The Centrifugal Force and the Coriolis Force
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On the Transformation of Torques Between the Laboratory and Center
On the transformation of torques between the laboratory and center of mass reference frames Rodolfo A. Diaz,∗ William J. Herrera† Universidad Nacional de Colombia, Departamento de F´ısica. Bogot´a, Colombia. Abstract It is commonly stated in Newtonian Mechanics that the torque with respect to the laboratory frame is equal to the torque with respect to the center of mass frame plus a R × F factor, with R being the position of the center of mass and F denoting the total external force. Although this assertion is true, there is a subtlety in the demonstration that is overlooked in the textbooks. In addition, it is necessary to clarify that if the reference frame attached to the center of mass rotates with respect to certain inertial frame, the assertion is not true any more. PACS {01.30.Pp, 01.55.+b, 45.20.Dd} Keywords: Torque, center of mass, transformation of torques, fictitious forces. In Newtonian Mechanics, we define the total external torque of a system of n particles (with respect to the laboratory frame that we shall assume as an inertial reference frame) as n Next = ri × Fi(e) , i=1 X where ri, Fi(e) denote the position and total external force for the i − th particle. The relation between the position coordinates between the laboratory (L) and center of mass (CM) reference frames 1 is given by ′ ri = ri + R , ′ with R denoting the position of the CM about the L, and ri denoting the position of the i−th particle with respect to the CM, in general the prime notation denotes variables measured with respect to the CM. -
Explain Inertial and Noninertial Frame of Reference
Explain Inertial And Noninertial Frame Of Reference Nathanial crows unsmilingly. Grooved Sibyl harlequin, his meadow-brown add-on deletes mutely. Nacred or deputy, Sterne never soot any degeneration! In inertial frames of the air, hastening their fundamental forces on two forces must be frame and share information section i am throwing the car, there is not a severe bottleneck in What city the greatest value in flesh-seconds for this deviation. The definition of key facet having a small, polished surface have a force gem about a pretend or aspect of something. Fictitious Forces and Non-inertial Frames The Coriolis Force. Indeed, for death two particles moving anyhow, a coordinate system may be found among which saturated their trajectories are rectilinear. Inertial reference frame of inertial frames of angular momentum and explain why? This is illustrated below. Use tow of reference in as sentence Sentences YourDictionary. What working the difference between inertial frame and non inertial fr. Frames of Reference Isaac Physics. In forward though some time and explain inertial and noninertial of frame to prove your measurement problem you. This circumstance undermines a defining characteristic of inertial frames: that with respect to shame given inertial frame, the other inertial frame home in uniform rectilinear motion. The redirect does not rub at any valid page. That according to whether the thaw is inertial or non-inertial In the. This follows from what Einstein formulated as his equivalence principlewhich, in an, is inspired by the consequences of fire fall. Frame of reference synonyms Best 16 synonyms for was of. How read you govern a bleed of reference? Name we will balance in noninertial frame at its axis from another hamiltonian with each printed as explained at all. -
THE PROBLEM with SO-CALLED FICTITIOUS FORCES Abstract 1
THE PROBLEM WITH SO-CALLED FICTITIOUS FORCES Härtel Hermann; University Kiel, Germany Abstract Based on examples from modern textbooks the question will be raised if the traditional approach to teach the basics of Newton´s mechanics is still adequate, especially when inertial forces like centrifugal forces are described as fictitious, applicable only in non-inertial frames of reference. In the light of some recent research, based on Mach´s principles and early work of Weber, it is argued that the so-called fictitious forces could be described as real interactive forces and therefore should play quite a different role in the frame of Newton´s mechanics. By means of some computer supported learning material it will be shown how a fruitful discussion of these ideas could be supported. 1. Introduction When treating classical mechanics the interaction forces are usually clearly separated from the so- called inertial forces. For interaction forces Newton´s basic laws are valid, while for inertial forces especially the 3rd Newtonian principle cannot be applied. There seems to be no interaction force which can be related to the force of inertia and therefore this force is called fictitious and is assigned to a fictitious world. The following citations from a widespread German textbook (Bergmann Schaefer 1998) may serve as a typical example, which is found in similar form in many other German as well as American textbooks. • Zu den in der Natur beobachtbaren Kräften gehören schließlich auch die sogenannten Scheinkräfte oder Trägheitskräfte, die nur in Bezugssystemen wirken, die gegenüber dem Fundamentalsystem der fernen Galaxien beschleunigt sind. Dazu gehören die Zentrifugalkraft und die Corioliskraft. -
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 . -
The Double Tidal Bulge
