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On the History of the Radiation Reaction1 Kirk T
On the History of the Radiation Reaction1 Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (May 6, 2017; updated March 18, 2020) 1 Introduction Apparently, Kepler considered the pointing of comets’ tails away from the Sun as evidence for radiation pressure of light [2].2 Following Newton’s third law (see p. 83 of [3]), one might suppose there to be a reaction of the comet back on the incident light. However, this theme lay largely dormant until Poincar´e (1891) [37, 41] and Planck (1896) [46] discussed the effect of “radiation damping” on an oscillating electric charge that emits electromagnetic radiation. Already in 1892, Lorentz [38] had considered the self force on an extended, accelerated charge e, finding that for low velocity v this force has the approximate form (in Gaussian units, where c is the speed of light in vacuum), independent of the radius of the charge, 3e2 d2v 2e2v¨ F = = . (v c). (1) self 3c3 dt2 3c3 Lorentz made no connection at the time between this force and radiation, which connection rather was first made by Planck [46], who considered that there should be a damping force on an accelerated charge in reaction to its radiation, and by a clever transformation arrived at a “radiation-damping” force identical to eq. (1). Today, Lorentz is often credited with identifying eq. (1) as the “radiation-reaction force”, and the contribution of Planck is seldom acknowledged. This note attempts to review the history of thoughts on the “radiation reaction”, which seems to be in conflict with the brief discussions in many papers and “textbooks”.3 2 What is “Radiation”? The “radiation reaction” would seem to be a reaction to “radiation”, but the concept of “radiation” is remarkably poorly defined in the literature. -
Classical Mechanics
Classical Mechanics Hyoungsoon Choi Spring, 2014 Contents 1 Introduction4 1.1 Kinematics and Kinetics . .5 1.2 Kinematics: Watching Wallace and Gromit ............6 1.3 Inertia and Inertial Frame . .8 2 Newton's Laws of Motion 10 2.1 The First Law: The Law of Inertia . 10 2.2 The Second Law: The Equation of Motion . 11 2.3 The Third Law: The Law of Action and Reaction . 12 3 Laws of Conservation 14 3.1 Conservation of Momentum . 14 3.2 Conservation of Angular Momentum . 15 3.3 Conservation of Energy . 17 3.3.1 Kinetic energy . 17 3.3.2 Potential energy . 18 3.3.3 Mechanical energy conservation . 19 4 Solving Equation of Motions 20 4.1 Force-Free Motion . 21 4.2 Constant Force Motion . 22 4.2.1 Constant force motion in one dimension . 22 4.2.2 Constant force motion in two dimensions . 23 4.3 Varying Force Motion . 25 4.3.1 Drag force . 25 4.3.2 Harmonic oscillator . 29 5 Lagrangian Mechanics 30 5.1 Configuration Space . 30 5.2 Lagrangian Equations of Motion . 32 5.3 Generalized Coordinates . 34 5.4 Lagrangian Mechanics . 36 5.5 D'Alembert's Principle . 37 5.6 Conjugate Variables . 39 1 CONTENTS 2 6 Hamiltonian Mechanics 40 6.1 Legendre Transformation: From Lagrangian to Hamiltonian . 40 6.2 Hamilton's Equations . 41 6.3 Configuration Space and Phase Space . 43 6.4 Hamiltonian and Energy . 45 7 Central Force Motion 47 7.1 Conservation Laws in Central Force Field . 47 7.2 The Path Equation . -
Power Sources Challenge
POWER SOURCES CHALLENGE FUSION PHYSICS! A CLEAN ENERGY Summary: What if we could harness the power of the Sun for energy here on Fusion reactions occur when two nuclei come together to form one Earth? What would it take to accomplish this feat? Is it possible? atom. The reaction that happens in the sun fuses two Hydrogen atoms together to produce Helium. It looks like this in a very simplified way: Many researchers including our Department of Energy scientists and H + H He + ENERGY. This energy can be calculated by the famous engineers are taking on this challenge! In fact, there is one DOE Laboratory Einstein equation, E = mc2. devoted to fusion physics and is committed to being at the forefront of the science of magnetic fusion energy. Each of the colliding hydrogen atoms is a different isotope of In order to understand a little more about fusion energy, you will learn about hydrogen, one deuterium and one the atom and how reactions at the atomic level produce energy. tritium. The difference in these isotopes is simply one neutron. Background: It all starts with plasma! If you need to learn more about plasma Deuterium has one proton and one physics, visit the Power Sources Challenge plasma activities. neutron, tritium has one proton and two neutrons. Look at the The Fusion Reaction that happens in the SUN looks like this: illustration—do you see how the mass of the products is less than the mass of the reactants? That is called a mass deficit and that difference in mass is converted into energy. -
Motion and Time Study the Goals of Motion Study
