Scientific American's Top 10 Stories of 2010

Check out the top 10 science related stories the editors from Scientific American selected for 2010. Some are certainly debatable, but I agree the top story was the Gulf oil spill. The poor engineering in its original design to the clever engineering that eventually plugged the well, to the ecological, chemical and biological consequences of the disaster make this a classic multi-disciplinary problem.

Where do Good Ideas Come From?

I read an interesting book over break, written by Steven Johnson, that gets into the ways great ideas have been developed throughout history. My thoughts about the book and the seven themes that are developed can be found here. Any feedback or thoughts are welcome, as always!

The Power of Analogy in Learning

In physics, we use a lot of analogies. We compare just about all aspects of rotational motion to linear motion analogues. We compare electrical resistance to electrons bouncing in a pinball machine. Electric circuits are like roller coasters and plumbing systems. Energy and matter are like steam and ice, two forms of the same stuff. So this is not new for us, and it can really help us not only conceptually, but also in problem solving. If you are OK doing the mathematics of air friction, you can do the math of RC circuits, or if you know how to handle springs and pendulums in simple harmonic motion, you can do problems with LC circuits and even a case of Schrodinger's equation in quantum mechanics.

But on a larger scale, there is an interesting post about the power of analogy and how some are now thinking it is the key to cognition and learning in general. The more ways you can think about a system in terms of others that are more familiar and understood by you, then the more likely you are to solve the new problem. By building and modifying what you know about things through analogy, the more creative a solution you might develop when confronted by new problems that can be made familiar to things you know.

There is also a video from Doug Hofstadter at a Stanford forum on this topic. Watch it if interested, and after 13 minutes is the bulk of this topic.

A Video that shows how friction between tire and road is Centripetal Force

An amazing bit of driving by Ken Block! Check out how friction is the centripetal force as well as the force responsible for the motion of a car. I wonder how many years of practice allows one to drive like this. :-)

New Life Form!

NASA scientists have discovered an entirely new life form on Earth. This bacteria has had phosphorous replaced by arsenic, which was thought to be an impossibility yesterday, but today it is a reality. Check out the article, which also has a video link with a simulation showing what may be happening to create a new type of DNA. Fascinating!

What a STEM background could mean for you

STEM (short for Science, Technology, Engineering and Mathematics)areas of study are going to be the growth areas for jobs in the future. Check out this video, which starts of with Steven Chu, Nobel winning physicist and Secretary of Energy, and other industrial CEOs, as they make mention that STEM backgrounds are key to just about any type of job and career a present student may wish for in the next decade. Check it out!

Wussup with Ammeters and Voltmeters?

A shout-out to Anja, for producing this video explaining how ammeters and voltmeters are set up, i.e. what the circuitry is in order for these devices to give us measurements of currents and voltage differences. Many thanks!

Record your screencast online

Teaching Math via Computers and Computer Programming: What Do You Think?

Conrad Wolfram has a presentation about what he feels is a weak, antiquated way of teaching math in school. Instead of all hand-written work on paper, use computers to get students thinking about everyday problems. He argues that problems are dumbed-down in school, and that real-world calculations are not done that would better engage students, as well as lead to better math skills that are necessary in today's world. Because math is done on computers in research and the workplace, this would allow students to build the knowledge, tools and skills that are relevant in today's world, rather than the knowledge, tools and skills that were necessary 50 years ago in an age of agricultural and manufacturing jobs.

Personally I think he has a good point. However, I am convinced that doing just about anything one-way is not a good idea. Variety is necessary. There is something to be said for doing things by hand to learn process and the nuts and bolts of a computation. But I do think technology can be and should be used more frequently than is presently done, as this is a student's future. Also, not everyone will likely learn more if done on a computer. Some students do in fact enjoy pencil and paper problems, and can learn a great deal with this technique. I also think that many learn, or at least gain greater insights, interest and relevance of math through applications in something like physics. I know I finally got a grip on what calculus was all about after using it in physics, and many students have told me the same thing.

I am interested in your take on this as students...what do you think?

Very Good video about gravity and Einstein's Idea

This is the snippet from Brian Greene's Elegant Universe. It deals with Einstein's general theory of relativity, and the notion of warped space-time leading to what we call gravity. There are some very good graphics which help us get some pictures in our heads as to how this all works. I encourage you to watch it, and also the 'how to' video below that has to do with relativity and the principle of equivalence, to see how Einstein reasoned light is bent by gravity.

Some Advice - To Embrace Complex Networks to Find Simple Solutions

Scientist Eric Berlow shows a few examples of how one can think about complex systems and networks in order to find simpler structures and solutions. In networks where there are hubs (i.e. agents of the network which have many connections compared to most agents), one can look and focus on the first few orders of connectivity to begin looking at the key components and eliminate 'noise.' Rather than be freaked by a complex problem, step back and look at the overall picture to pick out the key pieces of the problem. Sound familiar? This is the approach we take for something like those systems with tension. We only look at the forces that may affect the motion and don't worry about the others. So we continuously try to simplify the complexity into simpler pieces. Or in circuit analysis, we isolate smaller networks of resistors, and simplify those to single resistors, until a complex circuit is redrawn as a series circuit. This is the idea Berlow is promoting. Check it out, and let me know what you think!

Do keep in mind, though, that this is not foolproof. Some times this approach makes a problem more manageable and it can lead to some sort of solution, or at least some sort of approximation, but other problems have so many intricacies that this approach leads to nowhere. It is a strategy you may try to see where it takes you.

