Tag vectors

Basics: Forces and the momentum principle

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**Pre reqs:** [Free Body Diagrams](http://blog.dotphys.net/2008/09/basics-free-body-diagrams/), [Force](http://blog.dotphys.net/2008/09/basics-what-is-a-force/), [Kinematics](http://blog.dotphys.net/2008/09/basics-kinematics/)

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 don’t need to do anything to it. Example: fire rising. It just rises. (there was more to it than that, but you get the idea).
  • Violent motions: These motions are due to some interaction that forces them from their natural state. The natural state of a cart is to be at rest. If someone pushes on it, it will move. When you stop pushing (stop the violent motion) it returns to its natural state – at rest

I am talking about Aristotle, because these basic ideas are what most people think. If you push something it moves. If you stop pushing, it stops. And these people are correct. The problem is that there is always this extra force that no one thinks about – friction. Without friction, the rules change.

**New Rules (Newtonian ideas)**

If you push something with one force, it changes velocity. If you stop pushing, it stays at a constant velocity.

If you want to test your feelings for force, [try this force game I made on Scratch](http://scratch.mit.edu/projects/rhettallain/285748). The idea is that you need to move the box to the red circle. The arrow keys exert a **force** on the object.

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Basics: Free Body Diagrams

rhettallain 1 Comment

**Pre Reqs:** [Intro to Forces](http://blog.dotphys.net/2008/09/basics-what-is-a-force/), [Vectors](http://blog.dotphys.net/2008/09/basics-vectors-and-vector-addition/)

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 zero vector (I say that instead of just “zero” to remind you that the total force is still a vector). Physicists like to represent forces on an object by drawing a Free Body Diagram. This is simply a representation of an object and a graphical representation of all the forces acting on that object.

Simply put, in a free body diagram, all the forces acting on the given object are represented as arrows. Let me start with a simple case, a box sitting on a table.

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Basics: Relative Velocity

rhettallain 1 Comment

**pre reqs:** [Vectors and Vector Addition](http://blog.dotphys.net/2008/09/basics-vectors-and-vector-addition/)

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? But let me draw a picture of this situation:

![Screenshot 15](http://blog.dotphys.net/wp-content/uploads/2008/09/screenshot-15.jpg)

The important thing is: If the velocity of the ball is 5 m/s, that is the velocity with respect to what? In the diagram, I listed the velocity of the ball as *vball-train* this indicates it is with respect to the train. There are three velocities in this example.

  • The velocity of the ball with respect to the train
  • The velocity of the train with respect to the ground
  • The velocity of the ball with respect to the ground

These three velocities are related by the following:

![relative v](http://blog.dotphys.net/wp-content/uploads/2008/09/relative-v.jpg)

**note**: The way I always remember this is to arrange it so that the frames match up on the left side. That is to say v(a-b) + v(b-c) – you can think of this as the “b’s” canceling and giving v(a-c).

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Basics: Vectors and Vector Addition

rhettallain 7 Comments

**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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The Iron Cross – or: Why is Gymnastics so Darn Difficult?

rhettallain 2 Comments

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://blog.dotphys.net/wp-content/uploads/2008/08/example-2ofironcross.jpg)

(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).

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