Motion and Time Study The Goals of Motion Study • Improvement • Planning / Scheduling (Cost) •Safety Know How Long to Complete Task for • Scheduling (Sequencing) • Efficiency (Best Way) • Safety (Easiest Way) How Does a Job Incumbent Spend a Day • Value Added vs. Non-Value Added The General Strategy of IE to Reduce and Control Cost • Are people productive ALL of the time ? • Which parts of job are really necessary ? • Can the job be done EASIER, SAFER and FASTER ? • Is there a sense of employee involvement? Some Techniques of Industrial Engineering •Measure – Time and Motion Study – Work Sampling • Control – Work Standards (Best Practices) – Accounting – Labor Reporting • Improve – Small group activities Time Study • Observation –Stop Watch – Computer / Interactive • Engineering Labor Standards (Bad Idea) • Job Order / Labor reporting data History • Frederick Taylor (1900’s) Studied motions of iron workers – attempted to “mechanize” motions to maximize efficiency – including proper rest, ergonomics, etc. • Frank and Lillian Gilbreth used motion picture to study worker motions – developed 17 motions called “therbligs” that describe all possible work. •GET G •PUT P • GET WEIGHT GW • PUT WEIGHT PW •REGRASP R • APPLY PRESSURE A • EYE ACTION E • FOOT ACTION F • STEP S • BEND & ARISE B • CRANK C Time Study (Stopwatch Measurement) 1. List work elements 2. Discuss with worker 3. Measure with stopwatch (running VS reset) 4. Repeat for n Observations 5. Compute mean and std dev of work station time 6. Be aware of allowances/foreign element, etc Work Sampling • Determined what is done over typical day • Random Reporting • Periodic Reporting Learning Curve • For repetitive work, worker gains skill, knowledge of product/process, etc over time • Thus we expect output to increase over time as more units are produced over time to complete task decreases as more units are produced Traditional Learning Curve Actual Curve Change, Design, Process, etc Learning Curve • Usually define learning as a percentage reduction in the time it takes to make a unit. -
Physics 101 Today Chapter 5: Newton's Third
Physics 101 Today Chapter 5: Newton’s Third Law First, let’s clarify notion of a force : Previously defined force as a push or pull. Better to think of force as an interaction between two objects. You can’t push anything without it pushing back on you ! Whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. Newton’s 3 rd Law - often called “action-reaction ” Eg. Leaning against a wall. You push against the wall. The wall is also pushing on you, equally hard – normal/support force. Now place a piece of paper between the wall and hand. Push on it – it doesn’t accelerate must be zero net force. The wall is pushing equally as hard (normal force) on the paper in the opposite direction to your hand, resulting in zero Fnet . This is more evident when hold a balloon against the wall – it is squashed on both sides. Eg. You pull on a cart. It accelerates. The cart pulls back on you (you feel the rope get tighter). Can call your pull the “ action ” and cart’s pull the “ reaction ”. Or, the other way around. • Newton’s 3 rd law means that forces always come in action -reaction pairs . It doesn’t matter which is called the action and which is called the reaction. • Note: Action-reaction pairs never act on the same object Examples of action-reaction force pairs In fact it is the road’s push that makes the car go forward. Same when we walk – push back on floor, floor pushes us forward. -
HW 6, Question 1: Forces in a Rotating Frame
HW 6, Question 1: Forces in a Rotating Frame Consider a solid platform, like a \merry-go round", that rotates with respect to an inertial frame of reference. It is oriented in the xy plane such that the axis of rotation is in the z-direction, i.e. ! = !z^, which we can take to point out of the page. Now, let us also consider a person walking on the rotating platform, such that this person is walking radially outward on the platform with respect to their (non-inertial) reference frame with velocity v = vr^. In what follows for Question 1, directions in the non-inertial reference frame (i.e. the frame of the walking person) are defined in the following manner: the x0-direction points directly outward from the center of the merry-go round; the y0 points in the tangential direction of rotation in the plane of the platform; and the z0-direction points out of the page, and in the same direction as the z-direction for the inertial reference frame. (a) Identify all forces. Since the person's reference frame is non-inertial, we need to account for the various fictitious forces given the description above, as well as any other external/reaction forces. The angular rate of rotation is constant, and so the Euler force Feul = m(!_ × r) = ~0. The significant forces acting on the person are: 0 • the force due to gravity, Fg = mg = mg(−z^ ), 2 0 • the (fictitious) centrifugal force, Fcen = m! × (! × r) = m! rx^ , 0 • the (fictitious) Coriolis force, Fcor = 2mv × ! = 2m!v(−y^ ), • the normal force the person experiences from the rotating platform N = Nz^0, and • a friction force acting on the person, f, in the x0y0 plane. -
