Gravity and Gauss's law: Inside the Earth

Gauss's law for gravity can be used primarily to show what happens if the earth or other really large objects had different shapes.  We would find that spheres and point masses have 1/r^2 behavior, cylinders have 1/r behavior, and flat objects would have a uniform, constant force of gravity.

But Gauss's law can be used to figure out what happens inside objects as well.  There are two really fun cases to consider: i) a hollow earth, and ii) a solid earth with uniform density.  These situations are normally considered for solid charged objects (nonconductors) in electricity and magnetism units, but the same math and concepts can be used for gravity, too.

The key to Gauss's law is that the strength of the gravitational field at some radius from the center of the earth depends on how much mass is inside that radius.  If the earth is hollow, this means that once you drill a hole into the earth and jump in, because there is no mass inside then there would be no gravity inside!  You would be truly weightless and would simply float around inside a hollow earth!!

Because the earth is not hollow, we will not have a chance to test that prediction from Gauss's law.  But a solid earth can be analyzed.  If we assume the earth has a uniform density, and we were to drill a tunnel all the way through the center of the earth to the other side, what would happen if you jumped into that tunnel?

Check out the video to see more details, but the answer is you would oscillate back and forth through the earth as if you were attached to a spring!  The motion would turn out to be the same as that of something in simple harmonic motion!

How to set up Integrals for Gravity for Rings and Sticks

We are used to doing gravity problems with Newton's law of universal gravitation, F = -GMm/r^2, for things like planets and stars and point masses.  But we also can show that the shapes of objects matters for how gravity behaves, such as the difference between spheres (1/r^2), long cylinders (1/r) and large flat objects (uniform gravity).  This comes from Gauss's law for gravity.

However, once the shapes become even more different, such as rings and sticks with actual ends, Gauss's law does not work and we need to figure out how gravity behaves then.  This is when we need to break an object into point masses, use Newton's law of gravity for each small mass, and then add up all the results to get the total...this is what integrals do for us!  Check this out, with the focus being how to set up the integrals.  We are not so focused on the final results, but rather the thought process and setup.

Why is Gravity 1/r^2? Gauss's law and Gravity

Gravity is obviously a big deal in physics and in life.  But in class we are used to just one idea, which is Newton's law of universal gravity, F = -GMm/r^2.  This is usually just handed to students and we start using it to solve all sorts of problems, but here I wanted to justify WHY gravity behaves this way, with the inverse-square law of 1/r^2.  It turns out it is a result of geometry!

This video attempts to introduce the notion of Gauss's law, which is normally a big topic in electricity.  But it can be applied to gravity, as well.  Gauss's law is a formal way of defining something called flux, or the amount of stuff flowing through an area.  Mathematically, flux = (stuff)(area).  In our case, the 'stuff' is the gravitational field that all particles and massive objects creates all around itself, and will create the forces we experience when two or more objects are near each other.

We look at spheres, cylinders, and flat objects.  Gauss's law then shows us that the gravitational fields will behave differently with distance from the object.  Gravity is NOT always 1/r^2!!  This is just for spherical objects and point masses.  If the earth were cylindrical, for instance, gravity would fall off more slowly, as 1/r.  And if earth was flat, then gravity would be uniform, or constant, no matter how close or far away you were!  Check out what Gauss's law looks like and where these results come from.

Note there are how to videos for Gauss's law in electricity, specifically for electric fields, on our class blog.

How to Think About Band Theory

In chemistry, we learn about the three main types of materials in terms of their electrical properties: conductors (typically metals like copper or gold), non-conductors (most materials with covalent bonds), and semiconductors (something like silicon).  But how and why are there different behaviors - all atoms are made of the same pieces, so why the variety of materials?

The answer can begin to be found with a relatively simple model called band theory.  This uses the concept of fixed energy levels that you first learn about studying the Bohr model of an atom in chemistry.  Bound electrons of atoms can only have specific, fixed energies.  But this picture gets muddied when you start thinking about real materials with lots of atoms - all these atoms interact with each other because they are all made from electric charges.  These interactions cause the energy levels of individual atoms to shift slightly, where some increase in energy and others decrease.  Collectively, the energy levels blur and form more of a continuous energy band.  Specifically, two bands form, one where the bound electrons exist (valence band) and one where they have enough energy to move freely through the material (conduction band).  To be a conductor requires many free electrons in the conduction band.

