Thursday, December 24, 2015

Check out how Climate Models are put together and tested in order to have any confidence in them

This is a wonderful TED talk by a climate modeler named Gavin Schmidt. He explains what goes into the million line code that is the modern climate model  in terms of the science, and, most importantly, how climate scientists go about checking to see if the models are working. The method: take real data and trends, run the model with the appropriate initial conditions, and simply see if the output of the model looks anything like the real-world. This is how any type of simulation experiment works. When the model begins to become statistically consistent with real data, the model is called 'skillful.' Climate models have become skillful, as shown in this presentation.

What is really cool about having any type of reliable, tested, skillful model and simulation is that one can then make predictions. In the case of climate models, the user can put in any conditions and tweak as many parameters as they want, run the model over time, and see what the world will look like under those conditions. He shows this, as well, for three cases: cutting back on carbon emissions a little, cutting back on carbon emissions a lot, or doing nothing at all with things happening at current rates. What the world looks like comparing those three scenarios is eye-opening.

And, keep in mind that as scientists have fine-tuned the models using past data (and they go back tens of thousands of years), and tweak parameters based on the measurements, the way they get a world that looks like today's is by adding in the carbon emissions over the past century.

Monday, December 14, 2015

Physics Olympians

Old Olympiad exams...you'll want to check the F = ma exams and solutions. This is all about mechanics for the first round. This is the single best way of preparing for the types of questions and problems they put on this thing.

Mechanics videos on all sorts of topics, for review. They tend to put some rotations problems on, including parallel-axis theorem. Also simple harmonic motion, circular motion, and everything else that comes along with mechanics. There may also be a question or two about buoyancy. Check this out in the book, and an intro video.

Doc V's Olympiad page. Included on this are equation sheets to review (you do not get these on the test, though), mechanics objectives that may be worth reviewing over 10 minutes to remind yourself of all the possible topics, and an Olympiad syllabus, which is the packet given to physics Olympiad team members. This is a good review guide for mechanics.

Don't forget old AP exam problems, worked examples in the book, AP review books, and the chapter summaries in each chapter of our book. There is also the mechanics objectives, which is the point-by-point summary of everything we have had in mechanics. It is worth a 10 minute skim.

We can meet during 5th and 6th periods the week we return from break, and we can find a time during finals week. We will take the test on Monday, January 18, 9-10:30 am.

Sunday, December 13, 2015

Engineering-based Medicine

The University of Illinois at Urbana-Champaign has what is typically regarded as one of the top five engineering programs in the world, and next year the Carle College of Medicine will be the first medical school to be designed to fully incorporate engineering into its curriculum. Check out the site describing this new 21st century type of medical school, which will begin to contribute to medicine like UIUC contributed to the building of modern electronics in the 20th century.

If you are interested in medicine, engineering, or biomedical engineering, all aspects will be included in this new way of teaching, learning, administering, and doing medicine.

Saturday, December 12, 2015

Real life Rotational Physics!

Check out the article linked below...as the ice caps at the poles melt, much of the melt water makes its way towards the equator (why do you this is?). This is changing the mass distribution of the earth to some small degree. Another name for the distribution of mass relative to an axis of rotation is the moment of inertia, or rotational inertia. This is causing changes in the earth's rotation. Think fast before reading the article: If the water moves towards the equator, what should happen to the period of the earth's rotation?

See if you are correct!

Wednesday, December 9, 2015

Python Activity for Today: Using Python code to fit data sets, and 'discover' Dark Energy!

Up to now, we have begun to learn some basics of Python using Codecademy, then we began to use Python to develop simulations of a bouncing ball (how to put equations of motion into a program) and a double pendulum (which we cannot do with pencil and paper, and included a focus on making graphs and animations in a program). Today, we will use a Python program to analyze data, which happens to be the data used to determine the acceleration of the universe and prediction of Dark Energy.

The activity for today is here. We will open Canopy to do this, as in the past.

If you are interested in the physics behind all this, dark matter and dark energy are not the same things. Dark matter is a term used for matter we cannot see. It could be a mix of several things, such as 'ordinary' matter and some new types of matter, that we cannot see directly but presume it is there due to its gravitational effects on things like galaxies. Dark energy is a term used for whatever it is that makes the expansion of the universe accelerate - we do not know what dark energy is. Of course, there is the scientific model for how the universe began and why it is expanding in the first place, the Big Bang.

Minute Physics video on Dark Matter.
Minute Physics video on Dark Energy.

Thursday, December 3, 2015

Classes for Period 3-4

Today, check out the first half of "Runaway Universe," which is about the strange acceleration of teh expansion of the universe we have mentioned in class.

Then, take notes on situations where BOTH linear and angular momentum are conserved. This would be like hitting a pencil on a table top off center - it will both move forward and rotate as it goes. The two problems for tonight involve these concepts. The video is here.

Wednesday, December 2, 2015

For Afternoon classes

Happy Wednesday! Who's got it today?!

Watch and take notes on a video about potential wells. These are represented by graphs of potential energy, U, as a function of position, x.

The way to interpret this is to imagine a particle stuck at the origin of the graph, and then a second particle is moving around at different distances. The graph plots out the energy between the two particles at those separations.

On a U-x graph, we can also identify two types of equilibria - stable and unstable. Stable would be at the bottoms of dips, and unstable would be on hilltops of these graphs. Remember, Nature seeks lowest energy states.

Mathematically, we will be using the new gradient concept, F = -dU/dx. Force graphs can be drawn based on what the slopes are doing on the potential energy graph. Remember, dU/dx = slope of the energy graph!

After the video, you can get working on the spring lab. We are interested in measuring the stretch caused by different masses. The main product of the lab will be the graphs of F vs. x, where x = the stretch distance, or displacement, of your springs.

For homework, complete any parts of the lab that remain, and also write up a short summary of an article you find interesting. Thanks!

Wednesday, November 18, 2015

Python Activity - Double Pendulum (Chaotic system)

This activity builds off of the last one, where we begin to see and use an actual Python program to simulate the motion of real objects. Last time we looked at a tossed ball that bounces. Not only did we begin to see how to insert equations that the simulation runs over and over to calculate the points where the ball goes from time step to time step, but also had animations of the bouncing ball. That program is now a template for us to use - we can change the equations we put into the program in order to simulate other objects besides a bouncing ball.

