In Mechanics: Check out this video, and take notes, as it will go through the details about rolling objects that have NO SLIPPING.
The NO SLIPPING is a key concept because it allows us to connect linear and rotational terms using s = R(theta), v = Rw, and a = R(alpha). If there is slipping, these are no longer valid relationships. ALSO, NO SLIPPING means there is NO ENERGY LOSS...there is friction, which creates the torque on the object, but it is effectively static friction. There is no heat generated by static friction.
http://docvphysics.blogspot.com/2010/03/how-to-handle-rotations-and-linear.html
In E&M: Check out this video, and take notes, regarding mass spectrometers. This will be the outline for applying F = qv x B, and a method for identifying specific atoms, particles, and molecules (that are ionized) by determining their masses. This is done by mv^2/R = qvB (remember that charges move in circles when in a magnetic field). By measuring the radius of curvature of the particles, and knowing the speed, charge and B-field, the mass can be calculated.
Note that a velocity selector is when both a B-field and E-field are used in the same region to make charge move in a straight line. Only particles with a specific speed can make it through when both the electric force, qE, is balancing the magnetic force, qvB. Set qE = qvB and you get a speed of v = E/B. We select the two fields, and therefore can select the speed of the particles that enter the magnetic field. For a simulation of a mass spectrometer, check out this ActivPhysics simulation.
Monday, March 24, 2014
Monday, March 17, 2014
Gravitational Wave Effects Used to Find Evidence for Inflation
Check out the first published paper on this experiment and its findings here.
A major announcement came out today, by a group running the BICEP experiment, run from the South Pole. The group was able to find and accurately measure features of the microwave background radiation, left over from the Big Bang itself, which are caused by gravitational waves. Gravity waves are predicted from Einstein's general theory of relativity, and have been searched for over the past century. The observations match well with predictions from the inflation model of the Big Bang, which states the universe expanded very rapidly, just tiny fractions of a second after the Big Bang occurred. Only inflation predicts the observed effects, so this is direct evidence supporting details at nearly the instant of the creation of our universe! Also, this suggests that gravity should be quantized. This article has numerous links to understand teh science better. So in the world of physics, this is a MAJOR discovery and announcement. Congratulations to those involved with the experiment and analysis. Of course, this still has to go through a thorough peer review, but it is looking impressive at the moment.
A major announcement came out today, by a group running the BICEP experiment, run from the South Pole. The group was able to find and accurately measure features of the microwave background radiation, left over from the Big Bang itself, which are caused by gravitational waves. Gravity waves are predicted from Einstein's general theory of relativity, and have been searched for over the past century. The observations match well with predictions from the inflation model of the Big Bang, which states the universe expanded very rapidly, just tiny fractions of a second after the Big Bang occurred. Only inflation predicts the observed effects, so this is direct evidence supporting details at nearly the instant of the creation of our universe! Also, this suggests that gravity should be quantized. This article has numerous links to understand teh science better. So in the world of physics, this is a MAJOR discovery and announcement. Congratulations to those involved with the experiment and analysis. Of course, this still has to go through a thorough peer review, but it is looking impressive at the moment.
Sunday, March 16, 2014
Anyone up for the Photo Contest?
'Tis the season for the Physics Photo Contest. If you are into photography, or just have a cool natural or contrived picture of some phenomena, bring it in and perhaps we can send it in!! Always a good time.
With Pi Day/Einstein's Birthday Behind Us, How Many Nobels did Einstein Probably Deserve?
In class I have mentioned that in retrospect, Albert Einstein should have won 5 Nobel Prizes, had he lived long enough so his ideas and theories could be thoroughly tested. He won his in 1921 for his work on the photoelectric effect, which is really based on his theory of the photon. No one in that era was thinking of treating light as a true particle except Einstein, so it was the true birth of quantum theory.
But obviously he also deserved a Nobel for Special Relativity. It has fundamentally changed the way we think about space and time, mass and energy, and led to the development of matter waves. Einstein may have shared a prize, had it been given, with Lorentz, who had made major theoretical contributions and ideas that Einstein finally derived and put into a full framework. In fact, he could have easily shared the Nobel that Louis de Broglie won for matter waves, and may have been overlooked at his contribution and influence on de Broglie's work.
Then there is General Relativity. This is Einstein's masterpiece, and he essentially worked alone on it. No one else was even dreaming of warped spacetime and all the implications coming from this concept - and now we have much confirming evidence that his ideas are correct.
Einstein laid down the theory for stimulated emission, which is the foundation principle for the construction of the laser. And lasers have applications seemingly everywhere in our generation.
Then there is Bose-Einstein condensation, which Einstein predicted in the 1920's. This state of matter was confirmed in the 1990's. The basic idea he recognized was when bosons are at very low temperatures, they are more like waves than particles, and can occupy the same quantum state.
Einstein also had a major influence on multiple dimensions. He developed the notion of 3-D space to 4-D space-time in his relativity theories, which then led others to think about adding a 5th dimension to account for electromagnetism (Kaluza-Klein theory), and now there are 11-D string theories trying to unify all forces and particles together in a single theory - a so-called unified field theory. Where did this concept come from? Well, Einstein! He thought we should be able to create a single theory for all particles and forces, and he was unable to do it. But the idea is alive and well. Then there is the cosmological constant, which he famously said was his 'biggest blunder,' but now the concept of an anti-gravity force may be correct as we try to figure out why some distant galaxies are accelerating in their expansion rates (now we called this 'dark energy').