Non-conductors have a large gap between the valence and conduction bands; semiconductors have small gaps between the two bands, and conductors have an overlapping between the two bands, meaning all sorts of electrons are free to move through the material.  Some call this the 'sea of electrons' in a conducting material.  Check out the model!  Also, feel free to play with a PhET simulation where you can have 1 - 10 atoms (or wells) near each other, and see how the energy levels change to begin forming bands.

A Good Physics Blog

Find all sorts of information about a large variety of physics topics at the site http://www.physicscentral.com/buzz/index.cfm.  This is run through the American Physical Society, and has links to specific areas of physics as well as new applications of physics in everyday devices, and much more. Check it out!

The Power of Black Holes and their Jets

Black holes are among the most powerful and weird objects in the universe.  One aspect of these critters is that they eject jets of radiation and particles out from the accretion disk.  New studies suggest these jets come out at some 99.9% the speed of light and can extend for millions of light-years!  This constitutes an amazing amount of energy.  Check out an article here.

How to do Multi-loop Circuits

There is a type of resistor-battery circuit that is strange to the degree we cannot find the total resistance due to the presence of multiple batteries.  The trick, then, is to treat each part or loop of the circuit as an independent circuit, and use Kirchhoff's voltage rule to set up loop equations: the battery voltage = sum of voltages of components in the circuit. Check it out!

Drawing Electronics - New way of building circuits, courtesy MIT

Check this out, seniors, as we are about to start electric circuits...MIT engineers have figured out what materials can be used to sketch electronics on paper.  We will NOT be able to do this, yet, in class, but it is something for those of you with an interest in electrical engineering to take note of.  This could be a part of your future!  Really interesting possibilities are presented in this short TED talk.

Your Brain on Video Games

Check out research to see how gamers' brains are adapting to everyday skills, such as attention, eye sight, keeping track of multiple objects and details, and so on.  Overall, gaming improves many brain activities.  This is an interesting talk, and further research is necessary to see how this might be included in education in K-12 schools.

Why are Adolescents the way they are? Check their Brains!

It is common knowledge that teens behave a bit differently than adults.  With recent brain studies and new technologies for looking at the brain in action during different activities, such as functional MRIs (fMRI), researchers like Sarah-Jayne Blakemore can literally see differences between adults and adolescents.  Check it out.

Modern Microscopy - The Beauty of Nature at small size scales

Gary Greenberg shows a wide variety of natural beauty at its finest, and its smallest!  Modern microscopy allows us to go down to atomic sizes and take pictures of some type.  The details are quite spectacular, so enjoy this TED talk and check out some parts of the world that you may have never before seen.

Using Energy Conservation for Finding Speeds

Generally we have two ways of determining the motion of objects - Newton's laws (F = ma) and energy.  Newton's laws are useful for finding accelerations and forces, but this can also be trickier since these are vectors, and for non-constant forces, we need calculus.  When we need to find speeds, I strongly recommend that you try energy to solve the problem.

Energy has the advantage that it is a scalar, so there are no vectors or components to worry about. We can also avoid calculus for NON-constant forces, such as springs and gravity.  Here are two examples with springs and gravity, and how energy conservation provides an easier, quicker way to get the speed.  Our starting point is:  Uo + KEo  =  Uf + KEf + heat, where heat is the work done by friction.

NON-Gauss Problem: Find Electric Potential for Charged Sticks

Charged objects in real life generally are not in the 3 shapes we need for Gauss's law - spheres, long cylinders, or large plates.  Here, we look at how to set up the integrals necessary for finding the electric potential of charges sticks at arbitrary locations from the stick, where we do not have much in the way of symmetry to help simplify life.

The concept behind it is to break the problem into point charges.  The only thing we know exactly in electrostatics is how to deal with point charges, with E = kQ/r^2 and V = kQ/r.  So we need to break into point charges, find the small contributions from each charge, and add them all up, or integrate.  The one other piece of this so it works is to use a ratio of charge to length.  This allows for a substitution into the integral to make it solvable.

This video has two examples of sticks and finding electric potential.  I hope it helps!

Congratulations to Seniors for their Research!