This time, we will use a simulation for a more complicated type of motion, the double pendulum. This is a pendulum hanging from a pendulum. If we tried to calculate and plot points for this system, we could not do so by hand since it is too complicated (and also a chaotic system). So this is a case where we really do need a computer to solve the motion numerically so we can find out what it does. The activity for today is here. Some years ago, a former student wrote his own simulation for this, where he simulated two double pendula hanging from a rod, so they affected each other via vibrations through the rod (called coupled double pendula). His paper is is here if you are curious.

Thursday, November 12, 2015

Classes for November 16

Happy Monday, everyone!

4 Chem-Phys:

Take a couple minutes to compare work and answers on the multi-loop circuit problems. When you are OK with those, watch three short videos, and take good notes on both:

i. How do Kirchhoff's rules lead to the resistor rules for series and parallel? Hopefully this will make sense and you'll see where the weird reciprocal rule comes from for parallel.
ii. How do Kirchhoff's rules change for capacitors, and what are the rules for adding capacitance in a circuit? Turns out we have the same two rules as for resistors, but they are swapped.
iii. What are capacitor (only) circuits and how do we solve them? Keep in mind the main thing we will be looking for with capacitors is how much charge is stored by each capacitor in the circuit. The approach is basically identical to finding currents in resistor circuits: Find total capacitance, find total charge with Q = CV (this is like Ohm's law for capacitors), then redraw the circuit as a series circuit - each capacitor in series has the same total charge on it, and then you can find the voltage for the parallel branches using V = Q/C.

Keep in mind that there is a new unit for capacitance, called the farad (F; named after Michael Faraday). One farad is defined as a device that can store 1 coulomb of charge by using a 1 volt battery to hold that charge on the capacitor. A 1 F capacitor is actually quite large...you will see units of microfarads, and even as small as picofarads, in real devices.

After watching these, break into groups and you can try the following. There are no hard copies of the problems, but you can pull up an online version of the book on the screen. To do this, do the following:
Go to the Mastering Physics site.
Username = ethsphysics; PW = ethsphysics1
You can type in 812 in the page box at the top to get to the problems below.

HW Set for Tuesday: Chapter 24, Exercises #15, 16, 17, 21 on page 812, and 63 on page 815.

AP Physics C:

Take a few minutes and talk through the homework problems together. Are these torque problems making any sense to you?

Watch a video on equilibrium with rotations involved. Take good notes, and realize there is one new condition to equilibrium: not only do we balance forces in each dimension, but now we need to balance torques if there is an axis of rotation.

HW Set for Tuesday: Ch 11 #13, 19 (page 7 of packet)
Ch. 11 Either #46 or #70 (page 8)
Torque brain teasers (page 9 of packet); reach class consensus
If you have any time left over, definitely feel free to work on your lab. We are looking for the lab report on Wednesday.

I will see all of you Tuesday!

Wednesday, November 11, 2015

Classes for November 12

4 Chem-Phys:

Welcome back! I hope Chemistry went well this past unit; hopefully you had the correct solutions to your test.

We are going to get into circuit analysis, where we will be most interested in learning the basic rules of resistor circuits (we were introduced to some of these last time). We now have 'discovered' Ohm's law, V = IR. We also were given the rules for series and parallel resistors: R_s = R1 + R2 + R3 + ... and R_p = (1/R1 + 1/R2 + 1/R3 +...)^-1.

There are two other even more important and fundamental rules for circuits of all kinds (at least the types we will study this year), called Kirchhoff's 2 rules.
1. In series, all voltage losses will add to the total voltage put into the circuit (i.e. the battery voltage), or V_total = V1 + V2 + V3 + ...
2. In parallel, the currents in the branches add up to the total current that went into the parallel set, or I_total = I1 + I2 + I3 + ...

Keep in mind that in series, there is ONE CURRENT going through everything on that path.

In parallel, EACH BRANCH HAS SAME VOLTAGE DIFFERENCE across it, and each branch can have different currents.

A few have suggested checking out a video on Band Theory, just to (hopefully) have a clearer sense of where energy bands come from. This may help with understanding conductors from insulators and semiconductors a little better.
More importantly for now, check out the video on how to analyze a combination circuit; the main goal is to figure out how many amps of current flow through every part of a circuit.

Take good notes, since these introductions to the rules will be used over and over again, not only with resistor circuits but also circuits with capacitors and inductors. In fact, the Kirchhoff rule for series (about voltage losses adding up to the input voltage) is, for us, the most important rule of all, and will allow us to write equations down for every circuit we work with.

For HW, try the circuit problems on page 5-6 of the packet; start error analysis of the last quizzam (solutions are online, in Gauss folder).

Thank you for all your support and understanding, as my family has gone through this episode with my mother! You will never know how much it means to me. I will be out Friday, which should be the last day. See you soon!  :-)

Sunday, November 8, 2015

Classes, Nov. 9 and 10

3 Chem-Phys:
To get ready for the quizzam on Tuesday, there are practice problems on Doc V's 3 Ch-Ph school website. In the Newton's laws folder, there is the file Review set, which has questions/problems and solutions. There are general F = ma problems, and a couple circular problems, including a banked road. In the Gravity folder, there is a file Review set - PR Gravity with some practice questions. There is also a problem (don't worry about the elliptical orbit problem). There is a separate file with solutions. Also, don't forget there are numerous worked examples in your book, additional odd problems you can try and check yourself, and so on. There are videos on: binary orbits; circular motion problems; gravitational potential energy (with escape velocity and Schwartzshild radius of black holes); tension problems.

AP Physics C:
To get ready for the quizzam on Tuesday, there are practice problems on Doc V's AP Physics C mechanics website. In the momentum folder is a file Review Set - PR momentum. There is a separate file with the solutions. Work on these, any of the problem sets or AP problems (don't forget the AP Exam folder and the solution folder). In your book, there are numerous worked examples and other odd problems to try and check yourself. There are videos: momentum conservation; inelastic collisions.

For everyone: If you want to look at other AP exam examples for any type of problem, check out the file in the AP Exam folder called AP_Review_Mechanics_Problems_by_Topic_and_Year, where you can hopefully identify some problems in a hurry. This is the last file in the folder - scroll to the bottom.

Good luck on the quizzams. I should see you on Thursday.

Wednesday, November 4, 2015

Python Simulation Activity II: Double Pendulum

This activity builds off of the last one, where we begin to see and use an actual Python program to simulate the motion of real objects. Last time we looked at a tossed ball that bounces. Not only did we begin to see how to insert equations that the simulation runs over and over to calculate the points where the ball goes from time step to time step, but also had animations of the bouncing ball. That program is now a template for us to use - we can change the equations we put into the program in order to simulate other objects besides a bouncing ball.

