Newton's Third
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Rotational Motion (The Dynamics of a Rigid Body)
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 11: Rotational Motion (The Dynamics of a Rigid Body) Henry Semat City College of New York Robert Katz University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/physicskatz Part of the Physics Commons Semat, Henry and Katz, Robert, "Physics, Chapter 11: Rotational Motion (The Dynamics of a Rigid Body)" (1958). Robert Katz Publications. 141. https://digitalcommons.unl.edu/physicskatz/141 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Robert Katz Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 11 Rotational Motion (The Dynamics of a Rigid Body) 11-1 Motion about a Fixed Axis The motion of the flywheel of an engine and of a pulley on its axle are examples of an important type of motion of a rigid body, that of the motion of rotation about a fixed axis. Consider the motion of a uniform disk rotat ing about a fixed axis passing through its center of gravity C perpendicular to the face of the disk, as shown in Figure 11-1. The motion of this disk may be de scribed in terms of the motions of each of its individual particles, but a better way to describe the motion is in terms of the angle through which the disk rotates. -
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. -
The Great White Hoax
THE GREAT WHITE HOAX Featuring Tim Wise [Transcript] INTRODUCTION Text on screen Charlottesville, Virginia August 11, 2017 Protesters [chanting] You will not replace us! News reporter A major American college campus transformed into a battlefield. Hundreds of white nationalists storming the University of Virginia. Protesters [chanting] Whose streets? Our streets! News reporter White nationalists protesting the removal of a Confederate statue. The setting a powder keg ready to blow. Protesters [chanting] White lives matter! Counter-protesters [chanting] Black lives matter! Protesters [chanting] White lives matter! News reporter The march spiraling out of control. So-called Alt-Right demonstrators clashing with counter- protesters some swinging torches. Text on screen August 12, 2017 News reporter (continued) The overnight violence spilling into this morning when march-goers and counter-protesters clash again. © 2017 Media Education Foundation | mediaed.org 1 David Duke This represents a turning point for the people of this country. We are determined to take our country back. We're going to fulfill the promises of Donald Trump. That's what we believed in. That's why we voted for Donald Trump. Because he said he's going to take our country back. And that's what we gotta do. News reporter A horrifying scene in Charlottesville, as this car plowed into a crowd of people. The driver then backing up and, witnesses say, dragging at least one person. Donald Trump We're closely following the terrible events unfolding in Charlottesville, Virginia. We condemn, in the strongest possible terms, this egregious display of hatred, bigotry, and violence on many sides. On many sides. -
Chapter 5 the Relativistic Point Particle
Chapter 5 The Relativistic Point Particle To formulate the dynamics of a system we can write either the equations of motion, or alternatively, an action. In the case of the relativistic point par- ticle, it is rather easy to write the equations of motion. But the action is so physical and geometrical that it is worth pursuing in its own right. More importantly, while it is difficult to guess the equations of motion for the rela- tivistic string, the action is a natural generalization of the relativistic particle action that we will study in this chapter. We conclude with a discussion of the charged relativistic particle. 5.1 Action for a relativistic point particle How can we find the action S that governs the dynamics of a free relativis- tic particle? To get started we first think about units. The action is the Lagrangian integrated over time, so the units of action are just the units of the Lagrangian multiplied by the units of time. The Lagrangian has units of energy, so the units of action are L2 ML2 [S]=M T = . (5.1.1) T 2 T Recall that the action Snr for a free non-relativistic particle is given by the time integral of the kinetic energy: 1 dx S = mv2(t) dt , v2 ≡ v · v, v = . (5.1.2) nr 2 dt 105 106 CHAPTER 5. THE RELATIVISTIC POINT PARTICLE The equation of motion following by Hamilton’s principle is dv =0. (5.1.3) dt The free particle moves with constant velocity and that is the end of the story. -
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. -
A Culturally Based Healing Intervention for Commercially Sex Trafficked Native American Women
St. Catherine University SOPHIA Master of Social Work Clinical Research Papers School of Social Work 5-2016 A Culturally Based Healing Intervention for Commercially Sex Trafficked Native American Women Jennifer Hintz St. Catherine University, [email protected] Follow this and additional works at: https://sophia.stkate.edu/msw_papers Part of the Social Work Commons Recommended Citation Hintz, Jennifer. (2016). A Culturally Based Healing Intervention for Commercially Sex Trafficked Native American Women. Retrieved from Sophia, the St. Catherine University repository website: https://sophia.stkate.edu/msw_papers/594 This Clinical research paper is brought to you for free and open access by the School of Social Work at SOPHIA. It has been accepted for inclusion in Master of Social Work Clinical Research Papers by an authorized administrator of SOPHIA. For more information, please contact [email protected]. NATIVE AMERICAN CULTURAL HEALING 1 A Culturally Based Healing Intervention for Commercially Sex Trafficked Native American Women By Jennifer D. Hintz, B.S. MSW Clinical Research Paper Presented to the Faculty of the School of Social Work St. Catherine University and the University of St. Thomas St. Paul, Minnesota In Partial fulfillment of the Requirements for the Degree of Master of Social Work Committee Members Rajean P. Moone, Ph.D., (Chair) Jim Bear Jacobs, M.A Sister Stephanie Spandl, MSW, LICSW The Clinical Research project is a graduation requirement for MSW students at St. Catherine University/University of St. Thomas School of Social Work in St. Paul, Minnesota and is conducted within a nine-month time frame to demonstrate facility with basic social work research methods. -