A Short History of Physics (Pdf)
A Short History of Physics Bernd A. Berg Florida State University PHY 1090 FSU August 28, 2012. References: Most of the following is copied from Wikepedia. Bernd Berg () History Physics FSU August 28, 2012. 1 / 25 Introduction Philosophy and Religion aim at Fundamental Truths. It is my believe that the secured part of this is in Physics. This happend by Trial and Error over more than 2,500 years and became systematic Theory and Observation only in the last 500 years. This talk collects important events of this time period and attaches them to the names of some people. I can only give an inadequate presentation of the complex process of scientific progress. The hope is that the flavor get over. Bernd Berg () History Physics FSU August 28, 2012. 2 / 25 Physics From Acient Greek: \Nature". Broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves. The universe is commonly defined as the totality of everything that exists or is known to exist. In many ways, physics stems from acient greek philosophy and was known as \natural philosophy" until the late 18th century. Bernd Berg () History Physics FSU August 28, 2012. 3 / 25 Ancient Physics: Remarkable people and ideas. Pythagoras (ca. 570{490 BC): a2 + b2 = c2 for rectangular triangle: Leucippus (early 5th century BC) opposed the idea of direct devine intervention in the universe. He and his student Democritus were the first to develop a theory of atomism. Plato (424/424{348/347) is said that to have disliked Democritus so much, that he wished his books burned. -
1 the Principle of Wave–Particle Duality: an Overview
3 1 The Principle of Wave–Particle Duality: An Overview 1.1 Introduction In the year 1900, physics entered a period of deep crisis as a number of peculiar phenomena, for which no classical explanation was possible, began to appear one after the other, starting with the famous problem of blackbody radiation. By 1923, when the “dust had settled,” it became apparent that these peculiarities had a common explanation. They revealed a novel fundamental principle of nature that wascompletelyatoddswiththeframeworkofclassicalphysics:thecelebrated principle of wave–particle duality, which can be phrased as follows. The principle of wave–particle duality: All physical entities have a dual character; they are waves and particles at the same time. Everything we used to regard as being exclusively a wave has, at the same time, a corpuscular character, while everything we thought of as strictly a particle behaves also as a wave. The relations between these two classically irreconcilable points of view—particle versus wave—are , h, E = hf p = (1.1) or, equivalently, E h f = ,= . (1.2) h p In expressions (1.1) we start off with what we traditionally considered to be solely a wave—an electromagnetic (EM) wave, for example—and we associate its wave characteristics f and (frequency and wavelength) with the corpuscular charac- teristics E and p (energy and momentum) of the corresponding particle. Conversely, in expressions (1.2), we begin with what we once regarded as purely a particle—say, an electron—and we associate its corpuscular characteristics E and p with the wave characteristics f and of the corresponding wave. -
Newtonian Mechanics Is Most Straightforward in Its Formulation and Is Based on Newton’S Second Law
CLASSICAL MECHANICS D. A. Garanin September 30, 2015 1 Introduction Mechanics is part of physics studying motion of material bodies or conditions of their equilibrium. The latter is the subject of statics that is important in engineering. General properties of motion of bodies regardless of the source of motion (in particular, the role of constraints) belong to kinematics. Finally, motion caused by forces or interactions is the subject of dynamics, the biggest and most important part of mechanics. Concerning systems studied, mechanics can be divided into mechanics of material points, mechanics of rigid bodies, mechanics of elastic bodies, and mechanics of fluids: hydro- and aerodynamics. At the core of each of these areas of mechanics is the equation of motion, Newton's second law. Mechanics of material points is described by ordinary differential equations (ODE). One can distinguish between mechanics of one or few bodies and mechanics of many-body systems. Mechanics of rigid bodies is also described by ordinary differential equations, including positions and velocities of their centers and the angles defining their orientation. Mechanics of elastic bodies and fluids (that is, mechanics of continuum) is more compli- cated and described by partial differential equation. In many cases mechanics of continuum is coupled to thermodynamics, especially in aerodynamics. The subject of this course are systems described by ODE, including particles and rigid bodies. There are two limitations on classical mechanics. First, speeds of the objects should be much smaller than the speed of light, v c, otherwise it becomes relativistic mechanics. Second, the bodies should have a sufficiently large mass and/or kinetic energy. -