This time, we will use a simulation for a more complicated type of motion, the double pendulum. This is a pendulum hanging from a pendulum. If we tried to calculate and plot points for this system, we could not do so by hand since it is too complicated (and also a chaotic system). So this is a case where we really do need a computer to solve the motion numerically so we can find out what it does. The activity for today is here. Some years ago, a former student wrote his own simulation for this, where he simulated two double pendula hanging from a rod, so they affected each other via vibrations through the rod (called coupled double pendula). His paper is is here if you are curious.

Tuesday, November 3, 2015

For 3 Chem-Phys, watch the video on binary orbits. Take detailed notes on this, and feel free to go through any portions of it again if necessary. The homework problems will revolve around the video. After the video, you can work on those problems, and also you can get into your lab groups and work on the lab report. Remember that the report depends on the best-fit functions you get for the four graphs of data.

For AP Physics C, you can work in smaller groups of 3-4 and get data from the ballistic pendulum device. While you can get the data together and work together to ensure you are understanding the principles behind it, you should each write it up separately. As you rotate through getting data, you can work on the homework set, as well as the lab report for the air track data. The ballistic pendulum mini-lab is due Wednesday, the air track lab on Thursday. If anyone needs a review, there is a ballistic pendulum video going through the principles.

Tuesday, October 20, 2015

Python Programming Activity I: Bouncing Ball

Today we will actually try to modify a Python script written by Mr. Dempsey. The full exercise is on his website, and can be found here. Give it a try, help each other out, and do not hesitate to ask him questions. Also, pay attention to the techniques being used to actually do a simulation - these are built upon the concept of a time step. This is all outlined in this activity. Good luck!

Monday, October 19, 2015

Electric potential for shells

There are worked examples for finding the electric potential when you have shells of charge, as well as materials that are charged.  Check it out on the web page, it is entitled "Potential - Shells and Integration."

There is also a video on this with thin shells.

Wednesday, October 14, 2015

For Classes Thursday and Friday, Oct. 15, 16

For 4 Chem-Phys classes (1-2, 8-9):
On Thursday, begin with volunteers to be at the board and, as a class, reach consensus on the homework problems. In particular, you can pull up the solutions for the 2002 AP problem with the partial ring of charge. Go through these with small groups if there are questions, and talk them through.
Once done with the problems, you can begin the lab on equipotential lines and gradients. Before starting, Lucy (in period 1-2) and Danny (in period 8-9) will demonstrate how to get your data. You will ultimately make maps of equipotential lines on the white grid paper...do not draw on the black conductive paper. You should have time to get your data today, and any extra time can be spent working on the analysis.

On Friday, start off by doing the two collaborative problems, and turn them in before leaving. The rest of the time you have to work on the lab - keep in mind that you should individually do and turn in the AP problem, and do the ActivPhysics simulations on equipotential lines. Use Internet Explorer on the school computers, which seems to work better than Chrome or Firefox. If you are unable to complete the simulations here, finish it up over the weekend.

Over the weekend:
Take a look at the video, and take notes, about finding electric potential with multiple shells of charge. We will bring in voltage with the Gauss's law next week.
If interested, there is a video on band theory, which may help understand where the 'bands' come from.

For AP Physics C (3-4):
On Thursday, begin with volunteers to be at the board and, as a class, reach consensus on the homework problems. After that, watch and take notes, and discuss if necessary, a video on potential wells. This refers to graphs of potential energy as a function of position, and also makes use of the gradient concept F = -dU/dr.  When this is done, you have time to work on the homework set for potential wells (last page of packet), and also to try and complete the lab. Whatever is left, take as homework.

On Friday, reach consensus on the AP problems on potential wells. Pull up the 1995 'Nike' problem solutions if you all wish.
When this is done, watch the DVD on string theory. This is part 2 of The Elegant Universe. Take notes on it, since we will get into modern examples next week. Finish up any lose ends of the lab before leaving.

Over the weekend:
Watch and take notes on the video about gravitational potential energy.

Friday, October 9, 2015

Ladies, there is a competitive, full-tuition scholarship possibility through the Science Ambassador Scholarship program. This is for women who major in STEM, and could be for up to four years. Check it out if interested!

Wednesday, October 7, 2015

Nobel Prizes for 2015

Check out information on the 2015 Nobel Prize in Physics, for the discovery that neutrinos have mass. This was a major discovery in particle physics, since it showed direct evidence that neutrino oscillations can occur. Prior to that, neutrinos were thought to be massless and travel at the speed of light.

Check out information on the 2015 Nobel Prize in Chemistry, for work done on understanding how DNA repairs itself in a complex chemical environment known as a cell!

Check out information on the 2015 Nobel Prize in Physiology or Medicine, for work on understanding and attacking disease/infections from parasitic worms, as well as work on a novel therapy against malaria.

Friday, October 2, 2015

Classes for today.

Sorry to miss all of you on a Happy Friday, but there is an unexpected family matter I am attending to. Please take advantage of this time, however, to work with each other and get some of these Newton's laws problems that may have been confusing you more solidified in your mind, and also to get some work done with your lab group.

3 Chem-Phys classes:
- Try to reach a class consensus on the setups for the circular motion problems from last night. Please have a few volunteers come up to show their setups, and talk it through with each other. Note that there is a video with several circular motion examples, including the setup for a banked racetrack situation. Watch it if you would like to see examples again if some of this is confusing - hopefully the video will help.

- In the packet, try AP Problems from 1984 (stick to the wall ride) and 1988 (banked road - this tends to be the most challenging for students, see the setup in the video if you are lost!).

- If you want a head start on a review set for Newton's laws that we will focus on Monday, click here. It has the practice problems and multiple choice, and full solutions.

AP Physics C class:
- Work together on some gravity problems, copies of which the substitute has. Ch 13 #1,5,6,11. These have to do with the law of gravity, F = GMm/r^2.

- You can work with your lab group on your report for Monday. Leave out for the moment the procedure with the electronic force sensor. We will do this together on Monday, and can add it in as a class.

- If you want a head start on a review set for Newton's laws, which includes circular motion, we have the set from last time here.

Thank you, everyone! Again, do take advantage of the time to try and get things firmer in your brains. :-)

Friday, September 18, 2015

Interesting Mechanics Challenge: Pulling a Bicycle with a Rubber Band

Check out three situations of pulling a bicycle with a large rubber band. Think of the force diagram, and predict which way the bike should move. Then, check your prediction with the video of each situation. How did you do?!?!?

Review sets

For 4 Chem-Phys, you can work on an electrostatics and Gauss review set here.

