In today's episode we continue digging into examples concerning our linear equation y = mx+b, where m is the slope, and b is the y-intercept. Our second example involves finding the equation of a line which goes through the point (2,22) and has a y-intercept of 10. Below are my coffee-stained show notes which walk you through all the calculations. Enjoy!
On this day in physics: Cruising wikipedia I came across the following excerpt: "Higgs was presented with an engraved loving cup by the Rt Hon George Grubb, Lord Provost of Edinburgh, in a ceremony held at the City Chambers on Friday 24 February 2012. The event also marked the unveiling of his handprints in the City Chambers quadrangle, where they had been engraved in Caithness stone alongside those of previous Edinburgh Award recipients." [Source]
Word of the Day- Googol, it is a huge number. A googol is a 1 followed by 100 zeros. It is 10 to the 100th power. "Other names for googol include ten duotrigintillion on the short scale, ten thousand sexdecillion on the long scale." Likewise, a googolplex, is 10 to the googol power, or 10 followed by a googol's worth of zeroes.
Quote of the Day: "An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them." -Werner Heisenberg
Keywords: Googol, Googolplex, Math, Mathematics, Heisenberg.
On this day in physics: 23 February 1927, Werner Heisenberg writes a letter to his colleague Wolfgang Pauli, describing his infamous Heisenberg Uncertainty Principle.
Word of the day- Heisenberg Uncertainty Principle- A big dog. One of the biggest principles in quantum mechanics. So, as scientists, especially scientists who have done any type of real lab work, think that we have a really good handle on the ability to measure things. And, even if our scale is only good to a tenth of a pound, it is possible to build something good enough to measure down to the exact amount of weight? Right? Wrong. There are limits to what we can measure, and that's evident from the Heisenberg Uncertainty Principle. What this principle says is that at the most microscopic measurements, the uncertainty of the position multiplied by the uncertainty of momentum must be greater to or equal to a constant which we call h-bar divided by 2 (5.272859 × 10-35 m2*kg/s). Now, this might seem like a crazily small number, and for human scales, it's totally not affecting our life at all, but at the quantum scale, there is a limit to your ability to measure. So, on any measurement that you take, there is going to be some amount of uncertainty, example, your bathroom scale is probably good to about one hundredth of a pound, which means, plus or minus .01 lbs, the measurement is reliable. This is called the "uncertainty" of the measurement. What this means at quantum scales? The more precise you know the position, the less precise you'll know the momentum, and if you choose to have a high level of precision on the momentum, the higher the uncertainty of the position. And there is no way to "burn the candle at both ends" here. You cannot know the momentum and position of something with exact certainty. Sorry friends.
There is a great joke about this: Heisenberg is driving his car down the road, and he gets pulled over by a police officer for speeding. The officer walks to Heisenberg's car, and asks him "Do you know how fast you were going?", and Heisenberg says 'No, but I know exactly where I am!'. Get it? Because..you know..uncertainty....anyways....
Quote of the Day: "What we observe is not nature itself, but nature exposed to our method of questioning." -Werner Heisenberg
Keywords: Heisenberg, Uncertainty, Principle, Position, Velocity, Momentum, h-bar.
A On this day in physics: 22 February 1857- Happy Birthday to Heinrich Hertz who would have turned 159 today. He was a physicist who first proved the existence of electromagnetic waves. He is also the namesake for our unit of frequency, the Hertz.
Word of the day- Ion- An ion is an atom which has fewer electrons than protons, or more electrons than protons. We like to think of most atoms in their "steady state" as having an equal number of electrons orbiting the nucleus of protons and neutrons. Because there are an equal number, the amount of positive and negative charges cancels out, leaving a net charge of 0. However, this is not always the case. There are negative ions and positive ions, which can be highly attractive to electrons or other atoms, in an effort to create a situation where the net charge is zero.
Example: Sodium Chloride, or NaCl. Sodium, or Natrium (hence the Na), is an atom which can come in the flavor of a positive ion, with one fewer total electron count than proton count, giving a net charge of +1. Cholrine can come in the flavor of having one extra electron, giving a net charge of -1. These two ions will "stick together" and together, they will have a net charge of 0, a very steady molecule. Many of these molecules will form what's known as a lattice structure, with each particle changing between sodium and chlorine in the lattice, giving a net charge of 0 across the entire structure. This is what is in your salt shaker.