We just found out that seniors Laura Goetz, Sarah Posner and Marc Bouchet have been nationally recognized in the Siemens Science and Technology Competition, one of the biggest science contests for high schools.  Laura is a National Semifinalist, and Sarah and Marc, who worked together and are in the team portion of the competition, are Regional Finalists.  Sarah and Marc now advance to present their work at the University of Notre Dame in November, and are now in the running for large scholarships.  This is similar to what happened last year with Julia Crowley-Farenga and Patrick Loftus, who ended up winning a $40,000 scholarship after placing 3rd in the country for their work in astrophysics.

Laura worked in the Prof. Morimoto lab at Northwestern, and her research, which looked at identifying genetic modifiers of polyglutamine expansion toxicity in Caenorhabditis elegans, has implications for Hutchingston's disease research.

Sarah and Marc studied properties of tandem organic solar cells that they made in the lab of Prof. Tobin Marks at NU, and worked under the mentoring of graduate student Nanjia Zhou. They are the only Regional Finalists from Illinois.

I also want to recognize senior David McDonald for his paper on the segregation and stratification of mixtures of different sized granular materials.  This work has implications for agriculture and new drug development.  David worked in the lab of Profs. Richard Lueptow and Paul Umbanhowar at Northwestern.

A very small percentage of students nationwide do high-level, independent research like this, largely because of time but also because it is difficult and must require countless hours of study and work in the lab, so these students need to be given some recognition for their efforts and contributions to several fields of science!  WELL DONE!!

Nobel Prizes Being Announced This Week

The 2012 Nobel Prize for Physics was shared by French physicist Serge Haroche and American physicist David Wineland (U. of Colorado at Boulder) for their work in controlling quantum superposition states.  This means they figured out how to study individual photons and individual atoms, respectively, which is really tough to do, as one might imagine.  This work could help lead to breakthroughs in the dream of developing quantum computers, which would theoretically be much faster and more powerful than today's best supercomputers.

The 2012 Nobel Prize for Chemistry went to two Americans, Robert Leftkovitz (Duke) and Brian Kobilka (Stanford).  These scientists have been instrumental in figuring out how cells are able to 'smell out' chemicals, allowing the cells to know what is happening in the environment and determine how to respond to the environment.

The 2012 Nobel Prize for Physiology or Medicine was shared by English scientist John Gurden and Japanese scientist Shinya Yamanaka, for their discovery "that mature cells can be reprogrammed to become pluripotent."  This is a big step for stem cell research because one does not need to rely on the controversial stem cells from embryos.  They showed that mature, adult cells can be forced to act immature again, as a stem cell, and then can be used to form any other cell of choice.  For years, embryonic stem cell research was politically, religiously and ethically charged because of the debate over when life begins.  This research allows scientists to largely avoid those questions and still do studies into how stem cells behave.

The Future of Higher Education: Free Courses?!

A few years ago, several big-name colleges (MIT was a leader in this) began putting their courses online, where anyone would be able to 'take' them for free.  Now, you won't be able to get a free degree or even credit for the course, but for self-education, perhaps a course that can help you with your job or just something that you've always wanted to take but did not have the time or money to pursue, well, you can likely find it for free.

Take a look at Coursera, which is the latest, very popular site with numerous colleges adding courses to the list (including my alma mater, U. of Illinois).  If you are interested in a particular school, you may want to check out what their courses look like.  Some others that are out there include MIT's course site, and Oxford's courses. The future may be here, at least for many students, simply because the top schools may be pricing themselves out of many students' affordability range.  How much longer will families take out massive amounts of loans (which = debt) for a college degree?  It will be interesting to watch how this all plays out over the next few years, as more courses are offered online and more people take those courses.

Top Physics and Engineering Undergraduate Programs

Check out one set of rankings for the top ten undergraduate physics programs.  This is put out by Bright Hub, and is consistent with just about any rankings you find.  As they point out, many people consider a physics major at these types of schools to be among the most difficult of any major, and I can attest to that (UIUC Ph.D., class of 1995).  The order generally does not matter, as any of these schools will challenge you as far as you wish to go, and will prepare you for a diverse set of careers built around physics and problem solving.  The schools included on the list are:

MIT, Stanford, Harvard, Caltech, Princeton, Cornell, Berkeley, U. of Illinois, Santa Barbara, and U. of Chicago.