For AP Physics C, you can work on a Newton's laws review set here.

Tuesday, September 15, 2015

Gauss's law videos to check out

FOr 4 Chem-Phys, check out a video on Gauss's law for conductors, and see if you can do the 2008 AP problem for Thursday. We will also look at Gauss's law for non-conducting materials, so you may want to have a preview.

Friday, September 11, 2015

Relevant videos

For the 4 Chem-Phys group, check out a video on an electrical version of projectile motion, where a constant E-field replaces gravity from a 'normal' projectile problem. For a review of finding E-field vectors and electric potential at a point in space due to point charges, check out this video.

For the AP class, if you need to review our process for solving systems, check out this tension video.

Enjoy the weekend!

Monday, August 24, 2015

WELCOME BACK!!!!

Welcome back to ETHS for the 2015-16 school year!! We will have a LOT of fun while learning a bunch of physics and how it relates to your lives and to the way the universe works.

Doc V's schedule is:
3 Chem-Phys periods 1-2, 6-7, 8-9
AP Physics C periods 3-4
Free period 5

Friday, August 21, 2015

Pendulum Lab Training Video for CT-STEM

One of the lessons for the CT-STEM Project in physics is a classic, that most physics classes will do in mechanics: the simple pendulum. While this is a 'simple' experiment to run, this video outlines how to add in numerous computational thinking (CT) skills, which in turn will also address a number of bullet points within the Next Generation Science Standards (NGSS).

One point of emphasis is to have students do labs like this before formally studying the subject - we want students to do more of the process of science, and discover rules and principles of phenomena on their own, where these findings and student questions about the lab drive classroom discussions. In this case, students will need to do up to four individual controlled experiments to determine how the period depends on mass, length, angle, and the strength of gravity. By making plots, and finding best-fit functions through curve-fitting, students will develop an empirical formula (i.e. a mathematical model via data) for the period of the pendulum. They can then compare it to the accepted textbook formula, and get into good discussions of experimental uncertainties, scientific inquiry, building mathematical models, being critical of data, experimental design and methods, and so on.

It is also mentioned in the video that teachers can have students evaluate the effectiveness of measuring techniques - for one experiment use a stop watch, for a second an electronic force sensor, and a third video - for the period. And then, for gravity, the usefulness of computer simulations, using a PhET pendulum simulation.

Ohm's Law Lab Training Video for CT-STEM

One of the physics activities for the CT-STEM Project at NU is an Ohm's law lab. While not terribly complicated for students to do, the main point being made is for teachers to have students try this lab as a first-step when beginning a unit on basic circuits. Most students have little electricity knowledge or experience, and most have not heard of Ohm's law. By having students do this first, they can use real data to 'discover' how resistance and voltage affect electric current. Best-fit functions of those data will allow students to at least reach some conclusion of an empirical formula, which should be close to I = V/R.

This type of process, where labs are done first in units and students use data to find empirical relationships and equations through the use of computational thinking skills, will truly help our efforts addressing Next Generation Science Standards (NGSS).

An additional chance to apply computational thinking skills to this lesson is this PhET video on Ohm's law (especially if a school does not have the equipment to do the physical experiment), or a Netlogo simulation for resistance, where an electron can be isolated as it bounces its way through material.

Thursday, August 20, 2015

CT-STEM Lesson Notes: PhET Resonance Computer Lab

With science classes around the country being responsible for the Next Generation Science Standards  (NGSS), teachers will need to develop more labs and activities that get students doing the process of science, rather than learning just science facts and being given information - students will need to 'discover' some portion of the material studied in the class.

This example is for a computer-based lab from the PhET library, and it deals with a topic students will almost certainly not know, resonance. Students can do a series of controlled experiments, trying to see what combinations of mass, spring constant, amplitude, frequency, and even gravity, have on the system reaching a resonance state, where the oscillator and mass are in phase with each other. Being a computer simulation, there are also numerous computational skills and concepts that are addressed.

Variations of this could include students making a screencast of their experimental sessions, and then using Tracker or another video analysis package to get finer details and measurements, by having frame-by-frame options and so on. This type of simulation exercise can allow for many good conversations about experimental design, data collection (especially when the springs are going through transient phases in the simulation), and reaching conclusions when there are multiple physical parameters that might affect the spring oscillations. All of these types of skills and experiences fall under NGSS, and these are all computational thinking skills on top of it.

Whether it is this specific lesson or not, teachers can set up numerous other simulations in the same way to develop a set of CT lessons that address NGSS requirements.

How to do Video Screencast and Analysis of a Video Game to Determine the Physics

One of the primary tools STEM classes have to analyze various phenomena is video. With the cameras on cell phones, for instance, many new devices have high-speed options for video, such as up to 120 or 240 frames per second (fps). The same for most cameras and camcorders one can purchase as the prices come down.

This video gives another fun option to do some physics while playing video games. When playing an online game, you can use Screencast-o-matic to create a screencast video of you playing the game for a few seconds. Screencast-o-matic is nice because you can use it for free and do not have to download anything - just click 'Start Recording' and it begins!

With that video, you can import it into a program called Tracker, which can be downloaded onto your computer for free. Some schools may have Logger Pro, which is the software for Vernier sensors, and that has video analysis capabilities. Whatever the tool, check this out to see how Tracker can be used within a few minutes to get data for the game Asteroids, to find the speed of the spaceship. You can set size scales to make the scene as realistic as you wish. In the case of Asteroids, you can look up average sizes and densities of asteroids, find the size within the video game based on your size calibration and scale, and then determine the masses of asteroids. You could look up and use a reasonable size and mass for a spacecraft (many often use the space shuttle, looking it up in Wikipedia). Then, with those data, you can calculate speeds from motion graphs in Tracker, which leads to accelerations, forces, momenta, kinetic energies. You could calculate the gravitational forces between asteroids and your ship - are those significant? If so, does the video game account for those forces, or is gravity ignored? You could have some fun and calculate how much you would weigh on one of the asteroids, and what the escape velocity is - would you be able to jump off the asteroid and into space?

You could do a similar process and analysis with a billiards video game - and then determine from measurements in Tracker whether or not momentum is conserved, or if energy is conserved, and so on. You could also take video of a real game of billiards, or anything in life that has motion, and begin analyzing the video to see the physics! It is a really useful and powerful tool we can use for anything in life and any experiments we do in class. I hope this helps!

Thursday, August 6, 2015

Water Use and Aquifers in the U.S.