The Basic Principle of General Relativity - Principle of Equivalence

Einstein published General Relativity in 1915. Similar to special relativity, where he only considered frames of reference moving with constant relative velocity, general relativity is based on simple principles that lead to fantastic consequences. In this case, Einstein reasoned that the Principle of Equivalence was the fundamental building block concept for gravity. It states that the effects of acceleration on a system are indistinguishable from the effects of gravity on that system. This video shows an example of this principle in action, and shows how you can quickly figure out gravity should bend the path of light, even though light has no mass (so Newton would say this cannot happen)! This principle also explains why inertial mass (the mass in F = ma) is equivalent to gravitational mass (the mass in F = GMm/r^2), which is why all objects fall at the same rate in a gravitational field. Note that general relativity leads to the Big Bang, black holes, stellar evolution, gravitational red shifts, precession of planetary orbits, effects on time (which are needed for GPS to be so accurate), frame dragging as planets and objects move through space-time, and so on. All are confirmed through observation and experiments. Check it out!

How to do Inelastic Collisions where bullets stick in blocks

Here is a case where bullets are fired into blocks, and by measuring what happens afterwards allows us to figure out the speed of the bullet before the collision. A classic example is a ballistic pendulum, and this is compared to a similar spring problem. Because the collisions are INelastic, kinetic energy before and after is not the same (KEo > KEf). But, conservation of momentum is what connects the before and after pictures of such collisions. Check it out.

Dark Matter - Interactive Forum from Scientific American

Check out the interactive discussion about dark matter, a favorite topic in modern physics, particularly in the astrophysics and particle physics fields. Dark matter is a generic term for anything that cannot be seen in the electromagnetic spectrum, but affects other objects gravitationally. This could be known matter such as neutrinos, neutron stars, brown dwarfs, or just unseen stars and galaxies. Or, it could be new forms of matter outside of the standard model in particle physics. There are names like WIMPS, MACHOS, axions, and others. Always a good time checking into cutting-edge ideas!

Spring Problems and the use of Energy

Springs provide a nice example of NON-constant force. We know Hooke's law, F = -kx, where x is the displacement of the spring from its equilibrium position. Keep in mind the - sign is for direction: the force always tries to bring a spring back to equilibrium, which is in the opposite direction relative to the direction of the displacement (a point of stable equilibrium). Here are examples of using energy conservation to solve spring problems.

A Need for a Paradigm Shift in Education - Sir Ken Robinson

What do you think about the current education system? It is a factory-style process built for the Industrial Age. How should education systems look like for an age of globalization, though???? Check out the following video, which is an animated summary of a lecture given by Sir Ken Robinson, who has been a leader in real education reform, a need for creativity, and so on. In my humble opinion, this is a wonderful video presentation that should get you thinking!

Keep in mind that no solutions are offered as to how to change classroom teaching and learning to fit the new paradigm, but such presentations are most useful to get the general population thinking, and also to get policymakers (i.e. politicians who are in charge of education, and who almost exclusively have not taught before) thinking before they continue down the same status quo reform movements like No Child Left Behind (Pres. Bush) and even Race to the Top (Pres. Obama).

Please comment, as I really am interested in your thoughts.

Hubble Deep Field, 3-D!

A tip of the cap to former Chem-Phys student Lina, for passing along this link to me. It is really neat!

http://www.flixxy.com/hubble-ultra-deep-field-3d.htm

Words of Wisdom from Bill Gates

This is supposed to have come from a speech Bill Gates, who at any given time is either the first or second richest person on the planet. His point was to tell students the major differences between being in school and the actual world. I suspect most adults would concur on most, if not all, of Gates's observations. I'll let you enjoy his comments!

Bill Gates speech: 11 rules your kids did not and will not learn in school

Rule 1: Life is not fair - get used to it!

Rule 2: The world doesn't care about your self-esteem. The world will expect you to accomplish something BEFORE you feel good about yourself.

Rule 3: You will NOT make $60,000 a year right out of high school. You won't be a vice-president with a car phone until you earn both.

Rule 4: If you think your teacher is tough, wait till you get a boss.

Rule 5: Flipping burgers is not beneath your dignity. Your Grandparents had a different word for burger flipping: they called it opportunity.

Rule 6: If you mess up, it's not your parents' fault, so don't whine about your mistakes, learn from them.

Rule 7: Before you were born, your parents weren't as boring as they are now. They got that way from paying your bills, cleaning your clothes and listening to you talk about how cool you thought you were. So before you save the rain forest from the parasites of your parent's generation, try delousing the closet in your own room.

Rule 8: Your school may have done away with winners and losers, but life HAS NOT. In some schools, they have abolished failing grades and they'll give you as MANY TIMES as you want to get the right answer. This doesn't bear the slightest resemblance to ANYTHING in real life.

Rule 9: Life is not divided into semesters. You don't get summers off and very few employers are interested in helping you FIND YOURSELF. Do that on your own time.

Rule 10: Television is NOT real life. In real life people actually have to leave the coffee shop and go to jobs.

Rule 11: Be nice to nerds. Chances are you'll end up working for one.

Science and Democracy

I read a truly interesting book over the summer, called "The Science of Liberty" by Timothy Ferris, one of the best science writers we have today. The argument he poses is that the development of science is effectively responsible for the creation of American liberal democracy (not meaning the modern interpretation of liberal, which is associated with being a Democrat, but rather the creation of liberty as a basic human right). I wrote about this back in early July, but am pleased to see that others are taking interest in the book.

There is a new Skeptic article in Scientific American. In it, Michael Shermer gives his take on the premise of the book, and I encourage you to take a look at it and find out what you think. It is an interesting topic.

Let the Madness Begin!

Well, we are here, back in ETHS!! Welcome back. I anticipate a fantastic year as we pursue a journey to figure out some physics, and gain insight into how the universe works. This blog will have a variety of thoughts and questions throughout the year for us to ponder. It will have links to 'how to' videos for a large assortment of problems and concepts. From time to time I may request your feedback to certain posts, so we can get a class discussion going. It is important that you have some experience with using blogs since they are likely here to stay. We will do other forums in Moodle from time to time, as well, so we can make good use in sharing information and opinions with each other using a few different technologies. However, you are, of course, welcome and encouraged to leave comments any time you wish. You will need a Google account (by getting gmail, for example, at gmail.com).