None of these should be surprising, with the possible exception of Santa Barbara - not many people realize the work they do.  The others are all usual top names for powerhouse science and engineering schools.  All provide wonderful research opportunities for undergrads, and are also on lists for top graduate schools.

For Engineering, check out many of the same schools for the rankings:

MIT, Stanford, Caltech, Berkeley, Georgia Tech, U. of Illinois, Michigan, Carnegie Mellon, Cornell, Princeton.

Cannot go wrong with any of these!

Teach 1st Graders to Program?

Here's an interesting idea being in tried in the small country of Estonia - getting the principles and concepts related to computer programming to first graders.  One does not need to learn an actual language like Python, Java, or C++, but certainly the concepts can be picked up, even by six year olds.  There are so many ways of doing this, to teach them about how a computer does not think and instead needs to be told every small instruction.  Teachers can make a variety of games for young children to play, and the way young minds work, they will begin to learn to think like a programmer, and over time as they progress through elementary school simple commands and syntax can be added slowly but surely.  At some point visual programming languages such as Scratch and Starlogo can be used, then move them into a simple language like Netlogo, and eventually to more advanced languages if they choose.  The point is this is a powerful way to teach 21st century skills, remove the fear from computers, programming and technology in general, learn logical thinking and improve problem solving skills over an extended time.  Just like learning a foreign language is easiest when young, I am fairly certain the same is true for a computer language.

Scientists can now measure the mass of individual molecules

A new nanodevice is able to measure the mass of a single molecule.  The way this works is the device has a certain vibrational frequency.  This is like a spring that is oscillating at some frequency (simple harmonic motion).  But what we learn about springs is that the frequency depends on the mass that is attached to the spring.  What happens with this device is that when a molecule lands on the device, the frequency changes.  It is the change in frequency that determines the mass.

So this is a wonderful example of taking a basic physics principle and applying it in a new environment.  The engineering of the device is, of course, tricky, but the principle can be understood with the physics we study in class.  Very cool!

Special Relativity: From energy to particle-wave duality

In 1905, Einstein published what is now called special relativity.  We have the famous E = mc^2 as well as some other results: time slows down with speed, lengths get shorter with speed, and mass increases with speed.  If it helps, the idea of mass increasing makes sense straight from E = mc^2.  If an object moves faster, the total energy increases since there is more kinetic energy.  So the left side increases.  This means the right side must increase as well, but c cannot change (it is a constant, the speed of light).  This means the only thing that can and does change is the mass increases.

Einstein united space and time into a single 'fabric' we call the space-time continuum. Keep in mind that he also united mass and energy.  They aren't just related to each other, they are equivalent to each other!  It is sort of like saying they are two forms of the same stuff.  I like to think of ice and steam - there is no reason at all to think they are related just by looking at them, but with closer inspection they are both two forms of the same stuff, water.

In this video we will focus on the mass equation, and see what Einstein's energy equation is, where the notion of antimatter comes from, and where the idea of 'matter waves' comes from!  These are some of the foundations of modern science, and we can derive them in just a few minutes.  Check it out!!

Motion Graphs and the Meaning of Slope on These Graphs

Here we take a look at a more visual way of analyzing motion, motion graphs.  These refer to those graphs of position vs time, velocity vs time, and acceleration vs time.  What is cool about these is that when you get good at reading the graphs, you can picture the motion of the object the graphs are describing.  We will use one of the ActivPhysics simulations (1.2) to help connect the initial conditions, the actual motion of a car, and the motion graphs to each other.  I recommend playing with these simulations on your own (1.2, 1.3), and you will find yourself getting better and better of making all the connections.

Now, for us we will include the calculus.  Specifically, slopes of the motion graphs are important.  And we now know that derivatives are really just slopes of graphs, even if they are curves.  This is what we are after in this video lesson.

velocity = slope of position graphs = dx/dt
acceleration = slope of velocity graph = dv/dt

Focus on these definitions as you watch.

How to do Vector Addition to get Net Force

One basic skill we use over and over in physics and engineering is adding vectors to find the total, or resultant or net, vector.  Vectors are those quantities with BOTH magnitude and DIRECTION, such as forces.  Obviously, gravity has a direction of 'down' and is therefore a vector.

