basics
goodmath | December 7, 2009
I've got a bunch of stuff queued up to be posted over the next couple of days. It's
been the sort of week where I've gotten lots of interesting links from
readers, but I haven't had time to finish anything!
I thought I'd start off with something short but positive. A reader sent
me a link to a post on Reddit, with the following question:
Throughout elementary and high school, I got awful marks in math. I always
assumed I was just stupid in that way, which is perfectly possible. I also
hated my teacher, so that didn't help. A friend of mine got his PhD in math
from Harvard before he was 25…
sporte | April 21, 2009This is a video that a friend made that shows, very clearly, how to pour an agarose gel, load the samples and run it. I especially like the way he used a bit of time lapse photography to show the dyes separating as the gel ran.
goodmath | March 4, 2009 After my post the other day about rounding errors, I got a ton of
requests to explain the idea of significant figures. That's
actually a very interesting topic.
The idea of significant figures is that when you're doing
experimental work, you're taking measurements - and measurements
always have a limited precision. The fact that your measurements - the
inputs to any calculation or analysis that you do - have limited
precision, means that the results of your calculations likewise have
limited precision. Significant figures (or significant digits, or just "sigfigs" for short) are a method of…
goodmath | March 1, 2009 Another alert reader sent me a link to a YouTube video which is moderately interesting.
The video itself is really a deliberate joke, but it does demonstrate a worthwile point. It's about rounding.
The overwhelming majority of us were taught how to round decimals back in either elementary or middle school. (I don't even recall exactly when.) The rule that most of us were taught is:
If the first digit after the rounding point is 0, 1, 2, 3, or 4, then round the previous digit down;
If the first digit after the rounding point is 5, 6, 7, 8, or 9, then round the
previous digit up.
Here…
rallain | January 20, 2009So, you are taking a college science course. Maybe it is physics, maybe it is chemistry, maybe its a lab. Either way, you always end up with these problems that involve unit conversions. You think you have the hang of it, but sometimes you make some mistakes. Here is my explanation for converting units.
Convert units? Me? Why? I have google. Yes, that is true, google (for the most part) does an excellent job at unit conversions. But....I doubt your instructor will let you use google on your test. Don't you think you should have a good idea of how to do it? Don't worry. Unit conversion only…
rallain | December 12, 2008Pre Reqs: momentum principle, forces,energy, vectors
Really, there is not much new here. This is an introduction to objects that interact. To describe this, I will need to pull several different ideas together (that you have probably already looked at). Let me start with a simple case. Suppose I have two objects, maybe they are two asteroids in space. I will call them asteroid A and B:
In this situation, the two objects have different momentums but one interaction between them. Notice that the gravitational force on asteroid A is the same magnitude but opposite direction as the force…
rallain | November 4, 2008**Pre Reqs:** [Work-Energy](http://scienceblogs.com/dotphysics/2008/10/basics-work-energy.php)
You need to be familiar with work and energy to understand this. If you are not familiar, look at the pre requisite link. Ok? Now, let's begin.
Suppose a ball moves from point A (3 m, 3 m) to B (1 m, 1 m) at a constant speed as shown in the diagram below:
Suppose there is some other force (like my hand) also exerting a force on this ball to make it move along this path at a constant speed. What is the work…
rallain | October 20, 2008**Pre Reqs:** [What is a Force](http://scienceblogs.com/dotphysics/2008/09/basics-what-is-a-force.php)
[Previously, I talked about the momentum principle](http://scienceblogs.com/dotphysics/2008/10/basics-forces-and-the-moment…). Very useful and very fundamental idea. The other big (and useful) idea in introductory physics is the work-energy theorem. Really, with work-energy and momentum principle, you will be like a Jedi with a lightsaber and The Force - extremely powerful.
Well, what is work? What is energy? How are they related? In [another post, I talked about energy.](http://…
rallain | October 16, 2008Maybe you know I like numerical calculations, well I do. I think they are swell. [VPython](http://vpython.org) is my tool of choice. In the post [Basics: Numerical Calculations](http://scienceblogs.com/dotphysics/2008/10/basics-numerical-calculation…) I used vpython and excel to do something simple. I will do that again today (in that this problem could also be solved analytically). However, there is one big difference. This problem has a non-constant forces. Suppose I have a mass that is connected by a spring to a wall. This mass-spring is sitting on a table with no friction.
, [Momentum Principle](http://scienceblogs.com/dotphysics/2008/10/basics-forces-and-the-moment…)
What are "numerical calculations"? Why are they in the "basics"? I will give you really brief answer and then a more detailed answer. Numerical calculations (also called many other things - like computational physics) takes a problem and breaks into a WHOLE bunch of smaller easier problems. This is great for computers ([or a whole bunch of 8th graders](http://scienceblogs.com/dotphysics/2008/09/…
rallain | October 9, 2008**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…
rallain | October 6, 2008**Pre reqs:** [Free body diagrams](http://scienceblogs.com/dotphysics/2008/09/basics-free-body-diagrams.php)
Friction is an interaction between two objects in contact that opposes relative motion of those two objects. It is not something fundamental (like gravity, or electromagnetic force), but it comes up enough that it will be worthwhile to talk about it. Let me start with a simple example. Suppose I have a book on a table. Here is the free body diagram for the book:
Simple enough - right? There…
rallain | September 30, 2008**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…
rallain | September 26, 2008**Pre-reqs:** None.
I intend to talk about forces and force diagrams, but there is a more fundamental question to address first. What is a force? Most texts define it as a push or a pull. That really isn't a bad definition. Maybe a better (or maybe worse) definition would be "forces are things that change the motion of an object" (change being the key word). If I had to choose one definition of force, it would be something like this:
**Force:** *A force is an interaction between two objects. There are 4 known forces:*
Gravitational force: An attractive long range force between objects…
rallain | September 24, 2008**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?…
rallain | September 21, 2008**pre-reqs**: [kinematics](http://scienceblogs.com/dotphysics/2008/09/basics-kinematics.php) *I don't think you need [part I of this](http://scienceblogs.com/dotphysics/2008/09/basics-making-graphs-with-ki…) if you don't want*
So, you still want to make a graph with that kinematics data? You think that graphs on paper are too barbaric? Well, if you are ready, you can use a spreadsheet. But be careful. If you don't know what you are doing, you can cause some damage (much like flying a 747 after reading a blog about it). Spreadsheets allow you to do a couple of things.
make pretty graphs…
rallain | September 18, 2008**pre reqs:** [kinematics](http://scienceblogs.com/dotphysics/2008/09/basics-kinematics.php)
Suppose there is some experiment in which you throw a ball up and collect position and time data (with video analysis). What do you do with this data? Your instructor told you to make a graph, but how do you do that?
Here is the fictional data you (or I) collected:
Here is the text file with the data if you want to reproduce the graphs I make here [kinematics data](http://scienceblogs.com/dotphysics/kinematics_data.…
rallain | September 16, 2008**pre-reqs:** *none*
I know who you are. I have seen you before and talked to you before. You are taking introductory physics and you are scared. Why does this have to be so difficult? It seems like there are a bazillion equations. Calm down, I will try to help. First, realize that algebra and trig are typically a pre requisite course for introductory physics. Your instructor probably expects that you have already mastered this material. Perhaps you did well in algebra (maybe you earned a B). But maybe you just worked hard and never really "got it". That is ok. There are many…
rallain | September 14, 2008**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…
rallain | September 5, 2008**pre-reqs:** [kinematics](http://scienceblogs.com/dotphysics/2008/09/basics-kinematics.php)
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.
Let me start with a generic, one-dimensional kinematic equation:
This relates the position (s), the velocity…