Enjoy the first few days, and we'll get to work. I hope you had a wonderful summer, but it will be good to see all of you.

New School Year Almost Upon Us

In just a few weeks, we will be back at it at good ol' ETHS. I hope everyone has had a wonderful, relaxing summer, and is charged up to have some good times in Physics. I am looking forward to seeing everyone very soon.

Take it easy, and incoming seniors, do some work on those college essays now...you'll thank yourself when school is in session and those AP classes are loading you up with work. :-)

Evolution of Information

I will give the direct link to Zenpundit's post on this topic. It is a really interesting, non-technical, 8-minute history of the evolution of information since humans first began writing down information. Of particular interest is where information gathering and acessibility is headed in the next couple decades. I agree with the analysis presented in the video, and one can already see hints of things to come. We are in a 'pull' era, where individuals are expecting and demanding that they be able to gather information from all media resources, whenever and wherever they happen to be (this is a large part of the fate of traditional newspapers that cannot compete with online news sources, for instance; traditional newspapers are part of the 'push' era that we have been exiting over the last 5-10 years). This is also why 'smart phones' are becoming the tool of choice for millions, if not billions, of individuals worldwide, and they will take the lead in the 'pull' era.

An aside: It would be wise for educators to note this trend, accept it, and begin to allow students to use personal communications devices more frequently in the education process.

Graduate School in the Sciences

We had some Northwestern graduate students over today, who talked about their research with dielectrics for capacitors and transistors, as well as flexible video displays for a whole host of applications in the next decade or so. But another topic that came up was what is it like in graduate school?

Something that surprised many of the high school students is that graduate students get paid to go to school! This is absolutely true! Grad students in the sciences and mathematics generally are given assistantships, either teaching or research, when they come to a graduate college. For instance, during my first year of grad school I took my own classes and was a teaching assistant for one of the main introductory physics courses for premeds (essentially like AP Physics B). My tuition was paid for, and I got a salary - not a huge amount of money, but certainly enough for an apartment, living expenses, food, and so on. After my first year, I then was in a research group and hired as a research assistant by a professor who then became my adviser. I then completed my graduate courses, received my Masters Degree in Physics, and then lived on site at Fermilab for a couple years as we ran our detector and collected data sets for dissertations. I never paid a cent for tuition, and actually made enough to save and get married shortly before graduating with a doctorate. Not a bad deal!

Keep this in mind since most of you in Chem-Phys are considering technical majors and most will end up going to graduate school. Try to get involved in research as an undergraduate. Talk with professors, postdocs and graduate students, and make connections in areas of interest. There are so many neat opportunities in college, and many of those can prepare you for graduate school and beyond!

Genius in the Group-Think Era?

One other old post that relates to an issue we are discussing in class, as we think about complex systems, emergence and fractal geometry. Benoit Mandelbrot is another example of someone who was able to create a paradigm shift in the field of mathematics. But he was a loner in many ways, someone who was outside the mainstream of mathematics, and who was willing to think outside of what the traditional textbooks taught. He was a self-admitted 'oddball' who did not fit into the usual academia environment. Many others who changed their fields were also more isolated and were willing to question the textbooks of their day - Copernicus, Galileo, Newton, Darwin, Einstein, etc. These individuals were also willing and able to take the brunt of criticism from the "establishment" who were disturbed by the very thought that new knowledge in the field could exist. I do worry that we may have more limitations on such thinkers and shakers, and paradigm-shift makers, in the future because of too much connectivity that promotes 'group-think.' Like anything, problems tend to arise when focus goes too much in one direction. We need a mix of group think, but also individual time to question and be skeptical of the group. This has become a business model for companies like Google, where staff must take a rather substantial percentage of time to work on individual projects outside the company driven projects...they realize it is important to have a mix of thoughts and keep creativity and innovation at the forefront of what they do. xHere is a post from December of 2008:

Found an interesting article off Yahoo. It asked the question if Albert Einstein is the last great genius. This is a legitimate question in an age where 'group-think' is becoming the rage. There are obvious benefits to mass collaboration, largely making use of Web 2.0 tools and applications, and the best set of examples I have found are in the book Wikinomics.

One would like to think that individuals can still make a difference. I suspect this will still be the case, but less frequently than in the past. Ideas can blossom so quickly once numerous people share concepts and possible solutions to problems, but I would argue that there lies a chance that group-think may, in some cases, have one idea catch on that leads the pack on a path that ultimately runs into a dead-end. The notion of 'trends' and 'fads' hold true, and the 'latest craze' idea can attract most minds of the group. It may turn out that it will take an individual or small subset of the larger group to break from the group mindset, think outside the box, and develop an original idea that becomes the next focus of the group. Perhaps a good structure to a mass collaboration is to have numerous subsets working on different aspects of the problem from different points of view, so as to resist the temptation to fall into a 'fad' mentality. This falls in line with 'Mediciexity.' One example of the 'fad' mentality may be string theory. The concept of the 'string' is attractive to solving the ultimate questions of the universe, and over the past couple decades many of the most promising and powerful theoretical and mathematical minds have become part of that 'group.' However, all these years later there is not a viable, i.e. testable, theory that fits into the experimental realm of physics. Time will tell if this mass collaboration is worth it in the end...it may end up one brilliant idea, from one brilliant person, completely separated from the string theory group, will end up being correct. Individuals may still change the world.

Perhaps the notion of individual genius making its mark in the modern mass collaboration age is evolving to the point of the genius required to form the right group. Web 2.0 technology has been applied in an unprecedented way by Barack Obama and a small, few person group of advisers. The creativity, forward-thinking plan and then the discipline and message-delivery by Obama himself has taken a young, smart, but relatively unknown and inexperienced politician whose future was supposed to be a decade away (according the group-thinking of the more traditional political parties)to the presidency. It still takes individuals or very small groups to develop a concept and start the larger group/collaboration, so perhaps this is where we will see genius more often than not.

