# vectors

I rarely write about climate change. As much as it's been hashed out amongst climate scientists, and even many of the former "climate skeptics" have now changed their tune, I readily accept that climate change is happening, and is happening largely due to human activities. More importantly for my field, climate change is also having effects on human health in a number of different ways, from the movement of insect vectors into new areas, to warming of the seas leading to more extreme weather conditions, to the loss of coral reefs and the freshwater that these reefs protect from the…

Actually, it should be called Happy "Magnitude of the local Earth gravitational field" day. You know, 9.8 N/kg on September 8 (9/8). Get it? Well, the idea was for the physics students and faculty to build some stuff to do outside - projectile motion type stuff. Well, we had the idea a while ago and then kind of forgot about it.
In order to just get something done, I set up the "shoot the falling target" demo. (previously known as shoot the monkey). Here is a quick video demo (seriously - first take too).
What is going on here and what does this have to do with g? Well, it doesn't…

So, I hear you are starting your second semester of physics. One of the cool things about physics is that the second semester still uses stuff from the first semester. Maybe you forgot some of that stuff, so here are the bare essentials you will need to get by (this is assuming you are in the algebra-based second semester of physics)
Vectors
Really, just about the entire semester course is about the electric and magnetic field. Both of these are easiest to represent as vectors. So, you pretty much need to know how to deal with vectors. Here are some reviews:
How do you represent vectors…

Suppose I take a 1 kg ball and hold it near the surface of the Earth. What would be the gravitational force the Earth exerts on this ball?
And I could say "g" is:
The magnitude of this force would then be 9.8 Newtons. And, if I replaced the ball with a 10 kg ball, the force would be 98 Newtons. What does this have to do with the electric field? Well, you are probably already familiar with this idea of the gravitational force. Guess what? "g" is the gravitational field. Basically, it is the force per unit mass due to the Earth. This is only approximately constant. If I get very far…

Pre Reqs: vectors, forces
This is typically the first topic in the second semester of introductory physics - the interaction between objects with electric charge. There are 4 fundamental forces that physics typically looks at:
Gravity - an interaction between objects with mass - wow, I don't have a post on the universal law of gravity?
Electromagnetic - an interaction between objects with electric charge.
Weak Nuclear - an interaction between (let me just say for simplicity) leptons.
Strong Nuclear - an interaction between hadrons.
I know those last two are complicated - but I am not going…

Do you have an iPhone? I have an iPod Touch. Do you use vectors? Do you think RPN calculators are the bomb? Here is a RPN calculator for the iPhone that supports vector notation. VCalc by Silicon Prairie Ventures Inc. Oh - it is free. Here is a screen shot.
I played with it some, the only thing that would be cool would be a landscape mode.

Recently, I was talking about vectors. At that time, I had to stop and recall how I had been representing vectors. Ideally, I should stick with the same notation I used in Basics: Vectors and Vector Addition. But let me go over the different ways you could represent a vector.
Graphical
Maybe this is too obvious, but it had to be said. You can represent vectors by drawing them. In fact, this is very useful conceptually - but maybe not too useful for calculations. When a vector is represented graphically, its magnitude is represented by the length of an arrow and its direction is…

Suppose you want to move an empty paper clip box by shooting it with a toy dart gun. Why would you want to do this? Don't worry about that - this is my example and I am sticking with it. Should you shoot a dart that sticks to the box or should you shoot one that bounces off? I made a video of this exact situation. Note: you could obviously come up with other objects to do this with, but I always like to use more normal stuff.
In case it wasn't clear, the first dart bounced back and made the box go much faster (and farther) than the dart that stuck (inside) the box. The usual question is…

My dad and I had a disagreement. We were driving back from a trip and he let me take over the wheel for a while. His complaint was that I was driving too slow and it was driving him crazy. For me, I thought I was driving fast. My typical behavior is to drive 3 mph under the speed limit. That is just how I roll. In this case, I knew he wouldn't be able to handle this so I went the speed limit (70 mph).
Here is the problem. The speedometer said 70 mph. The gps thingy said the average speed was 69 mph. I think my dad feels that the gps is correct and that cars have speedometers that are…

**Pre reqs:** [Free Body Diagrams](http://scienceblogs.com/dotphysics/2008/09/basics-free-body-diagrams.php), [Force](http://scienceblogs.com/dotphysics/2008/09/basics-what-is-a-force.php)
The time has come to look at things that are NOT in equilibrium. The most basic question to ask yourself is: *"What do forces do to an object"*? Aristotle would say that forces make things move. Constant forces make things move constantly. Actually, Aristotle said there were two types of motion:
Natural motions: These motions don't need anything to happen, they just do. Example: a rock falling. You…

**Pre Reqs:** [Intro to Forces](http://scienceblogs.com/dotphysics/2008/09/basics-what-is-a-force.php), [Vectors](http://scienceblogs.com/dotphysics/2008/09/basics-vectors-and-vector-ad…)
Hopefully now you have an idea of what a force is and what it isn't. What do you do with them? The useful thing to do with forces is to determine the total force acting on an object. At the beginning of the introductory physics course, you will likely look at cases where the total force is the zero vector. This is called equilibrium. Even if you are looking at cases where the forces don't add up to the…

**pre reqs:** [Vectors and Vector Addition](http://scienceblogs.com/dotphysics/2008/09/basics-vectors-and-vector-ad…)
This was sent in as a request. I try to please, so here it is. The topic is something that comes up in introductory physics - although I am not sure why. There are many more important things to worry about. Let me start with an example. Suppose you are on a train that is moving 10 m/s to the right and you throw a ball at 5 m/s to the right. How fast would someone on the ground see this ball? You can likely come up with an answer of 15 m/s - that wasn't so hard right?…

**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…

I know the olympics are basically over. Really, I should have posted this earlier. Anyway, the gymnastics feat that always impresses me is the Iron Cross (I think that is what it is called). I know you have seen this, but here is a picture from wikipedia:
![Example 2ofironcross](http://scienceblogs.com/dotphysics/wp-content/uploads/2008/08/example-2…)
(http://en.wikipedia.org/wiki/Rings_(gymnastics))
Why is this so impressive? Why is this so difficult? Let me start with something completely different that is exactly the same (in some ways).
Here is a heavy box hung from a rope that has…