Quote of the Day: "All of physics is either impossible or trivial. It is impossible until you understand it, and then it becomes trivial." -Ernest Rutherford [Source]
Keywords: Ion, Electrical, Charge, Sodium, Chloride, Salt
A On this day in physics: 21 February 1953- Watson and Crick arrived at the conclusion that the DNA was a double helix structure using X-Ray crystallography. [Source]
Word of the day- Potential Energy is the ability for an object to do work. The most common example of this is gravitational potential energy. Remember from yesterday that an object can have kinetic energy by moving a certain velocity. Well, if you drop an object from a specific height, it will change velocity, how is this possible if we don't push it? Well, gravity is what is converting all that potential energy into kinetic energy. It is possible to calculate this potential energy by multiplying the mass, times the acceleration due to gravity (g or 9.81m/s^2) times the height above the ground. This is how much work can be converted into potential energy by gravity.
Quote of the Day: "I try to show the public that chemistry, biology, physics, astrophysics is life. It is not some separate subject that you have to be pulled into a corner to be taught about." -Neil Degrasse Tyson [Source]
Keywords: Potential, Energy, Height, Gravity, Mass
A On this day in physics: 20 February 1844- Happy Birthday to Ludwig Boltzmann, who would have turned 172 today. He is the Boltzmann of the Boltzmann constant, Boltzmann equation, Boltzmann distribution, Stefan-Boltzmann constant, Stefan-Boltzmann Law, to name a bit.
Word of the day- Kinetic Energy is the amount of energy that an object in motion has. This is not the same as momentum, but in some ways similar, because kinetic energy is dependent on both the mass and velocity, and can be calculated as .5*m*v^2. This is the amount of work required to get a mass m to the velocity v. Once at this velocity, the mass will continue to maintain this amount of kinetic energy until the speed changes, i.e. work of some sort is done on the object, whether it be friction, air resistance, or another active force, like a car putting on the brakes.
Quote of the Day: "In string theory, all particles are vibrations on a tiny rubber band; physics is the harmonies on the string; chemistry is the melodies we play on vibrating strings; the universe is a symphony of strings, and the 'Mind of God' is cosmic music resonating in 11-dimensional hyperspace." -Michio Kaku
Keywords: Boltzmann, Kinetic, Energy, Velocity
A On this day in physics: 19 February 1473- Happy Birthday to Nicholas Copernicus, astronomer extraordinaire who was certainly not the first to discover, but quite probably the impetus for the scientific revolution triggered by his publication which posited that the earth was not the center of the universe, but rather than the Earth orbits the sun. He published it while on his death bed, so that he would not be threatened for "heresy" during his lifetime.
Word of the day- Blueshift- Is a type of doppler shift which occurs with cosmic light. Like yesterday's word of the day, the same idea applies with light moving towards an observer. When light moves away from the observer, the wavelength gets longer, or shifts to the red side of the spectrum. When light moves closer, the wavelength gets shorter, this shifting towards the blue end of the spectrum. It does not necessarily indicate that blue light is emitted.
Quote of the Day: "The brain is like a muscle. When it is in use we feel very good. Understanding is joyous." -Carl Sagan
Keywords: Blueshift, Light, Doppler, Shift, Relativity
A On this day in physics: 18 February 1745- Happy Birthday to Alessandro Giuseppe Antonio Anastasio Volta, who turns 271 today. The inventor of the "voltaic pile" which was an early version of the battery. He invention pretty much started the entire field of electrochemistry.
Word of the day- Redshift- Is a type of doppler shift which occurs with cosmic light. Like yesterday's word of the day, the same idi applies with light. When light moves away from the observer, the wavelength gets longer, or shifts to the red side of the spectrum. It is possible to analyze the light from galaxies, if the light is redshifted, astronomers can decipher whether or not galaxies are moving away from us or not. When analyzing starlight, it is possible to identify critical frequencies which we know to be emitted from different elements. If the wavelength of the light is, for example, several nanometers longer than potassium, we know that potassium exists in the star and that it is moving away from us.