The easiest problem is when there are two vectors on the same line, called colinear vectors.  These we just add, if in the same direction, or subtract, if in opposite directions.  The trickier problems are when forces are pulling in multiple dimensions.  This is where the rules for right triangles are needed.  We can use sine, cosine, and tangent to figure out how much of each individual force is in the x and y directions.  We can also use these functions to determine the direction of the net force, and therefore the direction the object will actually start moving.  Remember Chief SOH-CAH-TOA for the definitions of these trig functions!

Check out this example with three force vectors.  Keep in mind to use a table of x and y components in all your problems to keep things organized - it will help.

Great Example of Computational Thinking/Modeling for an Everyday Physics Problem

Check out how mathematical modeling is applied to solving the motion of a rotating fan blade slowing down. It outlines the thought process and methods used to solve this commonly observed event.  Check it out! 

Femto-Photography is Here - 1 Trillion frames per second!

Modern technology has revolutionized many facets of life, but as much as any area, photography has gone bananas with high-speed photos and films.  As long ago as the 1960s, scientists and engineers figured out how to take pictures at one million frames per second.  Now, fifty years later, there is a camera that is one million times faster than that!   Yes, one trillion frames per second.  Check out this TED talk to see what it can do, where is actually follows a pulse of light itself...you can see a light pulse move.  I find this unbelievable, and truly fascinating.  Our ability to view Nature at this level has opened our eyes to details of all sorts of phenomena we could not dream of just a few years ago.

Big Day in Particle Physics - The HIGGS!!

The Higgs is here! After decades of looking for the bugger, confirming experimental results from Fermilab and CERN show that the Higgs boson is a real particle, which satisfies the prediction from the Standard Model.  It is also cool to see comments from two old friends from my Fermilab days, Rob Roser and Tom LeCompte, in this article.  Here is another article, and also an interview on CNBC below.  There are also a couple former students from Chem-Phys out at CERN (shout-out to Edmund and Dan!), who have helped keep me in the loop the past couple years.  Congrats to everyone involved!!

Visit msnbc.com for breaking news, world news, and news about the economy

High-speed Camera Fun

I just wanted to share this video of two guys (the Slo Mo Guys) buzzing their lips, simply because I find it hilarious!  Enjoy.

Einstein Still On Top - Neutrinos Not Faster Than Light

Just about all physicists, including this one, were skeptical about a year ago when a neutrino experiment in Europe announced it had evidence that neutrinos move a bit faster than light.  The OPERA collaboration is similar to an experiment at Fermilab, where neutrino beams are shot through the Earth to detectors hundreds of miles away.  This experiment published its results and wanted the scientific community to try to figure out if any mistakes were made, knowing that the significance of this result did nothing short of suggesting Einstein's theory of relativity was flawed.

But now, five independent groups have reproduced the experiment and verify neutrinos obey relativity and move slower than light.  A likely problem with the OPERA experiment is in its fiber optic timing system.

This is a wonderful example of how science is supposed to work.  Results are published, and other scientists need to be skeptical and open-minded about the results.  Repetition and reproducibility lie at the heart of the process of science, where ideally independent groups repeat experiments to confirm results.  Science works through observation and experimentation, where physical evidence rules the day.  So the foundational theories of physics, relativity and quantum mechanics, still come through in the heat of tests.

CONGRATULATIONS TO THE CLASS OF 2012!

The Class of 2012 is now done, and my heartfelt congratulations to all of you! This is a tremendous group of young women and men who are set to take on the top colleges in the country, and make their mark on the world! I am truly proud to have worked with each and every one of these students.

If you want a 3-D simulation that will allow you to view electric fields for a wide variety of charged systems, check out this Falstad simulation site. It is really a useful visual display!

Charged Particles in B-fields

Here's a case of charged particle flying through magnetic fields, and what happens to those particles. We know that fundamentally magnetism is formed by moving charges. So the moving charged particle has its own magnetic field. This field interacts with any external magnetic field, thus creating a magnetic force. We know this goes as F = qv x B. It is a cross product. But this then means the force is perpendicular to the motion of the particle. The consequence of this condition is circular motion, or mv^2/R = qvB. This video will show ActivPhysics simulations to get a sense of the 3-D nature of this motion. If the particle comes in 90-degrees to the magnetic field, we get a circular orbit. If the particle comes in at any angle other than 90-degrees or 0-degrees (parallel) to the field, then there is a component of motion perpendicular to the field (circular motion), as well as a component parallel to the field, which means no force and it keeps moving in that direction. A spiral/helix/corkscrew results! I also show a simulation of a mass spectrometer, where we use the circular motion to measure the mass of particles or ions. Check it out.