A new study from a research group at the University of Illinois at Urbana-Champaign (UIUC) and Lehigh University, led by civil and environmental engineers, have tracked water use taken from three of the most used aquifers in the U.S.  Fresh water is, of course, becoming an issue in the U.S. as well as around the world as the population is expected to go from a little over the present 7 billion people to 9 billion people by 2050. Understanding how and where the water taken from all supplies, particularly those from the more major water sources such as these three aquifers, is vital for policy makers as they plan for the future. There are all sorts of tradeoffs that come with such decisions, and this is where politics will play the key role in deciding who gets what with our most precious resource. This involves where and how many people can settle in communities, agriculture, economies (both local and global), a huge variety of industrial uses, and transportation; all of these sectors of our society have large lobbies that will try to sway votes to their cause, so one can imagine the pressures decision-makers are under and will be under in the next couple decades.

Check out an article about the study here. There is a nice graphic that helps understand where the water goes. The published study can be found here. This is a good way to see another aspect of what engineers do.

Thursday, July 16, 2015

Particle physicists find a Pentaquark particle

Back in the day, when I was at Fermilab, there had been a number of people who continued to speculate and predict the existence of a strange sort of particle, that could be formed from 5 quarks. Now, I use the word strange because in our lives, we only see two types of particles formed from combinations of quarks.

All particle made of quarks are referred to as hadrons. But there are then two main types of hadrons: mesons and baryons. Mesons are combinations of two quarks (a quark-anitquark pair), and baryons are made form three quarks. The quarks are held together by the strong nuclear force. You are made from electrons and baryons, better known as the proton (two up quarks and one down quark) and the neutron (two down quarks and one up quark), for instance.

No one has ever had confirmation of different combinations of quarks, until now. Check out the actual article published from CERN. Keep in mind that pentaquark particles are allowed and have been predicted for decades from the Standard Model, the main theory explaining all we know about particles and the forces between particles.

Monday, July 6, 2015

Check Out Some Real Astrophysics

Prof. Shane Larson is working with some Chem-Phys students on their research, and check out his notes from a Northwestern astrophysics class. The math is something we can do with first-year calculus, and he does a really good job of explaining and deriving some of the important results astrophysicists use! Nice job, professor!

Wednesday, June 10, 2015

Check out Powers of Ten.

Check out ActivPhysics.

Tuesday, June 9, 2015

Update on ITER (Thermonuclear fusion reactor)

The International Thermonuclear Experimental Reactor (ITER) is under construction in France. Here is an article updating how a reorganization of its leadership is refocusing its efforts to determine if the ultimate fantasy in energy production - harnessing the energy process of the Sun for human use - is technologically possible in a reactor. This was supposed to have been built in the U.S. originally, but funding was cut under the Bush administration. I personally am hoping there is a big U.S. scientific presence with this international collaboration, because of its importance in the long-term of our energy hungry civilization. This one is worth keeping an eye on the next few years...

Friday, June 5, 2015

Girls with Toys at UIUC Engineering

The Girls With Toys movement is alive and well at the University of Illinois at Urbana-Champaign. Check out their site here. This has been a wonderful attempt to get more women involved in STEM, with an emphasis on the 'E' for engineering. Keep in mind that UIUC Engineering has 15 top 5 programs, and this is a launching pad for engineering students into top positions and careers. I am always happy to plug my alma mater.   :-)

Sunday, May 31, 2015

Neil Tyson on a Deep Thought About Our Intelligence

I found this particular set of thoughts from Neil deGrasse Tyson really interesting and thought provoking. Think about this notion of if humans are only 1-2% different genetically different from chimps, and what this means in terms of how much more advanced we are from them, then what if there is some organism out there that is some very small percentage different from humans, in the direction of increased intelligence...then we humans would be their chimps! They would be SO far ahead of us, it is difficult to comprehend how much more advanced those beings would be. I have never thought about this, but what a truly intriguing thought!

Thursday, May 28, 2015

Read about Emmy Noether, a Great Mathematician and Forgotten Hero of Relativity - largely because she was a Woman

A wonderful summary of how Emmy Noether helped other great mathematicians get a handle on Einstein's General Relativity back in the first quarter of the 20th century can be found here.  Many of her contemporaries, including Einstein, suggested she is the most important woman in the history of mathematics. What is now known as Noether's theorem is at the heart of all physical theories, which states if there is a conservation law, then there must be a quantity that is invariant, and vice versa. For GR, she basically showed energy is still conserved, but it is much more challenging to see it, compared to classical systems and theories, because of the warping of spacetime by mass-energy densities.

Thursday, May 21, 2015

Putting the 'A' in STEM to get STEAM

Former Chem-Phys student Sarah Posner is in the U. of Michigan's Stamps School of Art and Design, and has some wonderful work posted on her Tumblr site. Check out many of the pieces that have a science and symmetry influence. The notion of design, especially in engineering, is a big deal, as well as some of the naturally beautiful patterns and objects scientists study - this is the push behind changing STEM to STEAM. Regardless of what to call it, just enjoy some wonderful art from a talented young lady!

Monday, May 18, 2015

Check Out Neil deGrasse Tyson on Bill Maher's Show

I had the pleasure to be at teh dinner at President Schapiro's house at Northwestern last wek, which was in honor of the evening's lecturer, Dr. Neil deGrasse Tyson. It was a wonderful time, of course, and Dr. Tyson gave a wonderful 2.5 hour popular talk about science, the media and how it reports science, modern issues in the U.S. and the world, and so on. Here is the link to the Maher interview.

Tuesday, April 28, 2015

Magnetism Check List

As the AP exam nears, here is a magnetism check list. Check it out - what do you need to review? Am I forgetting anything? There is also an EM Induction check list.

EM Magnetism Check List

-         Where does magnetism come from?
-         What are magnetic monopoles?
-         Do you know which way magnetic fields ‘flow?’
-         Can you draw magnetic field lines for different arrangements of magnets?
-         Can you use RHR and LHR to determine which way charged particles will get pushed?
-         Can you use F = qv x B and F = Il x B?
-         Why do charged particles go into circular paths when in magnetic fields?
-         Are you comfortable with mv2/R = qvBsinÎ¸?
-         What is a mass spectrometer?
-         What is a velocity selector?
-         How do you calculate the mass of particles in mass spectrometers?
-         When do particles move in spiral/helical paths in B-fields?
-         What are magnetic domains?
-         Why do magnets generally get weaker with heat? When striking or dropping the magnet?
-         Can you define Ampere’s law?
-         Can you use Ampere’s law for long wires? Long solenoids? Toroids?
-         What is current density?
-         Can you find B-fields inside wires with a uniform current density?
-         Can you find B-fields inside wires with a non-uniform density?
-         When and how do you use the curly RHR? Remember this is for the relationship between currents and B-fields those currents create – one is linear, the other circulates
-         How do you conceptually prove currents running through parallel wires in the same direction attract, and in opposite directions repel?
-         How do you find the strength of the magnetic force between wires with currents?
-         Can you define the Biot-Savart law?
-         How do you use B-S for wires with ends and for loops of currents?
-         How do you use B-S for moving charged particles?
-         What is Gauss’s law for a magnet (i.e. the total flux through a closed surface)?
-         What are superconducting magnets?
-         How do we make permanent magnets?
-         What creates the earth’s B-field?
-         How are auroras created at the poles?

