Kinematics of Rotational Motion

Kinematics of Rotational Motion tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất cả các lĩnh...

[...]... become one of the leaders in stop-motion animation 7 8 The Advanced Art of Stop-Motion Animation Another stop-motion feature made in the 1940s that barely had a screen release was a Belgian puppet version of The Crab with the Golden Claws, based on a comic book of the same name, featuring a young reporter named Tintin and produced by Wilfried Bouchery The film faithfully follows the story of Tintin’s... happened In 2006, I wrote my first book, The Art of StopMotion Animation (Figure I.1), as a practical guide for how stop-motion films were made xvii xviii The Advanced Art of Stop-Motion Animation Figure I.1 The Art of Stop-Motion Animation (2006) by Ken A Priebe At that time, we were just starting to see the advent of digital SLR cameras and their use for stop-motion photography, both in feature films... The Tale of the Fox was indeed the first fully animated puppet feature to be produced, and technically the first to be released as well, although it was delayed by several years because of technical problems with the soundtrack Although the animation was complete by 1930, it would not 6 The Advanced Art of Stop-Motion Animation Figure 1.2 The Lion King and Reynard the Fox from The Tale of the Fox (©... which represent the growth of stop-motion education and the online stop-motion community, celebrating the work of several artists who share their work through their websites and production blogs CD-ROM Downloads If you purchased an ebook version of this book, and the book had a companion CD-ROM, we will mail you a copy of the disc Please send ptrsupplements@cengage.com the title of the book, the ISBN, your... fan of stop-motion or any other kind of animation, I trust you will find plenty of good reading material in this book However, because it’s an advanced volume, if you are new to learning animation and want a book for guidance on how stop-motion is done, I would recommend my first book The basic principles covered in The Art of Stop-Motion Animation are important to grasp before moving on to the more advanced. .. getting them from one feature of entertainment to another The short format for stop-motion is a double-edged sword in the opportunity it has lavished on the medium For the most well-executed stop-motion sequences, such as Harryhausen’s 5-minute skeleton fight in 1963’s Jason and the Argonauts, the shorter format provided a solid frame to place as much quality as 1 2 The Advanced Art of Stop-Motion Animation. .. advanced the art form into new territories of Kinematics of Rotational Motion Kinematics of Rotational Motion Bởi: OpenStaxCollege Just by using our intuition, we can begin to see how rotational quantities like θ, ω, and α are related to one another For example, if a motorcycle wheel has a large angular acceleration for a fairly long time, it ends up spinning rapidly and rotates through many revolutions In more technical terms, if the wheel’s angular acceleration α is large for a long period of time t, then the final angular velocity ω and angle of rotation θ are large The wheel’s rotational motion is exactly analogous to the fact that the motorcycle’s large translational acceleration produces a large final velocity, and the distance traveled will also be large Kinematics is the description of motion The kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time Let us start by finding an equation relating ω, α, and t To determine this equation, we recall a familiar kinematic equation for translational, or straight-line, motion: v = v0 + at (constant a) Note that in rotational motion a = at, and we shall use the symbol a for tangential or linear acceleration from now on As in linear kinematics, we assume a is constant, which means that angular acceleration α is also a constant, because a = rα Now, let us substitute v = rω and a = rα into the linear equation above: rω = rω0 + rαt The radius r cancels in the equation, yielding ω = ω0 + at (constant a), where ω0 is the initial angular velocity This last equation is a kinematic relationship among ω, α, and t —that is, it describes their relationship without reference to forces or masses that may affect rotation It is also precisely analogous in form to its translational counterpart 1/10 Kinematics of Rotational Motion Making Connections Kinematics for rotational motion is completely analogous to translational kinematics, first presented in One-Dimensional Kinematics Kinematics is concerned with the description of motion without regard to force or mass We will find that translational kinematic quantities, such as displacement, velocity, and acceleration have direct analogs in rotational motion Starting with the four kinematic equations we developed in One-Dimensional Kinematics, we can derive the following four rotational kinematic