Check out Rotating Pulleys

Check out how to find the TWO tensions in the same rope for a real, spinning pulley problem. The video is here. Also, check out small oscillations (like a pendulum) here, or a more complicated one here.

Rotating Conducting Rod in B-field

The previous post outlined how to find the induced voltage across a moving metal rod in a B-field. Because of qv x B, we found the rod polarizes and therefore has an E-field and voltage difference because of a separation of charge. Here is a different situation. Suppose instead of moving linearly through the B-field, the metal rod is nailed down on one side, and rotates in the magnetic field?! It is a moving conductor, so we would still expect it to polarize, and therefore have a voltage difference across the rod. The trouble is, different points of the rod will have a different speed! How do we handle this situation? Check this out...

Moving a Conducting Rod through a B-field

Here's a case where by simply moving a metal stick through a magnetic field, the stick acts like a battery. The idea is that because it is a conductor, the rod has free electrons. By moving it in a B-field, we will have F = qv x B kick in. This causes the rod to become polarized, with one end positive and one end negative. But think about what else is set up if one separates charge on an object - you would have a voltage difference between the two ends. And if there is a voltage difference across a conductor, E = -dV/dr tells use there is an E-field running through the rod. This E-field produces an electric force on those same delocalized electrons. So a magnetic force points one way, and an electric force points in the opposite direction. At some point the electric force will balance the magnetic force, as long as the speed of the rod remains constant: qE = qvb.

I need student feedback.  For the how-to videos, is there a topic or problem that should have a video but does not?  Thanks for letting me know.

How to do LC Circuits - like Simple Harmonic Motion!

Here is an example of an LC circuit, where a charged capacitor is connected to an inductor.  The beauty of this circuit is that one can start an oscillating current (AC current).  This is the same as 'shaking' electrons, and this means electromagnetic waves are produced in the E-and B-fields.  These waves travel at the speed of light.  We will see that the math produces the same second-order differential equation we have in simple harmonic motion of oscillating springs!  So sines and cosines are the solutions to this equation.  Check it out!

SHM of Oscillating Stick due to Spring

Simple Harmonic Motion (SHM) is a periodic motion of some object caused by a restoring force that is proportional to the displacement, such as a spring.  Here is a different type of setup where a stick is lying on a frictionless table, with one end nailed to the table (which serves as the axis of rotation) and a spring attached near the other end of the stick.  If the stick is stretched slightly, so the stick forms a small angle relative to the vertical axis it had prior to stretching the spring, we can use the small angle approximation.  This says that for a small angle, the angle in radians is approximately equal to the sine of the angle.  Also, cosine of that small angle approaches 1.  We need both these approximations to solve this one!  Check it out.

A Very Cool Way of Looking at the Size Scales of the Universe

Check out this site, which is a very neat way of checking out the size scale of objects in the universe. It is similar to the classic Powers of Ten videos, but has better graphics. Enjoy!

Cool PhET Simulation of Planetary Orbits

Check out this PhET simulation for a planet orbiting a star. Experiment with it by changing masses, adding a moon, etc. Very useful to see orbital motion in action!

Click to Run

Faraday's law simulation

Here is a good visual for Faraday's law of em induction. Remember, it is all about changing magnetic flux! For more PhET physics simulations, go here.

Click to Run

EM Induction Simulation

Here is a PhET simulation for electromagnetic induction applications. These are great for visualization of what em induction principles look like in the world. For many more physics simulations from PhET, go here.

Click to Run

Interesting Talk About Alternative Energy Production for the Grid

Donald Sadoway of MIT talks about an aspect of energy issues not normally focused on - batteries, or at least some way of storing energy created by solar and wind sources. If the sun is not out, and the wind not blowing, we need to have back-ups so we can continue to have access to energy. Our society simply demands this, and it will only increase as the population grows.

We will not be able to conserve enough, or drill enough, to continue to match increasing demands, so energy storage is the key to future energy production and consumption. Check out this TED talk. It is also a wonderful application of the chemistry and physics we are learning!