There will always be a place for individuals, so we need to be careful not to push young minds, which tend to be the most creative and open to new ways of thinking, entirely into a group-think mindset...they still need to be encouraged to think for themselves, be skeptical of the group, and not be afraid to offer up 'outside the box' thinking and creative solutions. I want my students, at least, to never shy away from individual interests and ideas, and to not just go along with the latest fad if they don't agree with it. As always, I am not a proponent of going with one way of doing something, but rather using variety; not to fall into a 'whole language only' or a 'phonics only' way of learning, but rather taking the good things from each and using them. Variety, in this case group-think and individual-think, and the good that comes from each, is the spice of the new Web 2.0 life.

Problems that will Require Science for Solutions

This is a post I put on my other blog in December of 2008:

When one thinks about the variety of problems we face as both a national and global society, it becomes clear that science will be looked to to develop answers and solutions to many of these problems. It is also clear that we need to think of this as science in the broadest sense, as all areas and disciplines will need to contribute. This goes to the heart of the definition of consilience, as numerous areas of knowledge and expertise will need to mix together if we are to make solid progress in finding effective solutions.

To get the ball rolling, consider the following broad issues/problems. All of these will require contributions from a variety of scientific and technical areas of study...multidisciplinary tasks galore:

* Quality of air and water
* Fresh water supplies for much of the west and southwest
* Disposal of solid wastes (everyday garbage)
* Modernization and maintenance of national power grid
* New energy sources, better energy efficiency and conservation
* Climate change (both at an understanding level as well as preparing for consequences)
* Improved electronic encryption algorithms as we digitize everything (medical, financial records, etc)
* Transportation infrastructure
* Telecommunications networks, both development and maintenance
* Continued improvement and progress in computing technologies
* Mass electronic data storage
* Medical treatments for the disease of your choice. This includes stem cell issues, genetic engineering, drug R&D, and so on.
* Military related technologies
* Improved search technologies for earth-crossing asteroids (something I have yet to hear policymakers talk about publicly, but there are literally many thousands of sizeable objects that cross earth's orbit we should try to identify and monitor)
* Food supplies and quality control
* Disposal of nuclear wastes, nuclear proliferation issues
* Nanotechnology in general
* Security technology of all types
* Robotics
* Implementation of educational strategies and structures based on brain research and learning theory to best prepare the next generation of workers
* Continued development of network theory, game theory, etc., and progress in our understanding of complex systems for physical and social applications
* Materials science and development

I encourage comments with additional major issues that are technical in nature and subject to progress via scientific avenues; this is not at all a complete list. What we cannot forget is that further inclusion of other areas of study are intimately connected with just about everything on the above list, such as ethics, state/national/international law, economics, political science, sociology, public policy, military concerns, all areas of engineering, business/industry, job creation, international relations, anthropology, and countless subfields that fall under these larger areas of specialization.

The quicker we as a society recognize and realize the complexity, multidisciplinarity, and difficulty level of finding both short-term and long-term solutions to problems found in any of these areas, the better off we will be. The next president will need to address all of these during the course of an administration, as will every other prominent political figure in every nation across the globe. We will not be able to ignore any of them, and these loom as multi-generational issues that need to be solved. This will require leaders who are able to connect with the masses and communicate the seriousness of the issues, as well as move his or her nation toward a mindset of long-term planning and policy, something we seem to not be very good at.

We need to find and create massive numbers of people who are trained in the all of the sciences, mathematics, engineering and technology, and all the other fields mentioned above to remain competitive in a global marketplace, as well as the maintain and improve the quality of life for future generations. It is challenging work, but do we have any other choice but to address these challenges? Does our consumption-based and entertainment-driven society have the backbone and means to deal with these issues? Will we leave the world in better condition for our kids and grandkids than what we inherited?

Prepping for AP Exams

The Physics AP Exam is Monday, May 10, with mechanics at noon, E&M at 2 pm.

A class motto has been: 'A problem a day keeps the 1, 2, 3's away.' You should know by now the topics and types of problems that cause you headaches, so do those problems each day (takes about 20 or so minutes to try the problem and then check the solution) to fix your understanding or to develop the right question to ask me or another student at school, and you will be set for the real thing. There are LOTS of resources and practice problems, so take advantage of them, and just dedicating 20-30 minutes per night gets you away from having to cram all weekend. Try to have some fun with it, as you try to apply all that we have learned through the year to figure out some challenging, neat problems!

Good luck over the next week and a half, and see you at school!!

How to Handle Real Pulley in a Tension Problem

This is our old favorite - a couple masses tied together, string going over a pulley. In the good ol' days, the pulley was frictionless, and we simply could say that the tensions at the two ends of the (massless) string were the same, and set up F = ma for the system to get the acceleration. Worked out well.

But, in reality the pulley accelerates, too. How do we handle this? This means there has to be a net torque on the pulley in order to cause an angular acceleration. The only way for this to happen is if the tensions on the sides of the pulley, due to the hanging masses, are different. Here we see how to deal with this new situation, and apply F = ma on the two blocks, and torque = I*alpha on the pulley. We will assume there is no slipping between the string and the pulley, so we can relate linear motion of the blocks to the rotational motion of the pulley. Check it out.

List of How to Videos on the blog

Below are links to specific “How To” videos that are relevant to 3 and 4 Chem-Phys. These show how to access programs perhaps, or how to do certain problems. It has a voice-over and screencast from Doc V’s tablet computer, so it is similar to being in class as we model how to do certain problems or run certain programs. These can be useful if you were gone the day we covered the topic, or need more examples with explanations, or want to review things from class prior to quizzams.