-         From chemistry, what are ferro-, para- and diamagnetic materials?

Monday, April 20, 2015

Check out Richard Feynman talking about various subjects!

Had it not been for Einstein, Richard Feynman, in my mind, is likely the genius of the 20th century. Check out a series of videos of him casually discussing different phenomena, all from a conceptual, physical point of view. It is really interesting how he thought about things. Of course, he was then a magician with math, and could take his physical pictures and models and represent them with the math!

Friday, April 10, 2015

Classes on April 13, 2015

For periods 1-2 and 8-9:

Check out the quiz from before break, and talk through anything you may have missed with others in class. Then, check out and take notes on a video on something called the parallel axis theorem. This is a neat 'trick' for finding moments of inertia of objects, where the axis of rotation is NOT the center of mass, without having to do an integral - the only thing you need to know is the 'normal' moment of inertia for an object, where the axis of rotation is the center of mass. This can be useful for trickier problems and situations.

Next, check out an introductory video for simple harmonic motion. Take good notes, since the homework set will be based on the results.

For Periods 3-4:

Check out the quiz from before break, and talk through anything you may have missed with others in class. Then, check out a video (and take notes) of finding the flux via an integral. Next, check out an introductory video for our last type of circuit, where an inductor and capacitor are combined into a LC circuit. The homework set has to do with these two videos, so, again, take good notes. We will pick up on all this Tuesday.

Friday, April 3, 2015

Have a Wonderful Spring Break!

Everyone have a great break, and catch up on sleep to re-energize for the final sprint to the end of the year! You have earned it. And good luck to the WYSE team, which competes at the state finals the day back from break.

Monday, March 30, 2015

Classes March 30, 2015

For periods 1-2 and 8-9, check out and take notes on angular momentum conservation in collisions involving rotations. One of the videos gives two examples of conservation of angular momentum: click here.  A second video is similar to a ballistic pendulum: click here. From our angular momentum packet, try page 3 1981; page 6; page 7 2005.

For periods 3-4, check out two videos on circuits involving inductors. Keep in mind, these are, mathematically, at least, similar to RC circuits.  Take notes on each video. The first is when things are in series: click here.  The second is when an inductor and resistor are in parallel: click here. From the new inductor packet, try page 2 2005; page 5 1991; and page page 6.

Saturday, March 21, 2015

EM Induction Check List

Check out the check list:

EM Induction Check List
-          Can you define magnetic flux?
-          Can you define induction (in general)?
-          Can you define emf?
-          Do you know what Faraday’s law is mathematically?
-          Do you know the two main ways of changing magnetic flux?
-          Do you know why the – sign is placed in Faraday’s law?
-          Can you state Lenz’s law?
-          Can you apply Lenz’s law for increasing flux? Decreasing flux?
-          Do you know what happens to a conducting rod moving in a B-field?
-          Can you find the E-field strength in a moving conducting rod in a B-field?
-          Can you explain why a current turns on when the area is changing (i.e. the loop/circuit is moving)?
-          Can you explain why a current turns on when a B-field is changing (i.e. dB/dt)?
-          Can you find emf, current, IL x B forces, v(t), power, and heat energy when the loop/circuit is moving and the area is changing?
-          Can you find emf, current, IL x B forces, power, heat energy, and the induced circulating E-field when there is dB/dt?
-          Do you know what an inductor is?
-          Do you know what an inductor does in a circuit? And why?
-          Do you know how to find the energy stored in an inductor?
-          Can you derive i(t) in a series LR circuit?
-          Can you figure out the currents in a LR circuit when L and R are in parallel?
-          Do you know what happens when there is a LC circuit?
-          Can you determine a solution for q(t), i(t), di/dt in a LC circuit?
-          Can you find the frequency of oscillation of current in a LC circuit?
-          Can you explain, at least qualitatively, what resistance does in a LRC circuit, compared to an ideal LC circuit?
-          Can you explain the gist of how a radio works (or wireless technology in general), in terms of LC circuits?
-          Can you explain what the Maxwell displacement current is?
-          Do you know what the four Maxwell equations are?
-          Can you qualitatively explain how you can create an electromagnetic wave?
-          Do you know what a transformer is, and how it works?
-          Can you explain how various contraptions work in terms of em induction (think of all the devices in our lab)?

Friday, March 20, 2015

EM Induction Videos

Here are links to the videos relevant to EM Induction.

Here is a magnetic flux example, where a circuit is next to a long wire.

The simplest case of induction is just a conducting bar moving through a B-field. The B-field will polarize the rod, due to F = qv x B. To spice it up, you can rotate the bar in a B-field.

For Faraday's law of induction, the version emf = -B dA/dt.
For Faraday's law of induction, the version emf = -A dB/dt. Also with this version of Faraday's law is how to find the circulating electric fields that are induced when we have dB/dt.

Here's an example of a circuit falling through a B-field, and the magnetic braking force can lead to a terminal speed.

When we put solenoids in circuits, they are called inductors. Here's a series LR circuit.
Here is a LR circuit with the inductor and resistor in parallel with each other.

The last circuit we do is an LC circuit (inductor and capacitor in series with each other).

Finally, here is one about Maxwell's displacement current, which he needed to explain how capacitors really work and to complete Ampere's law.

Wednesday, March 18, 2015

For Classes, March 19, 2015

Periods 1-2, 8-9:

Watch and take notes on the two videos for so-called RL circuits. These are circuits that have an inductor, which is basically a solenoid, with a resistor. The symbol L stands for inductance, and it has a unit called a Henry (H). Yes, another name!

One thing that stands out as you watch these is the math analysis - it should look like RC circuits.
Check out the video on RL circuits in series.
Then, check out the video on RL circuits where things are in parallel.

When done with the videos, try to work your way through the problem set for tomorrow. On Friday, we will get into the combination of inductors with capacitors, and some interesting effects will take place!