equations (presented together with their translational counterparts): Rotational Kinematic Equations Rotational Translational ¯ θ = ωt − x= vt ω = ω0 + αt v = v0 + at (constant α, a) 1 θ = ω0t + αt2 x = v0t + at2 (constant α, a) 2 ω2 = ω02 + 2αθ v2 = v02 + 2ax (constant α, a) In these equations, the subscript denotes initial values (θ0, x0, and t0 are initial values), − − and the average angular velocity ω and average velocity v are defined as follows: ¯ ω= ω0 + ω ¯ and v = v0 + v The equations given above in [link] can be used to solve any rotational or translational kinematics problem in which a and α are constant Problem-Solving Strategy for Rotational Kinematics Examine the situation to determine that rotational kinematics (rotational motion) is involved Rotation must be involved, but without the need to consider forces or masses that affect the motion Identify exactly what needs to be determined in the problem (identify the unknowns) A sketch of the situation is useful Make a list of what is given or can be inferred from the problem as stated (identify the knowns) Solve the appropriate equation or equations for the quantity to be determined (the unknown) It can be useful to think in terms of a translational analog because by now you are familiar with such motion 2/10 Kinematics of Rotational Motion Substitute the known values along with their units into the appropriate equation, and obtain numerical solutions complete with units Be sure to use units of radians for angles Check your answer to see if it is reasonable: Does your answer make sense? Calculating the Acceleration of a Fishing Reel A deep-sea fisherman hooks a big fish that swims away from the boat pulling the fishing line from his fishing reel The whole system is initially at rest and the fishing line unwinds from the reel at a radius of 4.50 cm from its axis of rotation The reel is given an angular acceleration of 110 rad/s2 for 2.00 s as seen in [link] (a) What is the final angular velocity of the reel? (b) At what speed is fishing line leaving the reel after 2.00 s elapses? (c) How many revolutions does the reel make? (d) How many meters of fishing line come off the reel in this time? Strategy In each part of this example, the strategy is the same as it was for solving problems in linear kinematics In particular, known values are identified and a relationship is then sought that can be used to solve for the unknown Solution for (a) Here α and t are given and ω needs to be determined The most straightforward equation to use is ω = ω0 + αt because the unknown is already on one side and all other terms are known That equation states that ω = ...Regional Studies, Vol. 36.9, pp. 957–975, 2002 A New Map of Hollywood: The Production and Distribution of American Motion Pictures ALLEN J. SCOTT Center for Globalization and Policy Research, School of Public Policy and Social Research, UCLA, Los Angeles, CA 90095, USA. Email: ajscott@ucla.edu (Received September 2001; in revised form December 2001) S COTT A. J. (2002) A new map of Hollywood: the production and distribution of American motion pictures, Reg. Studies 36, 957–975. In this paper, I offer a reinterpretation of the economic geography of the so-called new Hollywood. The argument proceeds in six main stages. First, I briefly examine the debate on industrial organization in Hollywood that has gone on in the literature since the mid-1980s, and I conclude that the debate has become unnecessarily polarized. Second, I attempt to show how an approach that invokes both flexible specialization and systems-house forms of production is necessary to any reasonably complete analysis of the organization of production in the new Hollywood. Third, and on this basis, I argue that the Hollywood production system is deeply bifurcated into two segments comprising: (1) the majors and their cohorts of allied firms on the one hand; and (2) the mass of independent production companies on the other. Fourth, I reaffirm the continuing tremendous agglomerative attraction of Hollywood as a locale for motion-picture production, but I also describe in analytical and empirical terms how selected kinds of activities seek out satellite production locations in other parts of the world. Fifth, I show how the majors continue to extend their global reach by means of their ever more aggressive marketing and distribution divisions, and I discuss how this state of affairs depends on and amplifies the competitive advantages of Hollywood. Sixth and finally, I reflect upon some of the challenges that Hollywood must face up to as new cultural-products agglomerations arise all over the globe, offering potential challenges to its hegemony. Motion-picture industry Cultural economy Hollywood Agglomeration Regional development Globalization S COTT A. J. (2002) Une nouvelle carte de Hollywood: la SCOTT A. J. (2002) Eine neue Hollywoodkarte: Herstellung production et la