Student Independent Science Research
http://docvphysics.blogspot.com/2009/12/how-to-start-science-research-in-high.html


Mechanics

Air Friction – the math
http://docvphysics.blogspot.com/2009/10/how-to-deal-with-air-friction.html

Binary Orbits
http://docvphysics.blogspot.com/2009/12/how-to-find-basics-of-binary-orbits.html

Derivatives! What are they and how to do them.
http://docvphysics.blogspot.com/2009/10/how-to-define-and-find-derivatives.html

General Relativity and the Principle of Equivalence - Why does Gravity Bend Light?
http://docvphysics.blogspot.com/2010/11/basic-principle-of-general-relativity.html

Gravitational Potential Energy and Space Launches
http://docvphysics.blogspot.com/2009/12/how-to-find-gravitational-u-and-basics.html

Momentum Conservation – Why?
http://docvphysics.blogspot.com/2010/02/why-is-momentum-conserved-for-colliding.html

Momentum Conservation - How to do Inelastic Collisions
http://docvphysics.blogspot.com/2010/11/how-to-do-inelastic-collisions-where.html

Moment of Inertia Using the Integral – Disks
http://docvphysics.blogspot.com/2010/04/how-to-find-moment-of-inertia-for-solid.html

Moment of Inertia Using the Integral – Sticks
http://docvphysics.blogspot.com/2010/04/how-to-calculate-moments-of-inertia.html

Parallel Axis Theorem (finding moments of inertia)
http://docvphysics.blogspot.com/2010/03/how-to-use-parallel-axis-theorem-to.html

Pendulum: Simple Harmonic Motion for small angles
http://docvphysics.blogspot.com/2010/04/how-to-get-simple-harmonic-motion.html

Potential Wells
http://docvphysics.blogspot.com/2009/12/how-to-interpret-potential-wells.html

Quantum Numbers: Using Simple Harmonic Motion to help see where these come from
http://docvphysics.blogspot.com/2010/04/where-do-those-quantum-numbers-come.html

Rotations: Both Linear and Rotational Motion Simultaneously
http://docvphysics.blogspot.com/2010/03/how-to-handle-rotations-and-linear.html

Rotations: Collisions and Conservation of Angular Momentum
http://docvphysics.blogspot.com/2010/03/how-to-apply-conservation-of-angular.html

Rotations: NON-Constant Acceleration
http://docvphysics.blogspot.com/2010/03/how-to-do-rotational-motion-for.html

Simple Harmonic Motion: General Derivation of sine, cosine solutions
http://docvphysics.blogspot.com/2010/03/how-to-find-solutions-for-simple.html

Simple Harmonic Motion: Solving with specific initial conditions using phase angle
http://docvphysics.blogspot.com/2010/03/how-to-solve-simple-harmonic-motion.html

Special Relativity – mass and energy, where E = mc2 comes from
http://docvphysics.blogspot.com/2009/12/how-to-play-einstein-for-day-mass-and.html

Springs and Energy
http://docvphysics.blogspot.com/2010/11/spring-problems-and-use-of-energy.html

Tension problems with rotating pulleys: http://docvphysics.blogspot.com/2010/04/how-to-handle-real-pulley-in-tension.html

Tension problems with systems of objects: http://docvphysics.blogspot.com/2009/10/how-to-do-tension-problems.html



E&M

Ammeters and Voltmeters - How they work
http://docvphysics.blogspot.com/2010/12/wussup-with-ammeters-and-voltmeters.html

Ampere’s law applications
http://docvphysics.blogspot.com/2010/03/how-to-apply-amperes-law.html

Capacitance – how to find capacitance for the 3 types of capacitors
http://docvphysics.blogspot.com/2009/12/how-to-find-capacitance-for-each-type.html

Capacitor Circuits – How to find stored charge
http://docvphysics.blogspot.com/2009/12/how-to-find-charge-on-capacitors-in.html

Electric Circuit analysis
http://docvphysics.blogspot.com/2009/11/how-to-analyze-resistor-circuits.html

Electromagnetic Induction – how Induced Currents turn on (includes circulating E-field)
http://docvphysics.blogspot.com/2010/04/how-to-find-circulating-induced.html

Faraday’s law – Changing area with constant B-field
http://docvphysics.blogspot.com/2010/04/how-to-do-faradays-law-for-changing.html

Faraday’s law – Changing B-field with constant area
http://docvphysics.blogspot.com/2010/04/how-to-use-faradays-law-for-cases-where.html

Gauss’s law with conductors
http://docvphysics.blogspot.com/2009/10/how-to-do-gausss-law-with-conducting.html

Gauss’s law with NON-conductors: charge density
http://docvphysics.blogspot.com/2009/10/how-to-do-gausss-law-with-non.html

Gauss’s law with NON-uniform charge densities
http://docvphysics.blogspot.com/2010/04/how-to-do-gausss-law-with-non-uniform.html

Integration of E-fields to get Potential
http://docvphysics.blogspot.com/2009/11/how-to-integrate-and-find-electric.html

LC Circuit – similar to simple harmonic motion
http://docvphysics.blogspot.com/2010/04/how-to-do-math-of-lc-circuits.html

Magnetic Flux – Rectangular loop next to straight wire with current
http://docvphysics.blogspot.com/2010/04/how-to-find-magnetic-flux-straight-wire.html

Magnetic force between two current carrying wires
http://docvphysics.blogspot.com/2010/03/how-to-find-magnetic-forces-between.html

Mass Spectrometers and Velocity Selectors – magnetic forces, F = qv x B
http://docvphysics.blogspot.com/2010/04/how-to-think-about-mass-spectrometers.html

Point Charge Systems – finding total electric fields and potentials
http://docvphysics.blogspot.com/2010/04/how-to-find-electric-fields-and.html

Projectile Motion of Electric Charges
http://docvphysics.blogspot.com/2010/04/how-to-do-electrical-projectiles.html

RC Circuits – Charging Capacitor (series RC)
http://docvphysics.blogspot.com/2009/12/how-to-solve-charging-rc-circuit.html

RC Circuits – Discharging Capacitor (series RC)
http://docvphysics.blogspot.com/2009/12/how-to-solve-discharging-rc-circuit.html