Motion and Forces Notes Key Speed • to Describe How Fast Something Is Traveling, You Have to Know Two Things About Its Motion
Motion and Forces Notes Key Speed • To describe how fast something is traveling, you have to know two things about its motion. • One is the distance it has traveled, or how far it has gone. • The other is how much time it took to travel that distance. Average Speed • To calculate average speed, divide the distance traveled by the time it takes to travel that distance. • Speed Equation Average speed (in m/s) = distance traveled (in m) divided by time (in s) it took to travel the distance s = d t • Because average speed is calculated by dividing distance by time, its units will always be a distance unit divided by a time unit. • For example, the average speed of a bicycle is usually given in meters per second. • Average speed is useful if you don't care about the details of the motion. • When your motion is speeding up and slowing down, it might be useful to know how fast you are going at a certain time. Instantaneous Speed • The instantaneous speed is the speed of an object at any instant of time. Constant Speed • Sometimes an object is moving such that its instantaneous speed doesn’t change. • When the instantaneous speed doesn't change, an object is moving with constant speed. • The average speed and the instantaneous speed are the same. Calculating Distance • If an object is moving with constant speed, then the distance it travels over any period of time can be calculated using the equation for average speed. • When both sides of this equation are multiplied by the time, you have the equation for distance. -
Linear Impulse and Momentum
EXSC 408L Fall '03 Problem Set #5 Linear Impulse and Momentum Linear Impulse and Momentum Problems: 1. Derive the principal of impulse and momentum from an initial cause and effect relationship to show an object’s final momentum. 2. Imagine a 100 N person walking. He generates an average net vertical reaction force during right foot contact with the ground of 100 N. If the TBCM vertical velocity at right foot contact is -0.2 m/s and the contact duration is 0.25 s, what is the TBCM vertical velocity at right toe off? 3. What is the take-off velocity of a 68.0 kg long jumper if his initial velocity is 8.50 m/s and his take-off step produces a net force of 2700 N for 0.200 s? Use the equation from #1. 4. A USC runner with a body weight of 490.5 N runs across a force plate, making contact with the plate for 0.25 s. During contact, her velocity increases from 2.5 m/s to 4.0 m/s. What was the net horizontal force she exerted while in contact with the force plate? 5. If the net vertical impulse of a 580 N person is 1800 Ns over 0.500 s, what was the vertical force produced? If her initial vertical velocity was –0.200 m/s, what was her vertical take-off velocity? 6. The plot seen here is a plot of the horizontal force generated by a long-jumper at take-off. Given that the long- jumper has a mass of 68.0 kg, and his approach velocity was 8.30 m/s, calculate the following: 3750 2750 1750 Force (N) 750 -250 0.4 0.45 0.5 0.55 0.6 Time(s) a. -
Gravity, Orbital Motion, and Relativity
Gravity, Orbital Motion,& Relativity Early Astronomy Early Times • As far as we know, humans have always been interested in the motions of objects in the sky. • Not only did early humans navigate by means of the sky, but the motions of objects in the sky predicted the changing of the seasons, etc. • There were many early attempts both to describe and explain the motions of stars and planets in the sky. • All were unsatisfactory, for one reason or another. The Earth-Centered Universe • A geocentric (Earth-centered) solar system is often credited to Ptolemy, an Alexandrian Greek, although the idea is very old. • Ptolemy’s solar system could be made to fit the observational data pretty well, but only by becoming very complicated. Copernicus’ Solar System • The Polish cleric Copernicus proposed a heliocentric (Sun centered) solar system in the 1500’s. Objections to Copernicus How could Earth be moving at enormous speeds when we don’t feel it? . (Copernicus didn’t know about inertia.) Why can’t we detect Earth’s motion against the background stars (stellar parallax)? Copernicus’ model did not fit the observational data very well. Galileo • Galileo Galilei - February15,1564 – January 8, 1642 • Galileo became convinced that Copernicus was correct by observations of the Sun, Venus, and the moons of Jupiter using the newly-invented telescope. • Perhaps Galileo was motivated to understand inertia by his desire to understand and defend Copernicus’ ideas. Orbital Motion Tycho and Kepler • In the late 1500’s, a Danish nobleman named Tycho Brahe set out to make the most accurate measurements of planetary motions to date, in order to validate his own ideas of planetary motion.