Quote of the Day: "If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan
Keywords: Redshift, Light, Doppler, Shift, Relativity
On this day in physics: 17 February 1888- Happy Birthday to Otto Stern, the Physicist with the most Nobel Prize nominations of all time, with 87 total nominations between 1925 and 1945, and actually sealing the deal in 1943 for the infamous Stern-Gerlach experiment.
Word of the day- Doppler Effect- Continuing on waves, this is a special sort of relativistic wave phenomenon. Imagine a wave such as a sound wave, such as a horn, is being emitted from a moving vehicle at constant frequency. If the car is driving towards you, because of the velocity of the car, the emitted wave will pick up a little extra speed and have a higher pitch. As it drives past you, and moves away from you, the velocity away from you will "slow the wave down a bit" and give it a little lower frequency. This is known as the doppler effect.
Quote of the Day: "Somewhere, something incredible is waiting to be known." -Carl Sagan
Keywords: Doppler Effect, Wave, Velocity, Direction
On this day in physics: 16 February 1948- Uranus's moon, Miranda, was photographed for the first time. [Source]
Word of the day- Wavelength- Its pretty much what it sounds like. It's the length of the wave for one oscillation. The easiest way to measure it is to measure from crest to crest or trough to trough. The length of the wave is related to the speed of the wave divided by the frequency.
Quote of the Day: "All matter originates only by virtue of a force...We must assume behind this force the existence of a conscious and intelligent mind. This mind is the matrix of all matter." -Max Planck [Source]
Keywords: Wavelength, Wave, Crest, Trough
On this day in physics: 15 February 1786 - The Cat's Eye Nebula was discovered in 1786 by Astronomer William Herschel. Click for a fantastic image from NASA's astronomy picture of the day.
Word of the day- Amplitude- On a wave, the amplitude is the distance from the center of the wave to the highest point, known as the crest. The lowest point of the wave is known as the trough. So the amplitude is twice the distance from the crest to the trough. Think of a water wave on the beach, the crest of the wave is the highest point, which when it comes close to shore usually causes the wave to collapse, to the delight of beachgoers and surfers everywhere. The higher the amplitude, the larger the wave, and the more energy that it transfers, this is true of all waves. In radio signals, AM radio is referred to as amplitude modulation. In order to send your car radio the signal, the radio station varies the amplitude of the wave at a certain frequency in order to send the signal. As sort of a redaction to yesterday's FM explanation, the way the frequency modulation delivers the carrier signal is that the antenna is sensitive to changes in frequency to deliver the signal to your radio. (Sorry guys!) Think of amplitude modulation kind of delivering what you'd know as a longitudinal wave, changing the amplitude and keeping the same frequency, and frequency modulation as like a transverse wave of a spring, looking at the same amplitude, and of course modulating the frequency. There is a seriously excellent graphic illustrating this on the wikipedia entry for Frequency Modulation, so you can check that out here if you're so inclined.
Quote of the Day: "Arc, amplitude, and curvature sustain a similar relation to each other as time, motion, and velocity, or as volume, mass, and density." - Carl Frederich Gauss [Source]
Keywords: Cat's Eye, Nebula, Amplitude, Wave, Crest, Trough
On this day in physics: 14 February 1874 - The IOP, or Institute of Physics was founded. It's a 50,000 strong charity which furthers education and scientific research, as well as publishing many journals in the field of physics.
Word of the day- Frequency is the amount of repetitions something, most usually a wave, undergo in a certain period of time. Frequency is measured in Hertz, the unit of which is 1/s, or "stuff per time". In a wave, it is the amount of oscillations per unit of time. In waves, the frequency multiplied by the wavelength is equal to the velocity. This means the shorter the wave, the higher the frequency. The longer the wave, the lower the frequency. Radio waves are waves broadcast at very specific frequencies, and when you change your radio dial, you actually tune your radio to check for information at a different frequency of radio wave. F.M. stands for frequency modulation, meaning that in this type of radio wave, the frequency is tuned in order to change the stations.