RC Circuits – Resistor and capacitor in parallel
http://docvphysics.blogspot.com/2010/01/how-to-do-rc-circuit-with-r-and-c-in.html

RL Circuits – Current as functions of time
http://docvphysics.blogspot.com/2010/04/how-to-analyze-rl-circuits.html



Interactive Physics
Interactive Physics is software where you can design and create your own simulations; mostly for mechanics, but there are some E&M topics you can also work on. This is on school computers.
http://docvphysics.blogspot.com/2009/08/how-to-access-interactive-physics.html



iLab
See how to access the radioactivity iLab:
http://docvphysics.blogspot.com/2009/08/how-to-access-radioactivity-ilab.html

How to do the Math of LC Circuits

Interesting things happen when you combine loops of wire and metal plates in series. Inductors and capacitors together create AC currents at tunable frequencies, which in principle is the essence of our wireless society. In classical physics, the easiest way to create electromagnetic radiation is to accelerate (such as by shaking) electric charges, and that is exactly what you have in an AC current. Check this out to remind you of the math, and how LC circuits are the equivalent of simple harmonic motion of masses on springs from mechanics.

How to Find Magnetic Flux - Straight wire next to a loop

This is a classic type of problem, where a current in a straight wire is next to a rectangular loop, and we need to find the total magnetic flux through the loop. We need to break the loop into skinny strips of area, and find the flux through those skinny strips, then add them all up, i.e. integrate! Check it out to remind yourself.

How to do Electrical Projectiles

When a charge flies between the plates of a parallel-plate capacitor that is charged up, the particle will essentially be in a uniform electric field. This means there is a constant electric force, F = qE, and therefore we have a condition similar to a ball rolling off a table. The charge will move in a parabolic path as if it were a projectile...it has a constant horizontal speed, and a constant vertical acceleration. Check this out to remind yourself how to do the mechanics of a projectile.

How to think about mass spectrometers

We know that electric charges moving in magnetic fields feel a force, called the Lorentz force, which is a cross product: F = qv x B.

This force is always perpendicular to the motion and B-field, and because of this particles get pushed into circular paths. This means the centripetal force is determined by the magnetic force. No work is done, as the energy is unchanged, but just the direction of the particle is changed.

In order to get a mass spectrometer to work, we also need to know the velocity of the particles. We can use electric fields to create a velocity selector. Keep in mind there is a good ActivPhysics simulation for mass spectrometers, 13.10, you may want to check out, too.

How to Analyze RL Circuits

An inductor is like a small solenoid in a circuit. It behaves like any loop of wire with currents, and follows the rules of em induction, such as Lenz's law. Conceptually, inductors resist changes in magnetic flux. This means they fight batteries when first connected, and therefore prevent current from flowing initially, and after a long time become nothing more than wires in a circuit, with steady current flowing.

The voltage across an inductor was derived from Faraday's law to be V = -L di/dt. Inductors with current flowing around the loops of wire also has a B-field in the tube, and this field stores energy, U = (1/2)Li^2. Check out this video to see how to do the mathematical derivations of current as a function of time when inductors are in series with a resistor.

How to find electric fields and potentials for systems of point charges

One of the most essential and basic systems we study includes systems of stationary point charges. These bring out the essence of what charges do, which is produce a vector quantity, electric field, and a scalar quantity, electric potential.

We need to remember that finding electric fields includes us forgetting about the sign of a charge when calculating the fields. Being a vector, let the picture tell you whether we are dealing with positive or negative directions of components. But for potentials, which are scalars, we DO need to include the signs of charges numerically since positive charges produce positive voltage, and negative charges produce negative voltage, and we just add up the values.

How to do Gauss's law with NON-uniform charge density inside a non-conducting material

The vast majority of Gauss's law problems we do deal with uniform charge densities for non-conductors/insulators. These are the cases where there is charge inside the material, and therefore an electric field, and our job is to find the electric field inside. When the charge density, rho, is constant/uniform, the classic result is the field is linear with r. That is the result whether we have a sphere or a cylinder, and would be the same for gravity, electric fields, or magnetic fields (using Ampere's law).

But what about NON-uniform charge density, where rho depends on radius, r? What do we do with Gauss's law to find the electric fields inside these type of materials and objects? This video is an example of how to handle it. The gist is we need to set up an integral where we add the charges within skinny, hollow spheres of charge. Each little sphere has its own charge density value, and so the charge of each hollow shell is rho x dV. The trick is the dV = (4*pi*r^2)(dr), at least for a sphere. The dr is the small thickness of the hollow shell. The same idea holds for cylinders, where dV = (2*pi*L*r)(dr). I hope this helps!

How to find the Moment of Inertia for a Solid Disk

We have explicitly found the moments of inertia for point masses and also for sticks, and we have even defined the parallel-axis theorem. But what about more complicated objects, such as solid disks or cylinders that spin or roll? We have been given the inertia expression of (1/2)MR^2, and have used it quite a bit in problems, but where in the world does it come from? How do we use the integral definition of inertia to solve this? That is what this video is about, as a number of people have asked about where the inertia expressions for rolling objects come from. I hope this helps and makes sense.

How to Calculate Moments of Inertia with Integral - Sticks

When it comes to finding moments of inertia, the one thing we can find exactly is the inertia of a point mass, I = mr^2. Here, m is the mass, and r is the distance from the mass to the axis of rotation. But we run into some amount of difficulty when we have real objects that rotate and are made of countless point masses, i.e. atoms. How can we get the total moment of inertia?

We have an integral definition for I. What is is really telling us to do is break up the object into a bunch of small pieces of mass, dm. This is like saying break it up into a bunch of point masses, find each individual inertia, and then add (integrate) them all up to get the total. I will show how to do this with a stick in this video, which is the main case we would ever need to use the integral for class. Keep in mind that the other inertias we use for disks, balls, and so on, are found with this integral, too. I hope this helps. Keep in mind that I also have another video that shows how to use the parallel-axis theorem, which is a way around having to do the integration if you happen to know the moment of inertia of an object with the axis through the center of mass of the object.