A 'Boy Wonder' Tackling Nuclear Science

Check out this video about Taylor Wilson, who at age 17 has already taught a graduate level nuclear physics course, has built a small fusion reactor, and invented a cheap way of detecting nuclear materials in shipping containers for national defense purposes. He appears to be that rare, nearly once a generation type prodigy/genius who is making a difference while very young.

RL Circuit with Resistor and Inductor in Parallel

Here is a circuit where a resistor and inductor are in parallel with each other. This is similar to a RC circuit with a resistor and capacitor in parallel. We focus on t = 0 and a 'long time.'

The gist of this one is that inductors fight current initially because they do not like a change in magnetic flux. After a long time, an inductor is just a piece of wire with no resistance (at least for us!). Check it out.

How to Find Terminal Velocity of Conducting Loop Falling into B-field

Here is a different type of induction problem. This has to do with the long aluminum tube we have in the lab, and even though it is non-magnetic, a falling magnet in the tube falls with a terminal velocity. Huh?! The reason for this is as the magnet moves, it is changing flux in the loop. This induces a voltage (Faraday) and therefore a current (Ohm). In a tube these are called eddy currents.

But those currents then feel a force since they are in a magnetic field. This is F = Il x B. The force is upward, trying to stop the motion and therefore stopping the change in flux (Lenz). The mathematics turn out to be identical to that of a sky diver with air friction! We will get an exponential solution, and a terminal velocity. Check it out!

New Neutrino Results from an Independent Group - Einstein was Right

Results from a European research team called Icarus show that neutrinos do not move faster than light. The team is headed by Carlo Rubbia, who is a Nobel Prize winning particle physicist and former director of CERN. Icarus is a similar experiment to OPERA, which is the group that had measurements of neutrinos above the speed of light. Recent information from OPERA suggests the possibility that their measurements could be off due to some poor pieces of equipment in the experiment.

This is a wonderful example of how science works. One must have some thick skin at times, because when you publish results of any experiment, by definition it must then undergo the scrutiny and questioning of the community. Peer reviewed articles, reproducible experiments that can be tested and looked at independently, debate, talks and conferences, and so on, all provide opportunities for scientific world to question your work. It is necessary to be skeptical. It is necessary to keep an open mind. It is necessary to listen.

We will see how this continues to unfold and proceed, but it is interesting to watch and learn.

Leading Climate Scientist James Hansen - TED Talk

James Hansen is perhaps the leading climate scientist in the world. Check out his thoughts, as well as evidence for climate change, in this TED talk. This is a crucial issue for future generations.

TED Talk by Adam Savage (Mythbusters) - Simple Ideas Lead to Discovery!

Adam Savage of MythBusters fame, talks about how some simple ideas have led to great discoveries in science that have changed the world. I found it interesting, so enjoy and let me know what you think!

How to do Biot-Savart for Loop of Current

A second example of Biot-Savart is with loops of current. We know that any current will produce a magnetic field, but a circular loop of current produces a linear magnetic field along its central axis. This is like the Helmholtz coil we use in the lab. Check out how to set this up and get an expression for that central axis.

How to do Biot-Savart for Straight Wires with Ends

We have done some work already with Ampere's law for finding B-fields created by long wires, solenoids (with no ends) and toroids. But in reality wires have ends, and we must use the real thing, Biot-Savart, to get those magnetic fields. Check this out for finding the integral for a straight wire with ends.

Hacking into just about anything wireless - consequences of a wireless society

Check out this TED talk about how hackers can get into just about anything electronic and wireless. This is, in my mind, one of the great concerns for now and forever into the future. Electronic security systems are developed everyday, but it is a matter of time before hackers find a weakness to be exploited. Then the next newest, best security system is designed, only to be hacked in time. And so the game goes.

http://www.ted.com/talks/avi_rubin_all_your_devices_can_be_hacked.html

Treatment of Cancer Using E-fields!

Pretty relevant for seniors and the AP class, as there are electric field treatments for various medical conditions, such as certain types of cancer. Here is an interesting TED talk about this topic!

Check out a Remarkable Scale of the Universe Site!

I've always liked the powers of 10 video that most students have seen at some point. However, I may have a new favorite. Thanks to Sara D, a former student, who sent me the link to this. It is remarkable, in my humble opinion. Check it out!

http://onemorelevel.com/game/scale_of_the_universe_2012

New Experiments Create Galactic Strength Magnetic Fields

Thanks to Michael who found this article. Pretty timely as we begin magnetism!