Quote of the Day: "Physics isn't the most important thing. Love is." -Richard P. Feynman
Keywords: Wave, Frequency, Love, Valentine's Day, Institute, Physics
On this day in physics: 13 February 1912 - Robert Millikan began his famous Millikan Oil Drop experiment. The experiment consisted of dropping small droplets of oil between two plates which generated an electric field. The field was varied until the oil droplets were suspended in midair, this the force of the electric field counteracted that of gravity. It was then possible to calculate the charge of an electron knowing the voltage between the plates and the size/weight of the oil droplets. Millikan was able to calculate the charge of an electron to within 1% of our current value, 1.602e-19 C.[Source]
Word of the day- Wave- A wave is an oscillation which transmits energy, but very infrequently mass. The idea is to distinguish a wave from a traveling object. Waves can propagate in several ways. The first is called a longitudinal wave. Think of yourself holding the end of a string with the other end fastened, and shaking it periodically. This is known as a longitudinal wave because the oscillation is perpendicular to the motion of the wave. Another type of wave is a transverse wave, where the oscillation is in the same direction as the motion of the spring. Think of a spring, or slinky, hanging from the ceiling and being pulled straight down, the motion of the wave would be up and down, as would the motion of the wave. Both the example with the string and the spring are what are referred to as mechanical waves, because they involve physical systems through which the wave propagates. There is still another type of wave, the electromagnetic wave, which does not rely on the motion of matter, rather, the wave propagates through a "field", which affects matter in the vicinity of the field, but does not involve matter itself.
Quote of the Day: "If you want to understand the secrets of the universe, think in terms of energy, frequency, and vibration." -Nikola Tesla
Keywords: Wave, Physics, Millikan, Oil, Electron
On this day in physics: 12 February 1804- Happy Birthday to Heinrich Lenz, a physicist who made contributions to the field of electrodynamics, and the namesake of Lenz's Law.
Word of the Day: Lenz's Law- I want to go back to the idea of induction. Remember 2 days ago we were talking about the change of a magnetic field aka a flux, there will be an induced current, which is a flow of electrons through the wire. But which direction does the current flow in the wire? That's where Lenz comes in?
Lenz's Law states: "If an induced current flows, its direction is always such that it will oppose the change which produced it." [Source] So Lenz's law gives us the direction. In Faraday's law of induction, it is the minus sign in the equation, because it shows the direction of the induced current.
Quote of the Day: "In science there is only physics, the rest is stamp collecting." -Lord Kelvin
Keywords: Faraday, Lenz, Induction, Current
On this day in physics: 11 February 2016- New York Times publishes an article reporting that LIGO (Laser Interferometer Gravitational-Wave Observatory) has confirmed gravitational waves from the collision of two black holes, confirming the last of Einstein's predictions of General Relativity. [Source]
Word of the Day: Gravitational Waves are a prediction made by Einstein's General Theory of Relativity which were heretofore unobserved before last September. As we've talked about in a previous word of the day, Any mass causes a gravitational warping of the fabric of spacetime, letting the rest of the universe "know" how to move. Now this is where things get interesting. In physics, generally when we visualize the universe, everything is stationary. But that's not usually the case. The universe is a dynamic and changing place. So when you have something with a phenomenal amount of gravity, like a neutron star or black hole, which is MOVING, how does this warping in spacetime, the information of the gravity of this object, transmit to the rest of the universe? The answer is that this information ripples through spacetime at the speed of light. So, if we have two orbiting massive objects, say two orbiting neutron stars, even light years away, their gravity affects our spacetime fabric, and their motion will in a very small way, slightly change our spacetime, which should measurably change when massive objects drastically change.
Enter LIGO, a facility built to measure these changes. It is in the shape of an L, so it can check for waves in two dimensions, and each arm of the L is a long tunnel (like 2.5 miles long) which is created to be a vacuum, i.e. no air whatsoever. The purpose of the observatory is to measure the distance of each of these tunnels with extreme precision. As an example, gravity waves from neutron stars millions of light years away would change the length of something like LIGO less than one thousandth the diameter of a proton. This is the type of fluctuations the scientists are LIGO are looking for. The hope was that Neutron Stars "close" to us, i.e. 10^26 light years (HUGE distance btw), would do something colossal that could be measured at LIGO. For ten years, they listened for fluctuations. Nothing. Whatsoever. How hard do you think it would be to secure funding for a 200 million dollar facility for 10 years with no reportable findings? Then something happened. Two black holes, spiraled together, forming an even bigger black hole, creating a predictable pattern of gravitational waves, which were observed by both arms at LIGO. The findings were announced on 11 February 2016.