How to Find Circulating Induced Electric fields when there is dB/dt

We have seen that electric currents create magnetic fields that circulate around the moving charges. This is the essence of Biot-Savart and Ampere's laws. But in certain cases of electromagnetic induction, magnetic fields can vary with time. The easiest example is simply moving a magnet relative to a solenoid or loop of wire. The trouble is, when one considers the physical reason for the induced currents that we find, there is no magnetic force on the charges of the wire, since the wire is at rest (i.e. qv x B = 0). So how does a current begin?

Think of a moving charge. At some fixed point in space, a moving charge would mean that the E-field at the point is changing...think dE/dt. What is the result of this changing E-field? A circulating magnetic field! Could it be that a changing magnetic field then induces a circulating electric field around the magnetic field? Absolutely! And we even know how to mathematically handle a circulating field from Ampere's law.

Turns out that whenever there is a changing magnetic field, dB/dt, an E-field is induced that circulates around the magnetic field! It is basically Ampere's law for electric fields, and therefore it is actually an electric force, F = qE, that pushes the current in the circuit. This video walks through the details of how induced currents physically form.

How to do Faraday's law for Changing Areas of a Circuit

Here is an example of electromagnetic induction and Faraday's law for a constant B-field and a changing area. A conducting hoop/circuit moves into a B-field, and we determine the induced voltage (i.e. emf) and current. I'll make mention of two different magnetic forces that are relevant here: first, F = qv x B is the force that physically gets the current started since a conductor with free charges is moving through a B-field; second, once that current is turned on, F = Il x B turns on to try and slow the circuit down (magnetic brake). Lenz's law is also discussed.

One other aspect of this is the determination of the velocity of the circuit as a function of time. The magnetic braking force is analyzed with Newton's 2nd law, and we get a similar result as we did in mechanics with air friction, where the force is exponential in time. I hope this helps!

How to Use Faraday's law for cases where B-field Changes

Faraday discovered that any change in magnetic flux causes induced voltage (i.e. electromotive force, or emf) in a closed conducting circuit. Because there is a voltage, this means an electric current is also induced. Faraday's law, or
induced voltage = -d(flux)/dt, allows us to figure out how much voltage is induced. Ohm's law, i = emf/resistance, allows us to figure out how much current turns on, and Lenz's law tells us the direction of the induced current flow.

Lenz's law is "Nature abhors change," or also we could say, "Get the (change in) flux outta here!" All the induced effects fight the change in flux.

Faraday's law helps explain how generators, electric motors, transformers, the ring launcher, credit card scanners, magnetic brakes, and other devices work, so it is tremendously important for everyday life applications. I hope this video helps!

Where do those Quantum Numbers come from? Using Simple Harmonic Motion to gain some insight...

In Chemistry, you learn about electron configurations, which involves learning the rules for 4 quantum numbers. Three of these numbers are integers. But students tend to be mystified by where these suddenly and almost magically appear. Why integers? Why the values that you are forced to memorize?

It all starts with the heart and soul of quantum mechanics, which is the Schrodinger equation. This is the F = ma of quantum land. For this case, our system is an electron oscillating back and forth between two walls. It is a nice, neat 1-D system. When we see what the Schrodinger equation looks like in this case, it will be identical to what we get for a mass on a spring oscillating back and forth. Since we know the solution of simple harmonic motion is a sine or cosine, then the solution of what turns out to be the wave function for our electron is also a sine or cosine. We will see that the electron will be restricted in its energy, that it will have restricted energies determined by an integer that we get as part of our solution! It is a quantum number!

These quantum numbers are simply part of solutions to complicated equations you get from the Schrodinger equation. An exact solution exists for a hydrogen atom, for example. You get three integers for an electron in an atomic orbital because it is a 3-D system rather than the 1-D system we deal with here. But the idea is the same. Integers are natural parts of these solutions, and they then are part of energy solutions for atoms and particles, which tells us that the energies of the electron have specific, allowed values, and not a continuum of energy that we see for a superball bouncing between two walls in a big, macro-world. The micro-world follows a separate set of rules in quantum mechanics. I hope this helps.

By the way, for an example of how the quantum numbers play out for the periodic table, check out some rules of the game.

How to get Simple Harmonic Motion Solution for a Pendulum

A pendulum is technically NOT simple harmonic motion like a spring. SHM is defined when a force is proportional to the displacement of the object, just like a spring has F proportional to x. A pendulum is close, but the restoring force, being the tangential component of gravity, is proportional to sin(theta). Check out this video to see what we mean by the small angle approximation, or sin(theta) ~ theta (in radians) when theta is small, or about 10-degrees or smaller. This approximation works well, and you should check it on your calculator to prove it to yourself if you are not familiar with this. So for small angles, a pendulum is mathematically the same as an oscillating spring, and therefore is SHM and has a known solution of sine or cosine of wt plus a phase angle.

How to solve simple harmonic motion problems using initial conditions

We have seen how the general solution for simple harmonic motion involves sines or cosines. These functions are periodic functions, and it makes sense that they are used to solve period motion problems. But what about problems where we are given initial conditions (i.e. at t = 0)? How do we find specific solutions to specific problems? Well, here is an example of how to do this. We will have a case where a mass oscillating on a spring has BOTH initial position and initial velocity. We introduce the general solution that involves a phase angle. Check it out.

How to find solutions for simple harmonic motion (SHM)

Simple harmonic motion is a subset of periodic motion, defined as motion that depends on displacement. Springs certainly follow this definition since Hooke's law gives us F = -kx. This picture of a mass oscillating at the end of a spring also makes use of energy, U = .5kx^2. But our goal is to understand the motion as a function of time, as well as a function of position. Bringing time into the picture is the issue, and it turns out we need a second order differential equation. This video outlines how to get a solution for position of the mass on a spring as functions of time. Turns out these require sine or cosine functions. Other videos will focus on other details and specific problems to show a general solution we can use.

