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Circular Motion Dynamics
Problem Solving Circular Motion Dynamics Problem 1: Double Star System Consider a double star system under the influence of gravitational force between the stars. Star 1 has mass m1 and star 2 has mass m2 . Assume that each star undergoes uniform circular motion about the center of mass of the system. If the stars are always a fixed distance s apart, what is the period of the orbit? Solution: Choose radial coordinates for each star with origin at center of mass. Let rˆ1 be a unit vector at Star 1 pointing radially away from the center of mass. Let rˆ2 be a unit vector at Star 2 pointing radially away from the center of mass. The force diagrams on the two stars are shown in the figure below. ! ! From Newton’s Second Law, F1 = m 1a 1 , for Star 1 in the radial direction is m m ˆ 1 2 2 r1 : "G 2 = "m1 r 1 ! . s We can solve this for r1 , m r = G 2 . 1 ! 2s 2 ! ! Newton’s Second Law, F2 = m 2a 2 , for Star 2 in the radial direction is m m ˆ 1 2 2 r2 : "G 2 = "m2 r 2 ! . s We can solve this for r2 , m r = G 1 . 2 ! 2s 2 Since s , the distance between the stars, is constant m2 m1 (m2 + m1 ) s = r + r = G + G = G 1 2 ! 2s 2! 2s 2 ! 2s 2 . Thus the angular velocity is 1 2 " (m2 + m1 ) # ! = $G 3 % & s ' and the period is then 1 2 2! # 4! 2s 3 $ T = = % & . -
Assignment 2 Centripetal Force & Univ
LAST NAME______________________________ FIRST NAME_____________________DATE______ CJ - Assignment 2 Centripetal Force & Universal Gravitation, 5.4 Banked Curves Draw the vectors for a free body diagram of a car in an unbanked turn and a banked turn. For this situation assume the cars are turning to the left side of the drawing. Car in Unbanked Turn Car in Banked turn Is this car in Equilibrium? Is this car in Equilibrium? Do the same for the airplane. Airplane in Unbanked Turn Airplane in Banked turn Let’s be careful to fully understand what is going on with this one. We have made an assumption in doing this for the airplane which are not valid. THE BANKED TURN- car can make it a round a turn even if friction is not present (or friction is zero). In order for this to happen the curved road must be “banked”. In a non-banked turn the centripetal force is created by the friction of the road on the tires. What creates the centripetal force in a banked turn? Imagine looking at a banked turn as shown to the right. Draw the forces that act on the car on the diagram of the car. Is the car in Equilibrium? YES , NO The car which has a mass of m is travelling at a velocity (or speed) v around a turn of radius r. How do these variables relate to optimize the banked turn. If the mass of the car is greater is a larger or smaller angle required? LARGER, SMALLER, NO CHANGE NECESSARY If the VELOCITY of the car is greater is a larger or smaller angle required? LARGER, SMALLER, NO CHANGE NECESSARY If the RADUS OF THE TURN is greater is a larger or smaller angle required? LARGER, SMALLER, NO CHANGE NECESSARY To properly show the relationship an equation must be created. -
Philosophy of Science -----Paulk
PHILOSOPHY OF SCIENCE -----PAULK. FEYERABEND----- However, it has also a quite decisive role in building the new science and in defending new theories against their well-entrenched predecessors. For example, this philosophy plays a most important part in the arguments about the Copernican system, in the development of optics, and in the Philosophy ofScience: A Subject with construction of a new and non-Aristotelian dynamics. Almost every work of Galileo is a mixture of philosophical, mathematical, and physical prin~ a Great Past ciples which collaborate intimately without giving the impression of in coherence. This is the heroic time of the scientific philosophy. The new philosophy is not content just to mirror a science that develops independ ently of it; nor is it so distant as to deal just with alternative philosophies. It plays an essential role in building up the new science that was to replace 1. While it should be possible, in a free society, to introduce, to ex the earlier doctrines.1 pound, to make propaganda for any subject, however absurd and however 3. Now it is interesting to see how this active and critical philosophy is immoral, to publish books and articles, to give lectures on any topic, it gradually replaced by a more conservative creed, how the new creed gener must also be possible to examine what is being expounded by reference, ates technical problems of its own which are in no way related to specific not to the internal standards of the subject (which may be but the method scientific problems (Hurne), and how there arises a special subject that according to which a particular madness is being pursued), but to stan codifies science without acting back on it (Kant). -
April 2018 the Privileged View Steve Beste, President
