...Carlos L. Castillo, Ph.D. Spring T (t ) θ (t ) Time domain T (t ) = Kθ (t ) Frequency domain K K: spring constant T (s) = K θ (s) Impedance T (s) Z M= = K (s) θ (s) Viscous damper T (t ) θ (t ) Time domain dθ (t ) T (t ) = D dt Frequency domain D D: coefficient of Viscous friction T (s) = D s θ (s) T (s) Z M= = D s (s) θ (s) Impedance Inertia T(t) θ (t ) Time domain d 2θ (t ) T (t ) = J dt 2 J J: moment of inertia Frequency domain T ( s) = Js 2 θ ( s ) T (s) Z M= = J s 2 (s) θ (s) Impedance 1. First, we rotate a body while holding all other points still and place on its free-body diagram all torques due to the body’s own motion Then, holding the body still, we rotate adjacent points of motion one at the time and add the torques due to the adjacent motion to the free-body diagram. 2. ( J1s 2 + D1s + K )θ1 ( s ) − Kθ 2 ( s ) =) T (s − Kθ1 ( s ) + ( J 2 s 2 + D2 s + K )θ 2 ( s ) = 0 ( J1s 2 + D1s + K )θ1 ( s ) 2 − Kθ 2 ( s ) =) T (s − Kθ1 ( s ) + ( J 2 s + D2 s + K )θ 2 ( s ) = 0 Sum of impedances connected to the θ (s) − Sum of impedances θ (s) − Sum of applied between θ andθ 2 torques at θ 1 1 2 1 motion at θ1 Sum of impedances Sum of impedances Sum of applied θ1 ( s ) + connected to the θ 2 ( s) = − torques at θ between θ1and θ 2 2 motion at θ 2 ( s + s + 1)θ1 ( s ) − ( s + 1)θ 2 ( s ) = (...
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...the angular velocity of the flywheel ((s) and the precession of the gyroscope system((p). • Using Ws and (p above to calculate Izz (mass moment of inertia of the gyroscope) • Compare this experimental Izz to the theoretical Izz. A gyroscope is a mechanism consisting of a spinning flywheel, mounted on a base so that its axis can turn freely in any direction. The gyroscopic motion occurs whenever the axis about which the body is spinning is itself rotation about another axis. Gyroscope has a wide application in our daily life. The bicycle, for instance, is a good example of gyroscopic motion. The spinning wheel on bicycle act as a gyroscope, when we attempt to rotate the wheel about its axis, due to the procession of a gyroscope, the wheel will attempt to rotate about an axis perpendicular to the wheel axis. This procession keeps the wheel rotating either left or right so that the bicycle can stay upright. A gyrocompass is another example of the application of a gyroscope. The rotation of our earth about its axis gives it the properties of a huge gyroscope. The gyrocompass combines the action of the gyro rotor inside and the earth’s rotation to perform as a direction reference. II. Method 1) Apparatus used: • Gyroscope system(including a flywheel) • Electrical motor • Stroboscope • Stopwatch • Measuring ruler, pencil 2) Measuring angular velocity of the flywheel((s) • Rev up angular velocity...
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...BIOMECHANICS The term biomechanics means the study of the structure and function of biological systems using the methods of mechanics. Biomechanics studies the process of kinematics and used in the study of sports actions, such as the motion of throwing a baseball. Why do some golfers slice the ball? How can workers avoid developing low back pain? What cues can a physical education teacher provide to help students learn the underhand volleyball serve? Why do some elderly individuals tend to fall? We have all admired the fluid, graceful movements of highly skilled performers in various sports. We have also observed the awkward first steps of a young child, the slow progress of an injured person with a walking cast, and the hesitant, uneven gait of an elderly person using a cane. Virtually every activity class includes a student who seems to acquire new skills with utmost ease and a student who trips when executing a jump or misses the ball when attempting to catch, strike, or serve. What enables some individuals to execute complex movements so easily, while others appear to have difficulty with relatively simple movement skills? Although the answers to these questions may be rooted in physiological, psychological, or sociological issues, the problems identified are all biomechanical in nature. This book will provide a foundation for identifying, analyzing, and solving problems related to the biomechanics of human movement. Definition of Biomechanics The term biomechanics combines...