How to handle rotations with Rolling without Slipping

This is a classic rotations problem, where a ball rolls down a hill without any slipping. Because both linear and rotational motions happen simultaneously, we need to solve both motions simultaneously with F = ma and t = I(alpha). This would be true for any sort of 'rolling without slipping' problem, as well. Check it out!

How to Apply Conservation of Angular Momentum to Rotational Motion and Collisions

Here is a sliding block and hanging rod, where the block collides and sticks to the rod. Angular momentum is needed, and here is a case where conservation of angular momentum is used to figure out the initial speed of the block before the collision occurs. Take a look to see the general, symbolic setup for such a problem, which will be similar to a ballistic pendulum from linear momentum days. I hope this helps.

How to Use the Parallel Axis Theorem to Find Moments of Inertia

The parallel axis theorem is a neat shortcut that allows us to find moments of inertia for objects when the axis of rotation is somewhere other than the center of mass of the object. If you know the inertia for objects when going through the center of mass, you can quickly find the new value of I for any axis that is parallel to the center of mass axis and displaced by some distance from the center of mass, d. The theorem says I_new = I_cm + Md^2. We do not have to use the integral to apply the theorem, which is why it is such a nice shortcut.

This video shows a couple quick examples of how to apply the theorem. Hope it helps!

How to do Rotational Motion for a rotating, falling bar - NON-constant acceleration

Check out an example of a NON-constant angular acceleration problem, where a bar starting in static equilibrium (up = down, cw = ccw) goes into non-equilibrium and accelerates. You can see how torque = I*(alpha) gives us the angular acceleration of the bar at any given angle it has rotated through, and also how to use rotational energy and energy conservation to determine the angular speed at any given angle.

One thing to keep in mind as far as linear acceleration and linear speed is that each point of the bar has different values for these quantities, as determined by a = R*alpha and v = R*omega. Check it out...

Rotational Motion - New Concepts

For the 3 Chem-Phys sections, we are into rotational motion. This is typically a challenging topic because it is brand new. Keep in mind what makes it new revolves (ha, ha) around 3 new concepts:
- Torque
- Moment of inertia
- Angular momentum

Torques are produced by forces, and specifically those forces that cause a change in rotational motion. In other words, torques produce angular accelerations (analogous to forces causing linear accelerations). Mathematically, individual forces cause a torque = F(r)[sin(theta)]. Torque is a cross product vector, t = r x F.

Moment of inertia is analogous to mass in linear motion. It is a 'resistance to a change in rotational motion.' The higher the inertia, the smaller the angular acceleration from the same torque. Together, torque, t, and moment of inertia, I, are related through the 2nd law for rotations:
t = I(alpha)

The moment of inertia has units of kg m^2, and numerically tells us about the distribution of mass about the axis of rotation of the object or system.

Angular momentum, L, is also a cross product vector, L = r x p. The direction is found with the curly RHR, as we do in class. Remember the conservation of linear momentum? Momentum is conserved for a system if no external forces act on the system. Here is the analogy: angular momentum is conserved for a system if there is no external torques acting on the system. Individual objects can have angular impulse in collisions, but for the system it is conserved. We will get into this in a big way, and I'll soon have some how to videos up for rotations.

Let's have some fun with it!

How to Apply Ampere's Law

Ampere's law is to magnetic fields as Gauss's law is to electric fields. We only use it in 3 cases, just like Gauss, and it even looks similar to Gauss's law, only it is a 1-D integral compared to a 2-D integral. A line integral, or to some a path integral, basically means we are looking for the magnetic field times the length of the path the B-field follows. This can work for us with long, straight wires with current, a solenoid, and a toroid. Check out how to apply Ampere's law in 2 of the 3 cases, those being a straight wire and toroid.

How to Find Magnetic Forces Between Current Carrying Wires

Many electronic devices have parallel wires with currents flowing. Now, each current produces magnetic fields that circulate around the current, and these magnetic fields interact with the other current to produce a force, due to F = Il x B. Check out this video to see how to combine a couple concepts - Ampere's law determines the strength of the magnetic field from one of the currents, and then this goes into the force equation to determine the strength of the force. The right hand rule will help determine the direction of the force. Net result is that currents in the same direction attract, and in opposite directions repel. Hope this helps!

Why is Momentum Conserved for Colliding Objects?

A brief explanation of why momentum is conserved when multiple objects collide. It is important to distinguish between impulse, or a change of an individual's momentum, and conservation of momentum, which is true for a system that has no external forces acting on the system. When combined with the 3rd law of motion, for every action there is an equal and opposite reaction, impulse and the 3rd law show that the system's impulse is 0...momentum does not change for the system if all we have are the internal forces between the objects.

Impulse: Golf Club Hitting Ball

This is happening at 70,000 frames per second (a bit quicker than the 30 fps of a standard camcorder)at 150 mph. Enjoy! Check out the complete deformation of the ball, which is normally rigid and quite hard.

Congratulations to Aaron - Intel National Semifinalist

Congratulations go to Aaron Damashek for being named an Intel Science Talent Search National Semifinalist! His work on the finding stable planetary orbits in binary star systems, and then examining climate changes through computer simulations, earned him this honor. Finalists are named on Wednesday, Jan. 27. Finalists then compete for a top prize of $100,000 in college scholarships in this top science contest for high school students.

For any student interested in doing independent science research, see Doc V and we can try to find a project that fits your interests and timetable. It is a truly unique experience while still in high school!

How to do RC Circuit with R and C in parallel

Here is a case where we have an RC circuit, but with a resistor and the capacitor in parallel with each other. This is tricky mathematically, but we can do it conceptually and only worry about numbers when t = 0 and after 'a long time.' Let's take a look.