The reason that this is such a big deal is that gravitational waves were not observable, not unlike the Higgs Boson. A major theory of physics, General Relativity, had one lingering facet which had yet to be observed. Without observation, we cannot say for sure that it is correct. So observing a gravitational wave is a monster boost for general relativity, and physics in general. Plus we were able to detect two black holes colliding into a bigger black hole. How cool is that.
Quote of the Day: "If you ask me whether there are gravitational waves or not, I must answer that I do not know. But it is a highly interesting problem." - Albert Einstein [Source]
Keywords: Gravitational Waves, Einstein, Relativity, Black Hole
On this day in physics: 10 February 1961- Niagara Falls hydroelectric power plant goes on line. It took the large force of the niagara river and converted it into the largest hydroelectric power plant in the world. [Source]
Word of the Day: Induction- Electrical induction is a phenomenon first popularly discovered by Michael Faraday in the 1820's. What he discovered was that if a loop of wire is rotated between two magnets, that this induces a current in the wire. What this discovery meant was that the two magnets generate a magnetic field. As the loop of wire rotates, the amount of "magnetic field" which passes through the loop of wire changes. This is known as "Magnetic Flux". And, where there is magnetic flux, there is an induced current. So this current is generated, and can be stored. What happens on a very large scale at hydroelectric power plants like the one at Niagara Falls, is that using the immense force of flowing water, the water turns a turbine, which has attached to it something like a big loop of wire, which spins inside of a magnetic field, and induces a great deal of current, like enough to power a city or two or three. This is a passive, sustainable way to generate power on our planet. A great article on how hydropower works.
Quote of the Day: "Those who can, build. Those who can't, criticize." - Robert Moses
Keywords: Induction, Magnetic, Hydroelectric, Faraday
On this day in physics: 09 February 1953- Happy Birthday to String Theorist and popular Physics novelist Brian Greene who turns 53 today! Brian is one of the leading minds in string theory and has published several highly popular books on the topic, most notably The Elegant Universe and The Fabric Of The Cosmos.
Word of the Day: String Theory- Today's word of the day is an entire field of physics, although some may disagree At this point, its most popular flag bearer is our Birthday Boy, Dr. Brian Greene, who I think most people think of synonymously with the phrase String Theory. It is the closest thing we have to a "Theory of Everything", and it suggests that beyond quarks, strings are the fundamental unit of the universe. They are one dimensional objects, and how they vibrate turns them into up quarks, down quarks, neutrinos, et cetera. It further suggests that our universe is indeed a 26 dimensional one, with 20 of those dimensions curled into an infinitely small bundle, which is why they don't affect our every day life.
It sounds crazy, but the problem is it might be right. It explains an awful lot of things about our universe, and is also directly in line with the Standard Model of Physics. The other thing that String Theory really has going for it, is that it is able to show that Relativity and Quantum Mechanics are compatible, something the vast majority of theories are unable to reconcile. If it seems too good to be true, at the time of this writing, it definitely is. String Theory is as of yet unprovable, as we don't have the measuring devices to probe matter down to this level, or measuring devices which are sensitive enough to detect small anomalies over huge masses and areas (think galaxies or clusters of galaxies). It is a very exciting place to be in physics right now because this is red hot, the bleeding edge. If it's right, its creators and validators will have been on the cusp of probably the most profound theory of this century, quite possibly millennium, if it's wrong, it will be a major flop and blow to the physics community.
Quote of the Day: "Sometimes attaining the deepest familiarity with a question is our best substitute for actually having the answer." - Brian Greene, The Elegant Universe
Keywords: Brian Greene, String, Theory, Quantum, Mechanics, Dimensions.
In today's episode we start digging into examples concerning our linear equation y = mx+b, where m is the slope, and b is the y-intercept. Our first example is find the equation of a line with the points (1,8) and (7,26). Below are my show notes for this example.