Oh, also in 1905 was Einstein's theory for Brownian motion, which effectively laid down the mathematical theory for molecular motion. This is a major contribution to statistical physics.
Wow, that is A LOT from one person! Here is another article talking about Einstein's legacy and the number of Nobel Prizes he deserves.
But obviously he also deserved a Nobel for Special Relativity. It has fundamentally changed the way we think about space and time, mass and energy, and led to the development of matter waves. Einstein may have shared a prize, had it been given, with Lorentz, who had made major theoretical contributions and ideas that Einstein finally derived and put into a full framework. In fact, he could have easily shared the Nobel that Louis de Broglie won for matter waves, and may have been overlooked at his contribution and influence on de Broglie's work.
Then there is General Relativity. This is Einstein's masterpiece, and he essentially worked alone on it. No one else was even dreaming of warped spacetime and all the implications coming from this concept - and now we have much confirming evidence that his ideas are correct.
Einstein laid down the theory for stimulated emission, which is the foundation principle for the construction of the laser. And lasers have applications seemingly everywhere in our generation.
Then there is Bose-Einstein condensation, which Einstein predicted in the 1920's. This state of matter was confirmed in the 1990's. The basic idea he recognized was when bosons are at very low temperatures, they are more like waves than particles, and can occupy the same quantum state.
Einstein also had a major influence on multiple dimensions. He developed the notion of 3-D space to 4-D space-time in his relativity theories, which then led others to think about adding a 5th dimension to account for electromagnetism (Kaluza-Klein theory), and now there are 11-D string theories trying to unify all forces and particles together in a single theory - a so-called unified field theory. Where did this concept come from? Well, Einstein! He thought we should be able to create a single theory for all particles and forces, and he was unable to do it. But the idea is alive and well. Then there is the cosmological constant, which he famously said was his 'biggest blunder,' but now the concept of an anti-gravity force may be correct as we try to figure out why some distant galaxies are accelerating in their expansion rates (now we called this 'dark energy').
Oh, also in 1905 was Einstein's theory for Brownian motion, which effectively laid down the mathematical theory for molecular motion. This is a major contribution to statistical physics.
Wow, that is A LOT from one person! Here is another article talking about Einstein's legacy and the number of Nobel Prizes he deserves.
Monday, March 3, 2014
Classic example of resonance - Tacoma Narrows Bridge collapse
This is the bridge that, due to winds hitting at just the right speed and angle, caused vibrations within the superstructure of the bridge at the resonance frequency. Resonance is when an object vibrates at its natural frequency, such as a tuning fork has a natural frequency.
Another example of resonance is pushing someone on a swing. Your push needs to be in synch with the natural frequency of the swing (i.e. a pendulum) if you want to maximize the amplitude of the swing. If your push frequency is out of phase with the natural frequency of the swing, you will at times be 'working against' each other, and not achieve maximum amplitude.
Here is another example of a so-called 'wolf tone' on a string instrument, where a short piece of a string resonates with the full length of the string. Yet another is the Schumann resonance in the ionosphere each time there is a lightning bolt, and one last one is when a singer can find and hold a note that will make a wine glass resonate and explode! See the second video below to see the wine glass in slow motion.
Another example of resonance is pushing someone on a swing. Your push needs to be in synch with the natural frequency of the swing (i.e. a pendulum) if you want to maximize the amplitude of the swing. If your push frequency is out of phase with the natural frequency of the swing, you will at times be 'working against' each other, and not achieve maximum amplitude.
Here is another example of a so-called 'wolf tone' on a string instrument, where a short piece of a string resonates with the full length of the string. Yet another is the Schumann resonance in the ionosphere each time there is a lightning bolt, and one last one is when a singer can find and hold a note that will make a wine glass resonate and explode! See the second video below to see the wine glass in slow motion.
Saturday, March 1, 2014
How to do Equilibrium Problems Involving Possible Rotational Motion
In mechanics, it is important to be able to recognize and solve equilibrium conditions in problems. In the past, these all involved balancing forces so that objects had no acceleration. The object was either at rest or moving with constant velocity.
Now that we are doing rotational motion, there is one more possibility. Not only no linear acceleration, but also no angular acceleration. For this new condition to be true, there cannot be any net torques on the object. Remember that torque due to a force = FrsinB, where F is the force, r is the distance from the axis of rotation to the point where the force is applied, and B is the angle between that radius line and line of force.
The conditions we now must consider and set up in problems will be:
up = down right = left and something new: cw = ccw
This new condition means that any torques trying to make something rotate clockwise (cw) are balanced by torques trying to make the object rotate counterclockwise (ccw). This video gives an example of how to handle such a system. Let me know what you think!
Now that we are doing rotational motion, there is one more possibility. Not only no linear acceleration, but also no angular acceleration. For this new condition to be true, there cannot be any net torques on the object. Remember that torque due to a force = FrsinB, where F is the force, r is the distance from the axis of rotation to the point where the force is applied, and B is the angle between that radius line and line of force.
The conditions we now must consider and set up in problems will be:
up = down right = left and something new: cw = ccw
This new condition means that any torques trying to make something rotate clockwise (cw) are balanced by torques trying to make the object rotate counterclockwise (ccw). This video gives an example of how to handle such a system. Let me know what you think!
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