Check out http://arstechnica.com/science/news/2012/01/galactic-magnetic-fields-produced-in-a-lab-using-lasers.ars?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+arstechnica%2Findex+%28Ars+Technica+-+Featured+Content%29 to check out the latest experiments that deal, in the lab, with galactic strength magnetic fields for protostars and galaxies. Technologies like this will open up new experimental paths in astronomy, where, of course, it is difficult to experimentally test theoretical predictions since we cannot just go out and begin measuring stuff on a galactic scale! This also helps us realize how much more we have to learn and test in the sciences...we will never be able to find final answers to this crazy universe.

Energy Review Set Solutions

The solutions for the energy review set last Thursday are at http://sp.eths.k12.il.us/vondracekm/Shared%20Documents/Forms/AllItems.aspx.

How to do Circular Motion Problems

Any time we have a circular motion problem for some object, we need to think in terms of using our generic mv^2/R for the net centripetal force. As always, draw the force diagram. But this time, also note where the center of the circle is, and draw in the radius line. Use the picture to set up the math! Anything that points along the radius towards the center is a positive centripetal force, and anything that points away from the center is a negative centripetal force. Check out both horizontal and vertical examples.

Energy Review

Today, make good use of time to hit energy topics. The big ideas include kinetic and potential energies, that relationship between force and potential energy, F = -dU/dx, which is used with potential wells, and work. Power is also fair game. There are videos for potential wells, gravitational energy, and springs (elastic energy). You will also get a review set. For the 3-4 class, keep in mind the addition of rotational kinetic energy for rotations.

Mechanics Review

Here is a quick video discussing the topics for the final. In particular, motion and Newton's laws. Keep in mind all the resources you have available. Quizzam solutions are all on my school website, notes and Princeton Review materials, and of course Moodle with all the old AP exams and solutions. There are also 5 old multiple choice exams on Moodle. Be productive today, and try the review set together. Keep in mind that for the final you will be responsible for things like the derivation for air friction - there is a how to video for both the hockey puck and sky diver examples. There is also a how to video for systems (tension problems). I hope all this helps!

How to do a NON-Gauss's law problem - A Partial Ring of Charge

Here is another example of a NON-Guass's law problem, a partial ring of charge. This is a combination of sticks and rings, the two classic cases where we might have to calculate something like an E-field or potential on some axis. In any case like this, we need to use the fundamentals: point charges, which we know how to do exactly. We break the problem into a bunch of little charges, find the small contribution, and then add them all up using an integral! Let's check it out, and I hope it helps.

How to do NON-Guass's Law Problem - A Stick WITH Ends

Gauss's law provides a relatively easy way to find E-fields for charged spheres, long sticks or cylinders, and large plates. The last two, of course, are approximations in the end, but ends, edges, and corners really make for a difficult math problem. When stuck with such a problem, we have no choice but to stick (heh, heh) with the fundamentals. That is, point charges. We know how to handle point charges, and physically that is all a charged object is - a bunch of extra charged particles. So we need to set up an integral and add up a bunch of small fields or potentials! Check it out.

How to Find the Tension in a Pendulum - Circular Motion

Here is a case where we have vertical circular motion, a pendulum or swing, where it is a bit more complicated than horizontal circular motion. For a pendulum, the tension and gravity components vary with the angle, so we have non-constant forces and acceleration. This could be tough to solve with Newton's laws. However, with energy we can find speeds more easily, and this will allow us to find the tension in the string for any angle of its motion. Check it out.

MIT Game Changer - Next-Generation of Higher Education for FREE

MIT and several other powerhouse colleges have, for years, had free courseware for many of their classes. Now, MIT is offering access to interactive courses FOR FREE to anyone on the planet! This is to be called MITx. You will not be able to get an MIT degree, but this will provide ANYONE the highest-level supplements in any subject you are interested in! New resources that will become available for education will be amazing! Can't wait to see what this is like.

How-To Videos Coming Back to Life

Hopefully, good news. A number of students have asked if and when how-to videos would re-appear, after they all disappeared last spring when the company that stored them went under. Slowly but surely they are coming back. Check out the List of all how-to videos and check out those with the 'On YouTube' note. I'm trying to get those that are relevant for exams back up first. Thanks for your patience, and I really hope these help!!