answer of 5 feet, although this is only one possible answer. Let me illustrate this question with some pictures.

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Basics: Projectile Motion

**pre-reqs:** [kinematics](

My previous “basics” post was on kinematics (in one dimension). But what about two dimensions? In particular, what about projectile motion. My motivation here is that I was about to talk about analysis of a video that involved projectile motion and I don’t want to go over all the stuff again and again.

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Basics: Kinematics

**pre reqs:** *none*

Often I will do some type of analysis that I think is quite cool. But there is a problem. I keep having to make a choice. Either go into all the little details, or skip over them. My goal for this blog is to make each post such that someone could learn some physics, but I also don’t want it to go too long. So, instead of continually describing different aspects of basic physics – I will just do it once. Then, when there is a future post using those ideas, I can just refer to this post. Get it?

Fine. On with the first idea – kinematics. Kinematics typically means a description of motion (not what causes that motion). In particular, kinematics looks at position, velocity, and acceleration. In this post, I will try to stay in one dimension. This will make things look simpler without really losing too much. Later, when I talk about vectors, I will make it all better.

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