On this day in physics: 08 February 1700- Happy Birthday to Daniel Bernoulli who was a physicist and made large contributions to the field of fluid dynamics. He is also the Bernoulli of the famous "Bernoulli Principle" or "Bernoulli Equation" (more below).
Word of the Day: Bernoulli Principle- The Bernoulli Principle is something that describes fluids in motion, or flowing. Imagine fluid flowing through a pipe of a certain radius, it will have a certain pressure, and velocity. If this pipe was to narrow, the surface area and radius decrease and the velocity of the fluid will increase, but what about the pressure? The intuitive response is that the pressure increases. However, what Bernoulli tells us is that the pressure at this bottleneck is actually LOWER. What the heck? How can it be? Well, Bernoulli's principle is sort of just another expression of conservation of energy, or Newton's Second Law. Because the velocity increases, and there is no increased energy being injected into the system, as the Grateful Dead say in the song New Speedway Boogie "something's gotta give", and that thing is the pressure.
A phenomenal example of Bernoulli's Principle in action is a perfume atomizer. How does it work? Well, you have this bulb full of air travelling at no speed whatsoever, and then at the top of the perfume bottle there is a small tube or straw which runs down into the perfume. When you squeeze the bulb, what happens? The air (air is a fluid by the way) moves very quickly out of the nozzle, but what happens is that the pressure in this area goes way down. The liquid and bottle, now at a higher pressure, react by pushing the fluid up the tube and into the nozzle. The air also moving quickly pulls the liquid off in little tiny beads, which then make a beautiful perfume vapor in the air for ladies everywhere to enjoy.
Quote of the Day: "Nature always tends to act in the simplest way." - Daniel Bernoulli [Source]
Keywords: Bernoulli, Velocity, Energy, Pressure
On this day in physics: 07 February 1940- Happy Birthday to Toshihide Maskawa who turns 76 today. He is a Nobel Laureate who won one quarter of the prize in 2008 "for the discovery of the origin of the broken symmetry which predicts the existence of at least three families of quarks in nature."
Word of the Day: Range- Since today is Super Bowl Sunday, I thought we'd take a look at projectile motion, which anyone watching the Super Bowl tonight will see plenty of. As the quarterback throws the football, they will be putting an projectile, namely the football, in the air. It will follow the shape of a parabola as it reaches its (hopefully) destined target somewhere downfield. Now, there are many many different critical words relating to this parabola, but today we will talk about the range. Range is the total horizontal distance traversed by the projectile, in tonight's case, the football. The announcers, coaches, players, and referees will be highly concerned with the range of the projectile, aka a "30 yard pass", et cetera. In sports, they don't care much about the maximum height achieved, or the angle of the throw, but rather just how far it has gone, and where it lands. In physics, this is referred to as the range of the projectile.
Quote of the Day: "Winning can be defined as the science of being totally prepared" -George Allen
Keywords: Kinematics, Range, Football, x-direction
On this day in physics: 06 February 1802- Happy Birthday to Charles Wheatstone, a physicist who invented a myriad of things including the concertina and the stereoscope. A stereoscope is kind of like a viewfinder that children play with. A card will contain slightly different variations of the same image which when looked through the viewfinder produce a 3D image.
Word of the Day: Escape Velocity- the least velocity required in order to for an object to free itself from the gravitational attraction of a massive object. Objects which are traveling less than the escape velocity in range of a massive object orbit it. Example: The Earth is traveling less than its escape Velocity of the sun, and so the Earth orbits the Sun. Now, the escape velocity is dependent on the mass of the object you're trying to escape, and the distance you are from that object. The equation for the escape velocity is actually sqrt(2GM/r), where G is the gravitational constant G = 6.67×10−11 m^3kg^−1s^−2, M is the mass of the object to be escaped and r is the distance from that mass. Here are some examples of what escape velocities might look like.[Source] From the Sun's surface, you would need to be traveling 618 km/s to escape its gravitational clutches. From Earth, you would need to be traveling 11 km/s to escape Earth's gravity, and 42 km/s to escape the Sun's. At Jupiter, the tables turn. You would need to be traveling only only 18.5 km/s to escape the hold of the Sun, but 60 km/s to slip the grip of Jupiter itself. Lastly, from Neptune, 7.7 km/s to escape the Sun, and 24 km/s to escape Neptune itself. The escape velocity of anything at the event horizon of a black hole is the speed of light. Past the event horizon, there is no escape.