Monday, March 16, 2015

Another Confirmation of Einstein's Theories

A high precision, experimental confirmation that photons of varying frequencies/energies has been made from an analysis of radiation from a gamma ray burst. Check out an article here. Photons of a range of energies, that traveled billions of years to the earth, arrived within a tiny fraction of a second of each other. This is as Einstein predicted almost exactly 100 years ago, when his theory of general relativity was published in 1915. This measurement also restricts the notion of 'quantum foam" that is predicted from a variety of theories attempting to unify relativity with quantum mechanics. If quantum foam (basically think of space as being quantized, and not continuous) exists, then photons with different energies should be affected by different amounts, and the photons should not have arrived all together. This is published in Nature Physics.

Friday, March 13, 2015

PhET Simulations for EM Induction

Here is the set of simulations for our EM Induction computer lab. Or, you can click here to go to the PhET site.

Wednesday, February 18, 2015

Magnetism stuff

For our magnetism quizzam, how well do you know:

- where magnetism comes from
- magnetic domain concept
- magnetic forces on charges, current carrying wires
- cross products, RHR vs LHR, circular motion of particles
- velocity selector, mass spectrometer
- force between multiple wires
- Ampere's law (long wires, long cylinders, toroids)
- Biot-Savart law (point charges, straight wires, current loops)
- current densities and Ampere's law (uniform, NON-uniform)
- Hall effect concept

This post has quick links to a bunch of magnetism videos. There are good simulations on ActivPhysics, and lots of good examples in the book, old AP exams, Princeton Review, etc.

Monday, February 16, 2015

Ampere's law with NON-Uniform Current Density

Here is an example of how to do a worst case scenario with Ampere's law (for a long, straight wire): A NON-uniform current density flowing through the cross sectional area of the wire.

Current density is just the current / (cross sectional area the current flows through). If this flow is a function of the radius, then it is NON-uniform flow, and, like a non-uniform charge density for Gauss's law, we will need to integrate the current density function to find the current inside the region we want. It hopefully sounds worse than it is, so check out the video for an example. I hope it helps!

We have checked out magnetism in a big way the past couple weeks. We know that magnetic fields are strange and circulate around moving charges and currents. We know that magnetic forces are created by magnetic fields acting on moving charges and currents: F = qv x B and F = Il x B.

Because these forces are cross products, moving charged particles will be put into circular motion by the magnetic force, and we have used the flat-hand right-hand/left-hand rules to figure out the direction of the push. We have also seen a major application of these forces in velocity selectors and mass spectrometers.

We then worked on the fields and forces created between multiple parallel wires with currents. This is a nice application of combining Ampere's law with the RHR's and the magnetic force equation, F1 = (I1)l x B2 and F2 = (I2)l x B1.

We then got into the production of magnetic fields, using Ampere's law for three special, symmetric cases: long straight wires, long solenoids, and toroids. This is built upon the notion of a path integral, since magnetic fields follow either circular paths (straight wire and toroid) or a linear path (inside solenoid). With the 'long' approximations, we do not need to use calculus, and it is B*(length of path) = mu*I_inside.

Then we hit the most difficult portion of all this, with the Biot-Savart law. This is used to find the magnetic fields for every other case, and we focus on three: single moving charged particles, a loop of current (like in our lab) and a straight wire with ends.  We treat these cases as they really are - a bunch of moving point charges, where we add up all the little B-fields to get the total B-field, using integration. We also can use this to find the effects of multiple wires.

We even got into the worst-case example for Ampere's law of a NON-uniform current density in a wire, where we need to integrate to find the current inside a certain portion of the wire.

One last piece of the puzzle is the Hall effect. This is a phenomenon that happens when a material carrying a current is placed in a B-field (directed at an angle to the current flow), and the material is polarized due to the magnetic force on the current. That polarization of the material can be measured as a voltage difference, and if the material is known, the magnetic field strength can actually be measured (a so-called Hall probe).

There's quite a bit here for plain magnetism, so hopefully these videos are useful!

Tuesday, February 10, 2015

For the 4 Chem-Phys classes, check out this introductory video on Ampere's law. We are getting into the production of magnetic fields. This is like Gauss's law, only for magnetism, and will be useful for three shapes: straight wires, solenoids, and toroids (i.e. donut-shaped device).

For AP Physics C, check out a video on how we will need to integrate electric fields to find voltages when we have layers of charge (like capacitors).

Friday, February 6, 2015

Information for Classes, Jan. 6, 2015

Happy Friday everyone! We are at our WYSE regional competition today.

For 4 Chem-Phys, start off with two videos on magnetic forces and an application of those forces. Take notes on magnetic forces on electric charges, and then mass spectrometers and velocity selectors. These will be useful (hopefully!) for the homework set. After the videos, please check out the multiple choice questions from the semester final, and you should do an error analysis while recalling first semester information. Solutions to the final are here.

For AP Physics C, check out two videos on finding the electric fields of NON-Gaussian objects. This will involve integration. One case will be for charged sticks (but with ends...a little closer to reality!), and a second case for a curved stick (part of a charged ring). Take notes, as the homework problems will involve these techniques. After the videos, please complete the lab on equipotential lines and the potential gradient (i.e. electric field). Turn those in before leaving. You can use computers to access the ActivPhysics simulation as needed.

Thanks, and enjoy the weekend!

Saturday, January 31, 2015

49 Reasons I got into and love Teaching - In Honor of my 49 GTP Finalist Colleagues!

In late January, 1995, just having completed my Ph.D. defense at the University of Illinois at Urbana-Champaign in high energy physics, I started teaching the second semester of physics classes at Amundsen High School in the Chicago Public Schools. I did not know what to expect, as any first-year teacher knows, but now, almost exactly 20 years later, I have had an incredible ride and cannot imagine working in any other job. I have been at Evanston Township High School for 16.5 years, and now reflecting on why and what I love about teaching, I wanted to share 49 reasons - that number, 49, is in honor of the 49 colleagues from around the world who are finalists for the first Global Teacher Prize! I am not sure why I am mentioned in the same breath as this amazing group of teachers and human beings, but I am thrilled and humbled to have been selected.