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. -
Chapter 5 ANGULAR MOMENTUM and ROTATIONS
Chapter 5 ANGULAR MOMENTUM AND ROTATIONS In classical mechanics the total angular momentum L~ of an isolated system about any …xed point is conserved. The existence of a conserved vector L~ associated with such a system is itself a consequence of the fact that the associated Hamiltonian (or Lagrangian) is invariant under rotations, i.e., if the coordinates and momenta of the entire system are rotated “rigidly” about some point, the energy of the system is unchanged and, more importantly, is the same function of the dynamical variables as it was before the rotation. Such a circumstance would not apply, e.g., to a system lying in an externally imposed gravitational …eld pointing in some speci…c direction. Thus, the invariance of an isolated system under rotations ultimately arises from the fact that, in the absence of external …elds of this sort, space is isotropic; it behaves the same way in all directions. Not surprisingly, therefore, in quantum mechanics the individual Cartesian com- ponents Li of the total angular momentum operator L~ of an isolated system are also constants of the motion. The di¤erent components of L~ are not, however, compatible quantum observables. Indeed, as we will see the operators representing the components of angular momentum along di¤erent directions do not generally commute with one an- other. Thus, the vector operator L~ is not, strictly speaking, an observable, since it does not have a complete basis of eigenstates (which would have to be simultaneous eigenstates of all of its non-commuting components). This lack of commutivity often seems, at …rst encounter, as somewhat of a nuisance but, in fact, it intimately re‡ects the underlying structure of the three dimensional space in which we are immersed, and has its source in the fact that rotations in three dimensions about di¤erent axes do not commute with one another. -
Vision Series 2018: “Where We're Going: Push Back the Darkness” Matthew 5:14-16 We Are on Week 2 of Our Vision Series
Vision Series 2018: “Where We’re Going: Push Back the Darkness” Matthew 5:14-16 We are on week 2 of our Vision Series, and as you’ve already heard this morning from our Vision Team members and specifically from Molly Pitkin, we are going to spend this time looking deeply into our new mission statement which was revealed last week after a year of prayer, learning, and listening. Again, Colonial’s mission is “To be the light of Christ in a hurting culture so that the lost are found, the broken are made whole, the fatherless find hope, and our city is blessed.” As Molly mentioned, this mission statement was “discovered” by a team of people who spent many, many hours together in prayer, study, conversation, and discernment. Again, the Vision Team Members included Steve Aliber, our current Clerk of Session; Jim Cannon, our former Clerk of Session; Brian Mack, our Elder of Strategic Planning; Ken Kurtz…a current Elder at Wornall; Kevin Nunnally…a recent Elder at Wornall; Meda Green…Chair of Deacons at Quivira; Molly Pitkin…high school youth leader at Quivira; Ken Blume…Executive Director of Programs and Ministries; and me as the Lead Pastor. We benefitted greatly from our facilitator, Ted Vaughn, who guided us through a wonderful process of discovery. Now, before I jump into unpacking the Mission Statement, let me address some of your questions that I’ve been asked over the past week. First, I was asked why words like “making disciples” and “doing everything for the glory of God” were left out of our mission statement. -
SPEED MANAGEMENT ACTION PLAN Implementation Steps
SPEED MANAGEMENT ACTION PLAN Implementation Steps Put Your Speed Management Plan into Action You did it! You recognized that speeding is a significant Figuring out how to implement a speed management plan safety problem in your jurisdiction, and you put a lot of time can be daunting, so the Federal Highway Administration and effort into developing a Speed Management Action (FHWA) has developed a set of steps that agency staff can Plan that holds great promise for reducing speeding-related adopt and tailor to get the ball rolling—but not speeding! crashes and fatalities. So…what’s next? Agencies can use these proven methods to jump start plan implementation and achieve success in reducing speed- related crashes. Involve Identify a Stakeholders Champion Prioritize Strategies for Set Goals, Track Implementation Market the Develop a Speed Progress, Plan Management Team Evaluate, and Celebrate Success Identify Strategy Leads INVOLVE STAKEHOLDERS In order for the plan to be successful, support and buy-in is • Outreach specialists. needed from every area of transportation: engineering (Federal, • Governor’s Highway Safety Office representatives. State, local, and Metropolitan Planning Organizations (MPO), • National Highway Transportation Safety Administration (NHTSA) Regional Office representatives. enforcement, education, and emergency medical services • Local/MPO/State Department of Transportation (DOT) (EMS). Notify and engage stakeholders who were instrumental representatives. in developing the plan and identify gaps in support. Potential • Police/enforcement representatives. stakeholders may include: • FHWA Division Safety Engineers. • Behavioral and infrastructure funding source representatives. • Agency Traffic Operations Engineers. • Judicial representatives. • Agency Safety Engineers. • EMS providers. • Agency Pedestrian/Bicycle Coordinators. • Educators. • Agency Pavement Design Engineers.