Quote of the Day: "Once someone gets a little escape velocity going, ain't no play in the world that will keep them from leaving." -Junot Diaz, Drowned
Keywords: Escape, Velocity, Mass, Gravity, Distance, Sun, Earth.
On this day in physics: 05 February 1915- We say Happy Birthday to Robert Hofstadter, an American Physicist and winner of the Nobel Prize in 1961. He shared the prize with Rudolf Mössbauer, however they won for separate contributions. According to the Nobel Prize official award, "The Nobel Prize in Physics 1961 was divided equally between Robert Hofstadter "for his pioneering studies of electron scattering in atomic nuclei and for his thereby achieved discoveries concerning the structure of the nucleons" and Rudolf Mössbauer "for his researches concerning the resonance absorption of gamma radiation and his discovery in this connection of the effect which bears his name"." [Source] [Source]
Word of the Day: Centripetal Acceleration is an inward acceleration experienced by an object experiencing curved or circular motion. So, consider F = ma, Force is equal to Mass times Acceleration. So, we have examined in two previous words of the day what mass and acceleration are. So if we have an object of constant mass, and it starts to experience curved motion, the velocity is changing all the time, because THE DIRECTION OF THE VECTOR IS CHANGING. In circular motion, the acceleration is always pointed radially inwards towards the center of the circle. The force generated by this acceleration is known as centripetal force. Many people confuse this with centrifugal force. Now, imagine you're driving a race car around a track about to take the first half-circle curve. We know the radius of this circle, and can read from the speedometer the speed. The centripetal force can be calculated as F = m*v^2/r. So the force is dependent on the radius of the curve, because this defines how tight the curve is, how fast you're going, and the mass of your car. Now, a body moving wants to travel in a straight line, so there must be an unbalanced force in order to create the circular motion of your car. What gives this force is the friction between the tires and the track. This friction will only sustain a car going in a circle up to a certain velocity for a given radius of curve. After that, the car will begin to move in a straight line again, and is what causes cars to skid on curves.
Quote of the Day: "The fact that mankind persists shows that the cohesive force is greater than the disruptive force, centripetal force greater than centrifugal." -Ghandi
Keywords: Centrifugal, Force, Acceleration, Curve, Circular, Motion, Centripetal, Friction.
On this day in physics: 04 February 1600- Johannes Kepler begins work with Tycho Brahe. Tycho Brahe was one of the most prolific astronomers of all time, and had years and years of astronomical data. Johannes Kepler had the mathematical know how and intrigue to take this wealth of data and transform it into Kepler's Planetary laws of motion, which describe how planets move around the Sun.
Word of the Day: Centrifugal Force- A centrifugal force is what is known as a "fictitious" or "false force" experienced by objects undergoing some sort of curved motion or circular motion. When turning in a circle, the object experiences the sensation of an outward force. Imagine your clothes in the dryer going through the final spin. All of the clothes stick to the outside of the dryer, spinning in a circle. It is possible to experience this sensation on many amusement park rides. The force is so strong that on some rides, while spinning at a certain rate, the floor can be lowered or removed, and riders will be pushed to the outside rim of the ride. Imagine swinging a ball on a string in a circle. In this scenario, the only force truly acting on the ball is the tension of the string pulling inwards. However, the ball is not flying outwards, so there must be a balancing force. This is the centrifugal force at work. This is what allows centrifuges to sort matter by density, or what causes the remnants of an almost empty ketchup jug to move to the nozzle when you swing it in a circle.
Quote of the Day: "The fact that mankind persists shows that the cohesive force is greater than the disruptive force, centripetal force greater than centrifugal." -Ghandi
Keywords: Centrifugal, Force, Acceleration, Curve, Circular, Motion.
On this day in physics: 03 February 1966- The Soviet Luna 9 Spacecraft landed on the moon, making it the first "soft landing" on a non-earthen body in human history. A soft landing is a controlled landing (i.e. not a crash) where there is no major damage to the craft. The probe was unmanned, it did contain a camera to take pictures which were sent back to earth until 6 February when the batteries finally died. [Source].