Here goes: Why did I go into teaching, and why do I love working with high school students?
1. To inspire;
2. To motivate;
3. To encourage;
4. To make students think and wonder about the world around us;
5. To help students grow intellectually, socially and personally;
6. To think creatively about problems;
7. To help students become better problem solvers;
8. To help them build confidence and self-esteem;
9. To (hopefully) be a positive role model;
10. To mentor;
11. To show the role of STEM in everyday life;
12. To listen;
13. To share an enthusiasm for learning;
14. To teach physics at whatever level students can handle;
15. To show how science is connected to politics, history and economics.
16. To learn from colleagues;
17. To coach;
18. To advise on student research;
19. To collaborate with colleagues in ETHS and at Northwestern University;
20. To help students prepare for the next level - college and/or career;
21. To help guide and prepare the next generation of teachers;
22. To promote teaching as an essential profession for all of society;
23. To help create educated, scientifically literate citizens and voters;
24. To show how science is necessary to solve numerous national and global problems;
25. To do science with students;
26. To share ideas with colleagues, either through professional development training or publications;
27. To share resources with students around the world (e.g. the class blog and how to videos online);
28. To relate science to other core classes all students take;
29. To form strong relationships with students so I know what works for them as individuals;
30. To brag about students in many hundreds of letters of recommendation for college and jobs;
31. To help develop the next generation of science education tools and pedagogy;
32. To discuss STEM related careers;
33. To provide guidance to college science programs;
34. To improve students' technical writing and communication skills;
35. To create and share countless, bad science puns! I live for moans and groans after a bad pun!
36. To meet with parents to help them with their children's futures;
37. To have daily laughs and giggles with all the crazy situations students get into;
38. To provide opportunities outside of the classroom for students to pursue personal interests;
39. To work on the achievement gaps between different groups of students, such as in Project Excite;
40. To create a safe environment for all of us to fail, and then learn with each other from those failures;
41. To create and use a wide variety of lessons, to reach every individual student;
42. To create a growth, capable of anything mindset for each student;
43. To help each student realize their strengths and weaknesses and interests, and then improve;
44. To allow the freedom to try new things and promote creativity;
45. To allow students to share with each other;
46. To share experiences as a scientist;
47. To be passionate about learning, and compassionate towards all;
48. To have one and only one rule: The Golden Rule (except for the cell phone rule: if a phone goes off
during class, that person must dance on a lab bench for the class! Students made this one up!)
49. To never give up on any student, and to not allow them to give up on themselves!

Here is to teachers everywhere - Thank you for all you do! And to the other GTP Finalists, thank you for a shot of teaching adrenaline because of the AMAZING things you are doing - your biographies can only inspire me and any other teacher on the planet!!!

Thursday, January 29, 2015

Details on Air Friction

Thanks to Nathan H. for finding this site.

There is a useful NASA site that gets into air friction a little deeper than we do in class. This link takes you to a description of the drag coefficient (like the constant we use) - see some of the details and other factors that go into the drag term, which leads directly to an understanding of how strong air friction will be on an object. Have fun with it!

Sunday, January 25, 2015

Time Dilation equations for Gravity (from General Relativity)

Thanks to Dan M and Colby for finding the Wikipedia link for gravitational time dilation.

We have mentioned in class that Einstein, from his general theory of relativity (which is our modern theory of gravity), figured out that gravity should affect time. Two clocks that start off synchronized should 'run' at different rates in different gravitational fields. This can be deduced from the principle of equivalence, which states that the effects of acceleration are indistinguishable to the effects of gravity. Acceleration is a change in motion, and Einstein showed how motion (i.e. speed) slows time in his special theory of relativity, so accelerating motions should also slow time. If acceleration affects time, then gravity must, too! This is all verified through experiments using atomic clocks.

We can get some sense of how big (or actually, how tiny!) these gravitational effects are for a few different situations.
- As a function of height above the earth, we can use an approximation:
T = 1 + gh/c^2     This tells us how much time dilation there would be if one clock was on the ground and one was at a height h. This assumes h is very small compared to the size of the earth (or whatever object we are using for g). Because c^2 is very large, 9 x 10^16, you can see that this is a tiny effect for the earth! So the difference between the times being kept by the two clocks is in that term gh/c^2.

- Above a spherical, non-rotating object
t_surface = (t_far)*sqrt [1 - 2GM/(rc^2)]
This tells us the difference in two clocks, one on the surface of a spherical object and one far away from the object. M is the mass of the object and r is the distance from the center of the object, which is not rotating. Note that the term 2GM/c^2 is the Schwartzshild radius, which is the radius one would need to crush the object to make it a black hole (escape velocity > c).

- A special case of being above a spherical object is if you are in circular orbit around that object. The above expression becomes
t_surface = (t_satellite)*sqrt[1 - 3GM/(rc^2)]

In any case, this is very cool stuff! Have fun just by playing around with these expressions and discovering how large or small the effect would be for any scenario/object you wish!
Note I have videos on equivalence principle, warped space-time (from Elegant Universe), basics of general relativity, Gauss's law for 1/r^2, Gauss's law inside Earth, gravitational potential energy, and integration to find g-fields for rings and sticks. There is also videos for E = mc^2, and Einstein's energy equation and consequences.

Tuesday, January 20, 2015

For 3 Chem-Phys (periods 1-2, 8-9), click here for solutions to the semester I final exam.

For AP Physics C (periods 3-4), click here for solutions to the semester I final exam.

Go over your answers/solutions, and do an error analysis and/or make corrections on your exam. Be sure things make as much sense as possible, and save any remaining questions for me or a classmate who might have an understanding of it.

Sunday, January 18, 2015

Buoyancy - When do submerged objects rise or sink?

Buoyancy is a neat force, which is that upward push a fluid places on an object. Swimming would be a bit difficult if buoyancy was not there, since then everything and everyone would just sink!

Archimedes figured out long ago that the buoyant force = the weight of the displaced fluid. This video gives a brief example and proof to something that you may be aware of, that whether things sink or float depends on the relative densities. In chemistry, oil floats on water if it is less dense than water - well, here is the 'proof' of this phenomenon using Newton's 2nd law. I hope it helps!

Center of mass of systems: Position and Velocity

The center of mass is a really useful concept. It can be used to reduce a large object, say a planet or star, to a single point that has the entire mass of the object at that location. This is the key concept for calculating the gravitational force between the objects, for example.

But this is also a useful concept for system of objects or particles. We can define the center of mass for a system with a weighted average of
x_cm = [sum of (individual mass)(individual x-coordinate)] / (total mass of system)

We have used this to find the center of mass of a binary system, which is then the center of each object's orbit. But for even more numerous particles, the center of mass of a system describes the motion of the entire system, even if all the particles are flying around seemingly at random. This video presents two simple 1-D collision problems to show how the momentum of the center of mass of a system is conserved, and moves at a constant velocity (assuming no external forces acting on the system that would cause the center of mass to accelerate).