Volume 18 – 04 www.FlyingClub1.org April 2018 The Privileged View Steve Beste, President Maker Faire. When something breaks, who you gonna call? If it’s your car or your Cessna, you put it into the shop and get out your checkbook. But if you fly an experimental or Part 103 aircraft, it’s not so simple. That’s why - when newbies ask me about our sport - I find out if they’re tinkerers and do-it-yourselfers. If all they bring to a problem is their checkbook, then they’re better off going with the Cessna. The tinkerers and builders, though, they’re my kind of people. That’s why I went with Dick Martin to the annual Maker Faire at George Mason in mid-March. I thought we’d find a modest event that focused on 3D printing for adult hobbyists, but I was so wrong. They had 140 exhibitors filling three buildings. With several thousand visitors, there were lines outside the buildings by mid-afternoon. Yes, they had 3D printers, but so much more. And so many kids! The focus of the event was clearly on bringing young people into the world of making stuff. The cleverest exhibit was the one shown below. They set up four tables with junk computer gear and told kids to just take things apart. Don’t worry about putting anything back together again. It’s all junk! Rip it apart! See how it’s made! Do it! It looked like a destruction derby, with laptops and printers and even a sewing machine being reduced to screws and plates. -
The Experimental Verdict on Spacetime from Gravity Probe B
The Experimental Verdict on Spacetime from Gravity Probe B James Overduin Abstract Concepts of space and time have been closely connected with matter since the time of the ancient Greeks. The history of these ideas is briefly reviewed, focusing on the debate between “absolute” and “relational” views of space and time and their influence on Einstein’s theory of general relativity, as formulated in the language of four-dimensional spacetime by Minkowski in 1908. After a brief detour through Minkowski’s modern-day legacy in higher dimensions, an overview is given of the current experimental status of general relativity. Gravity Probe B is the first test of this theory to focus on spin, and the first to produce direct and unambiguous detections of the geodetic effect (warped spacetime tugs on a spin- ning gyroscope) and the frame-dragging effect (the spinning earth pulls spacetime around with it). These effects have important implications for astrophysics, cosmol- ogy and the origin of inertia. Philosophically, they might also be viewed as tests of the propositions that spacetime acts on matter (geodetic effect) and that matter acts back on spacetime (frame-dragging effect). 1 Space and Time Before Minkowski The Stoic philosopher Zeno of Elea, author of Zeno’s paradoxes (c. 490-430 BCE), is said to have held that space and time were unreal since they could neither act nor be acted upon by matter [1]. This is perhaps the earliest version of the relational view of space and time, a view whose philosophical fortunes have waxed and waned with the centuries, but which has exercised enormous influence on physics. -
Classical Spacetime Structure
Classical Spacetime Structure James Owen Weatherall Department of Logic and Philosophy of Science University of California, Irvine Abstract I discuss several issues related to \classical" spacetime structure. I review Galilean, Newto- nian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students in philosophy; the presentation avoids mathematical formalism as much as possible. 1. Introduction One often associates spacetime|a four-dimensional geometrical structure representing both space and time|with relativity theory, developed by Einstein and others in the early part of the twentieth century.1 But soon after relativity theory appeared, several authors, such as Hermann Weyl (1952 [1918]), Elie´ Cartan (1923, 1924), and Kurt Friedrichs (1927), began to study how the spatio-temporal structure presupposed by classical, i.e., Newtonian, physics could be re-cast using the methods of four-dimensional geometry developed in the context of relativity. These reformulations of classical physics were initially of interest for the insight they offered into the structure of relativity theory.2 But this changed in 1967, when Howard Stein proposed that the notion of a \classical" spacetime could provide important insight arXiv:1707.05887v1 [physics.hist-ph] 18 Jul 2017 Email address: [email protected] (James Owen Weatherall) 1The idea of \spacetime" was actually introduced by Minkowski (2013 [1911]), several years after Einstein first introduced relativity theory. 2And indeed, they remain of interest for this reason: see, for instance, Friedman (1983), Malament (1986a,b, 2012), Earman (1989b), Fletcher (2014), Barrett (2015), Weatherall (2011a,b, 2014, 2017d,c), and Dewar and Weatherall (2017) for philosophical discussions of the relationship between relativity theory and Newtonian physics that make heavy use of this formalism. -
Why Spacetime Is Probably a Substance Author(S): Tim Maudlin Reviewed Work(S): Source: Philosophy of Science, Vol