Word of the Day: Inertial Reference Frame- An inertial reference frame is one that is not accelerating. It is a theoretical construct, but very useful in the theory of relativity. Imagine yourself right now, sitting. To you, you're not moving, even if you're driving, or riding, or running, or walking. But, for this argument, let's say that you are sitting, totally still. You're holding a ball (why not) and decide to throw it. Once it's thrown, it is subject to the acceleration of gravity, and so if you're the physics type, you'd be able to do some calculations about its motion, and would be able to say for certain that from your inertial reference frame of not moving, that the ball had a certain velocity, a certain acceleration, etc. And all those calculations are totally valid considering your perspective of being totally motionless, but then remember that you're on a planet, spinning around its axis, which is revolving around the sun, which is in an arm of a spiral galaxy. So you're not really stationary. But, theoretically you're totally still. If you were to be sitting on the couch, and in front of you there was an elevator which was to be rocketed upwards exactly opposing the acceleration of gravity. Once the rocket launched, someone inside the elevator would have a perceived weightlessness, and there is no experiment that could be done from within the elevator to find out if he was truly motionless, or undergoing correspondingly opposing accelerations. If you were to leave earth's atmosphere, and enter a truly weightless environment, far from the shackles of planetary gravity, and the rocket were to continue accelerating at the same rate of gravitational acceleration, 9.81 m/s^2, anyone inside the elevator would feel as though they were standing on Earth, and they would not be able to tell if they were being accelerated by a rocket, or if they were being gravitationally attracted by a mass. This led Einstein to the conclusion that mass warps spacetime. The problem is that there is no truly inertial reference frame from which all measurements can be made, because something is always moving with respect to something else, or so we believe in 2016. Tune in in 100 years to see if this podcast still holds water.
Quote of the Day: "Nothing happens until something moves."- Albert Einstein [Source]
Keywords: Inertial, Reference, Frame, Space, Time, Acceleration, Gravity.
On this day in physics: 02 February 1937- Happy Birthday to C.R. Hagen, a theoretical physicist, who is still currently a professor of theoretical physicist at the University of Rochester. He published one of the first papers to describe the "Higgs Mechanism" and be theory on the Higgs Boson, with five other physicists, one of course being the particle's namesake, Peter Higgs. [Source].
Word of the Day: Higgs Boson- The elusive Higgs Boson is a particle in the standard model of physics which was theorized to exist since the 1960s, but was only officially discovered to exist this decade at the Large Hadron Collider (LHC). So what is it. It's a boson, it has no spin, no electrical charge, or "color charge". It lives for about 10^-22 seconds. So why the heck is it important? It is something that is necessary for the standard model in physics to be correct. The Standard Model is what classifies all of matter, like electrons, photons, quarks, bosons, etc. In order for everything to work, there needs to be what is known as a Higgs Field, and a particle known as the Higgs Boson. The Higgs Boson is what allegedly gives matter its mass.
Let's try and understand how it works Imagine putting together a 250 piece puzzle. It's hard, because you don't have the box to see the full picture, but no matter, we're smart people. We get the frame of it together, and start working on the inside. Great, great. But now, we've finished about a quarter of the inside, and we see that two pieces are missing. They are totally framed out by the other pieces that we have, so we know that they need to be there to make the puzzle, but they are gone. So you start to look for them, and 50 years later, you find them. Can you imagine your excitement?
So now that it has been verified to exist, it gives physicists a great confidence that the Standard Model of Physics is correct. In science if you make a theory, and can't back it up with evidence, out it goes. So, physicists for the last 50 years had been tenuously supporting the theory, while trying to make modifications in the event that the Higgs Boson was never found. Now those modifications are unnecessary. It also gives great credence to the Standard Model because the model is able to predict particles that we can then look for and observe, and find to be real.
Quote of the Day: "I never expected this to happen in my lifetime and shall be asking my family to put some champagne in the fridge."- Peter Higgs (on the discovery of the Higgs Boson) [Source]
Keywords: Higgs, Boson, Fisld, Standard, Model, Physics
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