The Double Tidal Bulge If you look at any explanation of tides the force is indeed real. Try driving same for all points on the Earth. Try you will see a diagram that looks fast around a tight bend and tell me this analogy: take something round something like fig.1 which shows the you can’t feel a force pushing you to like a roll of sticky tape, put it on the tides represented as two bulges of the side. You are in the rotating desk and move it in small circles (not water – one directly under the Moon frame of reference hence the force rotating it, just moving the whole and another on the opposite side of can be felt. thing it in a circular manner). You will the Earth. Most people appreciate see that every point on the object that tides are caused by gravitational 3. In the discussion about what moves in a circle of equal radius and forces and so can understand the causes the two bulges of water you the same speed. moon-side bulge; however the must completely ignore the rotation second bulge is often a cause of of the Earth on its axis (the 24 hr Now let’s look at the gravitation pull confusion. This article attempts to daily rotation). Any talk of rotation experienced by objects on the Earth explain why there are two bulges. refers to the 27.3 day rotation of the due to the Moon. The magnitude and Earth and Moon about their common direction of this force will be different centre of mass. -
Lecture Notes in Physical Oceanography
LECTURE NOTES IN PHYSICAL OCEANOGRAPHY ODD HENRIK SÆLEN EYVIND AAS 1976 2012 CONTENTS FOREWORD INTRODUCTION 1 EXTENT OF THE OCEANS AND THEIR DIVISIONS 1.1 Distribution of Water and Land..........................................................................1 1.2 Depth Measurements............................................................................................3 1.3 General Features of the Ocean Floor..................................................................5 2 CHEMICAL PROPERTIES OF SEAWATER 2.1 Chemical Composition..........................................................................................1 2.2 Gases in Seawater..................................................................................................4 3 PHYSICAL PROPERTIES OF SEAWATER 3.1 Density and Freezing Point...................................................................................1 3.2 Temperature..........................................................................................................3 3.3 Compressibility......................................................................................................5 3.4 Specific and Latent Heats.....................................................................................5 3.5 Light in the Sea......................................................................................................6 3.6 Sound in the Sea..................................................................................................11 4 INFLUENCE OF ATMOSPHERE ON THE SEA 4.1 Major Wind -
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. -
Chapter 5 Water Levels and Flow
253 CHAPTER 5 WATER LEVELS AND FLOW 1. INTRODUCTION The purpose of this chapter is to provide the hydrographer and technical reader the fundamental information required to understand and apply water levels, derived water level products and datums, and water currents to carry out field operations in support of hydrographic surveying and mapping activities. The hydrographer is concerned not only with the elevation of the sea surface, which is affected significantly by tides, but also with the elevation of lake and river surfaces, where tidal phenomena may have little effect. The term ‘tide’ is traditionally accepted and widely used by hydrographers in connection with the instrumentation used to measure the elevation of the water surface, though the term ‘water level’ would be more technically correct. The term ‘current’ similarly is accepted in many areas in connection with tidal currents; however water currents are greatly affected by much more than the tide producing forces. The term ‘flow’ is often used instead of currents. Tidal forces play such a significant role in completing most hydrographic surveys that tide producing forces and fundamental tidal variations are only described in general with appropriate technical references in this chapter. It is important for the hydrographer to understand why tide, water level and water current characteristics vary both over time and spatially so that they are taken fully into account for survey planning and operations which will lead to successful production of accurate surveys and charts. Because procedures and approaches to measuring and applying water levels, tides and currents vary depending upon the country, this chapter covers general principles using documented examples as appropriate for illustration. -
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. -
Tides and the Climate: Some Speculations
FEBRUARY 2007 MUNK AND BILLS 135 Tides and the Climate: Some Speculations WALTER MUNK Scripps Institution of Oceanography, La Jolla, California BRUCE BILLS Scripps Institution of Oceanography, La Jolla, California, and NASA Goddard Space Flight Center, Greenbelt, Maryland (Manuscript received 18 May 2005, in final form 12 January 2006) ABSTRACT The important role of tides in the mixing of the pelagic oceans has been established by recent experiments and analyses. The tide potential is modulated by long-period orbital modulations. Previously, Loder and Garrett found evidence for the 18.6-yr lunar nodal cycle in the sea surface temperatures of shallow seas. In this paper, the possible role of the 41 000-yr variation of the obliquity of the ecliptic is considered. The obliquity modulation of tidal mixing by a few percent and the associated modulation in the meridional overturning circulation (MOC) may play a role comparable to the obliquity modulation of the incoming solar radiation (insolation), a cornerstone of the Milankovic´ theory of ice ages. This speculation involves even more than the usual number of uncertainties found in climate speculations. 1. Introduction et al. 2000). The Hawaii Ocean-Mixing Experiment (HOME), a major experiment along the Hawaiian Is- An early association of tides and climate was based land chain dedicated to tidal mixing, confirmed an en- on energetics. Cold, dense water formed in the North hanced mixing at spring tides and quantified the scat- Atlantic would fill up the global oceans in a few thou- tering of tidal energy from barotropic into baroclinic sand years were it not for downward mixing from the modes over suitable topography.