Buckets of Water and Waves of Space: Why Spacetime Is Probably a Substance Author(s): Tim Maudlin Reviewed work(s): Source: Philosophy of Science, Vol. 60, No. 2 (Jun., 1993), pp. 183-203 Published by: The University of Chicago Press on behalf of the Philosophy of Science Association Stable URL: http://www.jstor.org/stable/188350 . Accessed: 28/12/2012 20:13 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press and Philosophy of Science Association are collaborating with JSTOR to digitize, preserve and extend access to Philosophy of Science. http://www.jstor.org This content downloaded on Fri, 28 Dec 2012 20:13:44 PM All use subject to JSTOR Terms and Conditions Philosophy of Science June, 1993 BUCKETS OF WATER AND WAVES OF SPACE: WHY SPACETIME IS PROBABLY A SUBSTANCE* TIM MAUDLINtt Department of Philosophy Rutgers University This paper sketches a taxonomy of forms of substantivalism and relationism concerning space and time, and of the traditional arguments for these positions. Several natural sorts of relationism are able to account for Newton's bucket experiment. Conversely, appropriately constructed substantivalism can survive Leibniz's critique, a fact which has been obscured by the conflation of two of Leibniz's arguments. -
Physics/0409010V1 [Physics.Gen-Ph] 1 Sep 2004 Ri Ihteclsilshr Sntfound
Physical Interpretations of Relativity Theory Conference IX London, Imperial College, September, 2004 ............... Mach’s Principle II by James G. Gilson∗ School of Mathematical Sciences Queen Mary College University of London October 29, 2018 Abstract 1 Introduction The question of the validity or otherwise of Mach’s The meaning and significance of Mach’s Principle Principle[5] has been with us for almost a century and and its dependence on ideas about relativistic rotat- has been vigorously analysed and discussed for all of ing frame theory and the celestial sphere is explained that time and is, up to date, still not resolved. One and discussed. Two new relativistic rotation trans- contentious issue is, does general[7] relativity theory formations are introduced by using a linear simula- imply that Mach’s Principle is operative in that theo- tion for the rotating disc situation. The accepted retical structure or does it not? A deduction[4] from formula for centrifugal acceleration in general rela- general relativity that the classical Newtonian cen- tivity is then analysed with the use of one of these trifugal acceleration formula should be modified by transformations. It is shown that for this general rel- an additional relativistic γ2(v) factor, see equations ativity formula to be valid throughout all space-time (2.11) and (2.27), will help us in the analysis of that there has to be everywhere a local standard of ab- question. Here I shall attempt to throw some light solutely zero rotation. It is then concluded that the on the nature and technical basis of the collection of field off all possible space-time null geodesics or pho- arXiv:physics/0409010v1 [physics.gen-ph] 1 Sep 2004 technical and philosophical problems generated from ton paths unify the absolute local non-rotation stan- Mach’s Principle and give some suggestions about dard throughout space-time. -
Arxiv:1704.03334V1 [Physics.Gen-Ph] 8 Apr 2017 Oin Ffltsaeadtime
WHAT DO WE KNOW ABOUT THE GEOMETRY OF SPACE? B. E. EICHINGER Department of Chemistry, University of Washington, Seattle, Washington 98195-1700 Abstract. The belief that three dimensional space is infinite and flat in the absence of matter is a canon of physics that has been in place since the time of Newton. The assumption that space is flat at infinity has guided several modern physical theories. But what do we actually know to support this belief? A simple argument, called the ”Telescope Principle”, asserts that all that we can know about space is bounded by observations. Physical theories are best when they can be verified by observations, and that should also apply to the geometry of space. The Telescope Principle is simple to state, but it leads to very interesting insights into relativity and Yang-Mills theory via projective equivalences of their respective spaces. 1. Newton and the Euclidean Background Newton asserted the existence of an Absolute Space which is infinite, three dimensional, and Euclidean.[1] This is a remarkable statement. How could Newton know anything about the nature of space at infinity? Obviously, he could not know what space is like at infinity, so what motivated this assertion (apart from Newton’s desire to make space the sensorium of an infinite God)? Perhaps it was that the geometric tools available to him at the time were restricted to the principles of Euclidean plane geometry and its extension to three dimensions, in which infinite space is inferred from the parallel postulate. Given these limited mathematical resources, there was really no other choice than Euclid for a description of the geometry of space within which to formulate a theory of motion of material bodies. -
6 Space Substantivalism and Relationism Newton's Argument For