distribution des films ame ´ ricains, Reg. Studies und Verteilung amerikanischer Spielfilme, Reg. Studies 36, 36, 957–975. Cet article cherche a ` remettre en question la 957–975. Dieser Aufsatz stellt eine Neuinterpretation der ge ´ ographie e ´ conomique du soi-disant nouvel Hollywood. Le Wirtschaftsgeographie des sogenannten neuen Hollywood raisonnement se de ´ roule en six e ´ tapes. Premie ` rement, on vor. Zuerst wird die Debatte um die industrielle Organi- examine le de ´ bat sur l’organisation industrielle a ` Hollywood sation, die die Literatur seit Mitte der achtziger Jahre bescha ¨ f- qui a eu lieu dans la lite ´ rature depuis le milieu des anne ´ es tigt, kurz untersucht, mit der Schlußfolgerung, daß sie 80, et on affirme que le de ´ bat s’est polarise ´ inutilement. unno ¨ tig polarisiert worden ist. Danach wird versucht, zu Deuxie ` mement, on essaie de de ´ montrer comment une zeigen, inwiefern eine einigermaßen vollsta ¨ ndige Analyse approche qui invoque a ` la fois la spe ´ cialisation flexible et des der Produktionsorganisation im neuen Hollywood eine Ein- formes de production dites ‘system houses’ est necessaire a ` stellung verlangt, die sowohl an flexible !" # $ ! " # $ % ' # & & % ! ( * !& + - " ( ( ! % & # + & % * " ( ) ( $ " ) * # - . $ / $ + % & + , ! & # * $ $ ! " ! # $ ! ! ! ! ! !! ! !) # % # ' !! & !'# ( * + , !! + !! !'# !! , + + !! ! !! ) !! & - ! + ! + ! ! !!! !) ! . + ) - / !/ " 0 !/ " 0 !/! ( !/! ( !/!! !/!) + % 12 % 3 * !, * !/!/ 4'+ 5 ! !0 !! !/ ) !/ ) $ !0 ) ! 6 ' ) ! - ) !! # ) !) $ - !& 5 + 5 !& + 5 $ !* 47$ ) )! )) " )& / )& / )& / ! # / ) 4 )* # /! /! " /! /0 " + /! 8 /! ! /! ) '$ 2 2 " / 0 4 0! 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University of Technical Education, Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City Abstract The analytic expression of molar heat capacity under constant volume of molecular cryocrystals of nitrogen type with hcp structure is obtained by the statistical moment method and the self-consistent field method taking account of the anharmonicity in lattice vibrations and molecular rotational motion Numerical results for molecular cryocrystals of N2 type (β-N2 ,β-CO) are compared with experiments I INTRODUCTION The study of heat capacity for molecular cryocrystals of nitrogen type is carried out experimentally and theoretically by many researchers For example, the heat capacity of solid nitrogen is measured by Giauque and Clayton [1], Bagatskii, Kucheryavy, Manzhelii and Popov [2] The heat capacity of solid carbon monoxide is determined by Clayton and Giauque [3], Gill and Morrison [4] Theoretically, the heat capacity of solid nitrogen and carbon monoxide is investigated by the Debye heat capacity theory, the Einstein heat capacity theory, the self-consistent phonon method (SCPM), the self-consistent field method (SCFM), the pseudo-harmonic theory and the statistical moment method (SMM) [5, 6, 7] In [5, 6] the heat capacities at constant volume and at constant pressure of β−N2 and β−CO crystals are calculated by SMM only taking account of lattice vibration and the obtained results only agreed qualitatively with experiments The heat capacity at constant volume of crystals of N2 type in pseudo-harmonic approximation is considered by SCFM only taking account of molecular rotations [8] In this report we study the heat capacity at constant volume of α−N2 and α−CO crystals in pseudo-harmonic approximation by combining SMM and SCFM taking account of both lattice vibrations and molecular rotations In section 2, we derive the heat capacity at constant volume for crystals with hcp structure taking into account lattice vibrations by SMM and for crystals of N2 type taking into account molecular rotations by SCFM Our calculated vibrational and rotational heat capacities for β−N2 and β−CO crystals are summarized and discussed in section 181 II THEORY 2.1 The heat capacity at constant volume of crystals with hcp structure by SMM The displacement of a particle from equilibrium position on direction x (or direction y) is given approximately [6] by: ux0 ≈ i=1 γθ (kx + kxy )2 where: 2kx − kxy kxy 3γ a1 = (1 − X) − X, a2 = a1 X + kx kx kx + kxy a4 = − i , , a3 = 3kx + 2kxy 18γ a21 2X − kx (kx + kxy ) kx + kxy 108γ ∂ ϕi0 a (X − 1) , X ≡ x coth x, θ = k T, k ≡ x B ∂u2ix kx (kx + kxy )2 i  ∂ ϕi0 ∂ ϕi0  ∂ ϕi0 kxy ≡ + ,γ ≡ ∂uix ∂uiy eq ∂u3ix eq ∂uix ∂u2iy i i ≡ mωx2 , x = eq ωx , 2θ  , (1) eq Here kB is the Boltzmann constant, T is the absolute temperature, m is the mass of particle at lattice node, ωx is the frequency of lattice vibration on direction x (or y), kx , kxy and γ are the parameters of crystal depending on the structure of crystal lattice and the interaction potential between particles at nodes, ϕi0 is the interaction potential between the ith particle and the 0th particle and uiα is the displacement of ith particle from equilibrium position on direction α(α = x, y, z) The lattice constant on direction x (or y) is determined by a = a0 + ux0 ,where a0 is the distance a at temperature 0K and is determined from experiments The displacement of a particle from equilibrium position on direction z approximately is as follows [6]: uz0 ≈ i=1 θ kz 1/2 i bi , where : τ1 τ1 τ2 +τ3 2 kz ux0 , b2 = kz Proc Natl Conf Theor Phys 37 (2012), pp 150-156 THERMODYNAMIC PROPERTIES OF MOLECULAR CRYOCRYSTALS OF NITROGEN TYPE WITH FCC STRUCTURE: CONTRIBUTION FROM LATTICE VIBRATIONS AND MOLECULAR ROTATIONAL MOTION NGUYEN QUANG HOC Hanoi National University of Education, 136 Xuan Thuy Street, Cau Giay District, Hanoi NGUYEN NGOC ANH, NGUYEN THE HUNG, NGUYEN DUC HIEN Tay Nguyen University, 456 Le Duan Street, Buon Me Thuot City NGUYEN DUC QUYEN University of Technical Education, Vo Van Ngan Street, Thu Duc District, Ho Chi Minh City Abstract The analytic expressions of thermodynamic quantities such as the Helmholtz free energy, the internal energy, the entropy, the molar specific heats under constant volume and under constant pressure, etc of molecular cryocrystals of N2 type with fcc structure are obtained by the statistical moment method and the self-consistent field method taking account of the anharmonicity in lattice vibrations and molecular rotational motion Numerical results for molecular cryocrystals of N2 type ( α − N2 , α − CO) are compared with the experimental data I INTRODUCTION Molecular crystals, comprising a vast and comparatively scarcely investigated class of solids, are characterized by a diversity of properties Up to now only solidified noble gases have systematically been investigated and this is due to the availability of the relevant theoretical models and to the ease of comparing theories with experimental results Recently experimental data have been obtained for simple non-monoatomic molecular crystals as well, which in turn has stimulated the appearance of several theoretical papers on that subject This paper deals with the analysis of thermodynamic properties of the group of non-monoatomic molecular crystals including solid N2 and CO that have similar physical properties These crystals are formed by linear molecules and in their ordered phase, the molecular centres of mass are situated at the site of fcc pattern, the molecular axes being directed the four spatial diagonals of a cube (space group P a3) The characteristic feature of the intermolecular interaction in such crystals is that the non-central part of the potential results from quadrupole forces and from the part of valency and dispersion forces having the analogous angular dependence as quadrupole forces, and further, that dipole interaction either does not exist (N2 ) or is negligible (CO) to influence the majority of thermodynamic properties In addition, all crystals considered have a common feature, namely their intrinsic rotational temperatures B = /2I (I is the momentum of inertia 151 of the corresponding molecule) are small compared to the energy of non-central interaction In the low-temperature range, it is reasonable to apply an assumption successfully used by the authors [1, 2] that translational motions of the molecular system are independent As shown [3] there are two types of excitations in molecular crystals phonons and librons and furthermore, the thermodynamic functions can be written as a sum of two independent terms corresponding to each subsystem In such a treatment, the translational orientational interaction leads to a renormalization of the sound velocity and of the libron dispersion law only The investigation of the librational behavior of molecules is usually carried out within the framework of the harmonic approximation However, anharmonic effects for the thermodynamic properties are essential at temperatures substantially lower than the orientational disordering temperature The effect of molecular rations in N2 and CO crystals not restricted by the assumption of harmonicity of oscillations has been calculated numerically in the molecular field approximation by Kohin [4] Full calculations on thermodynamic properties of molecular crystals of type N2 are given by the statistical moment method (SMM) in [5, 6] and by self-consistent field method (SCFM) in [9] In [7], the low temperature heat capacity at constant volume of the .. .Kinematics of Rotational Motion Making Connections Kinematics for rotational motion is completely analogous to translational kinematics, first presented in One-Dimensional Kinematics Kinematics... in angular velocity without any consideration of its cause Section Summary • Kinematics is the description of motion • The kinematics of rotational motion describes the relationships among rotation... linear kinematics. ) Rotational kinematics (just like linear kinematics) is descriptive and does not represent laws of nature With kinematics, we can describe many things to great precision but kinematics