6 Space Substantivalism and relationism abstract entities vs concrete entities. regions is commonly thought to be concrete but that isn’t in the category of material objects. realists would say regions or space do exist. Anti-realists about space would say, regions are an unnecessary addition. God creating the universe The realist about regions thinks that God has first to make an enormous container – the regions – in order to put the objects in. The anti-realist thinks that all God has to do to make the universe is make a bunch of objects, and then arrange them in a certain way. Those who are realists about regions are called substantivalists, whilst those who are anti- realists about regions are often called relationists. Newton’s argument for absolute space Dirction + Speed = velocity # Velocity + acceleration = innertial forces Newton’s bucket Newton’s argument for substantivalism – if velocity has to be relative to something, and acceleration is a change in velocity, then acceleration has to be relative to something as well. But, says Newton, it’s possible for one object to accelerate even though there’s no object that the acceleration could be relative to. But, as it must be relative to something, it must be relative to something that was not an object: it must be relative to space itself; ergo, space must exist. Stage 1: The rope is twisted but has not been let loose. The bucket and the water are at rest with respect to one another. Stage 2: The rope has been let loose and the bucket has started to rotate. -
FAA-H-8083-3A, Airplane Flying Handbook -- 3 of 7 Files
Ch 04.qxd 5/7/04 6:46 AM Page 4-1 NTRODUCTION Maneuvering during slow flight should be performed I using both instrument indications and outside visual The maintenance of lift and control of an airplane in reference. Slow flight should be practiced from straight flight requires a certain minimum airspeed. This glides, straight-and-level flight, and from medium critical airspeed depends on certain factors, such as banked gliding and level flight turns. Slow flight at gross weight, load factors, and existing density altitude. approach speeds should include slowing the airplane The minimum speed below which further controlled smoothly and promptly from cruising to approach flight is impossible is called the stalling speed. An speeds without changes in altitude or heading, and important feature of pilot training is the development determining and using appropriate power and trim of the ability to estimate the margin of safety above the settings. Slow flight at approach speed should also stalling speed. Also, the ability to determine the include configuration changes, such as landing gear characteristic responses of any airplane at different and flaps, while maintaining heading and altitude. airspeeds is of great importance to the pilot. The student pilot, therefore, must develop this awareness in FLIGHT AT MINIMUM CONTROLLABLE order to safely avoid stalls and to operate an airplane AIRSPEED This maneuver demonstrates the flight characteristics correctly and safely at slow airspeeds. and degree of controllability of the airplane at its minimum flying speed. By definition, the term “flight SLOW FLIGHT at minimum controllable airspeed” means a speed at Slow flight could be thought of, by some, as a speed which any further increase in angle of attack or load that is less than cruise. -
General Relativity and Spatial Flows: I
1 GENERAL RELATIVITY AND SPATIAL FLOWS: I. ABSOLUTE RELATIVISTIC DYNAMICS* Tom Martin Gravity Research Institute Boulder, Colorado 80306-1258 [email protected] Abstract Two complementary and equally important approaches to relativistic physics are explained. One is the standard approach, and the other is based on a study of the flows of an underlying physical substratum. Previous results concerning the substratum flow approach are reviewed, expanded, and more closely related to the formalism of General Relativity. An absolute relativistic dynamics is derived in which energy and momentum take on absolute significance with respect to the substratum. Possible new effects on satellites are described. 1. Introduction There are two fundamentally different ways to approach relativistic physics. The first approach, which was Einstein's way [1], and which is the standard way it has been practiced in modern times, recognizes the measurement reality of the impossibility of detecting the absolute translational motion of physical systems through the underlying physical substratum and the measurement reality of the limitations imposed by the finite speed of light with respect to clock synchronization procedures. The second approach, which was Lorentz's way [2] (at least for Special Relativity), recognizes the conceptual superiority of retaining the physical substratum as an important element of the physical theory and of using conceptually useful frames of reference for the understanding of underlying physical principles. Whether one does relativistic physics the Einsteinian way or the Lorentzian way really depends on one's motives. The Einsteinian approach is primarily concerned with * http://xxx.lanl.gov/ftp/gr-qc/papers/0006/0006029.pdf 2 being able to carry out practical space-time experiments and to relate the results of these experiments among variously moving observers in as efficient and uncomplicated manner as possible.