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...Optical Pumping Lab Report [Basic Principle] Before discussing the optical pumping, we have to mention the energy levels of the atom and their splitting due to the interaction between the spin of electron, orbital angular momentum of electron and spin of nuclei. We denote them with S, L, and I respectively. And the total angular momentum of electron is denoted by J, (Grand) total angular momentum is denoted by F. Therefore we will have to deal with the LS interaction, IJ interaction and later the interaction between the Grand total angular momentum and external magnetic field. A very schematic picture of the energy levels of 87Rb under a weak external field is shown in Fig. 1. After applying an weak external magnetic field on the atom, the formally degenerated energy level with same F will further split into 2F+1 sublevels, denoted by mF which is the projection of Grand total angular momentum to the direction of external field B0. Fig. 1 Until now we haven't mention any thing about the optical pumping. Now we have the atom well prepared, the only thing we have to do is to illuminate the vapor of Rubidium with some well tuned highly polarized light. Well tuned means the spectrum of the incident light is better to be narrow, this can be achieved by using a interference filter to screen out the unwanted light and let only the D1 line pass, namely when this light illuminated on the Rb vapor, only transitions between sublevels originated from 5S1/2 and sublevels originated...
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...ME 3456 Technical memorandum Report to: | TA | from: | HN, 3.36 | subject: | Vibration due to rotational Unbalance | date: | 3/27/2014 | Date Submitted: | 4/20/2014 | | | Introduction This experiment was conducted in order to study the relationship between rotational unbalance and , the basic attributes of a rotational system. This involves determining equivalent rotational quantities such as deflection, natural frequency, stiffness, moment of inertia, equivalent damping constant, logarithmic decrement and other attributes of this rotational system to determine the effect of rotational unbalance on a larger mass system. The experiment involved use of a bar fixed at one end, with suspension by a spring in the vicinity of the opposite end, as well as a dashpot to remove energy from the system. The aim of the investigation is to determine the relationship between the voltage, frequency, and amplitude in relation to the natural and damped frequencies: especially in terms of approaching and leaving the resonance. Equipment Description Equipment used included: I. Vibrating beam apparatus (in diagram, A-D) II. Power supply (2) III. Motor with power supply (C, G) IV. Contact tachometer (to measure rpm) V. LVDT (linear variable differential transformer) with voltage source from power supply (F, I) VI. Oscilloscope (H) VII. Fixed Mass of 500g (E) The LVDT measured the motion of the beam end with a range of ±2 inches. The voltage source...
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...It is not a strange realization to see that walking foot over foot on a tightrope takes balance in any scenario. The ability to walk on a tightrope however does revolve physics and its properties. Angular rotation, (w=L/I), angular momentum, (L=IW), and moment of inertia,(I=mr^2), are three major physical categories and characteristics that play a part in a tightrope walker’s ability to stay on the rope and not fall to his potential demise. But how does a tightrope walker increase his chances of staying on the rope? Often times one can see a tightrope walker carrying a large pole, a pole with heavy weights on the end, bending his knees, or extending their hands outward. All of these actions help to increase the ropewalker’s chances of success. Picture the rope as the axis. When a tightrope walker embarks on his journey, he must stay constantly positioned over that axis to maintain balance. Carrying a pole horizontally helps to distribute the ropewalker’s mass laterally in a direction away from the axis, or rope. Having a pole in hand helps to increase stability because the ends of the pole are constantly being acted upon by a variety of forces that are trying to change their position in the air with every step. The heavier the pole the more force will be needed to alter the poles position and begin rotation around the rope. Heavy weights can sometimes be placed on the end of the pole increasing stability. More force will be needed to move the heavier pole. The weights essentially...
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...Digital y analógico son, básicamente, los dos métodos utilizados hoy en dia, para el procesamiento electrónico de información. A su vez, por información entendemos todo aquello que tiene significado para nosotros, desde la palabra hasta la música. Hay que tener en cuenta que la información no existe sino en el cambio. El sonido, por ejemplo, no es más que la vibración del aire (o cualquier otro fluido). Una fotografía es también la variación de algo, en este caso de tonalidades a lo largo y ancho de una superficie; una hoja de papel en blanco, por el contrario, no contiene información alguna. Sabiendo esto, es fácil entender que procesar información por medios electrónicos no consiste sino en provocar variaciones dentro de esos medios, que de alguna manera se correspondan con las variaciones originales de aquel medio que contenía la información en su forma primaria. La manera más sencilla de representar la información electrónicamente consiste en hacer variar alguna magnitud eléctrica, como el voltage, en proporción exacta a las variaciones del medio original. Un ejemplo claro de esto es el micrófono. Un micrófono típico tiene una membrana delgada que está acomplada a un fino alambre de cobre enrollado en torno a un a un imán (ver figura). Cuando el micrófono se expone a las ondas sonoras, estas hacen vibrar a la membrana, con lo cual el enrollado de cobre también vibra respecto al imán. Este movimiento relativo del enrollado respeto al imán, induce una corriente eléctrica...
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...SRI SHANMUGHA COLLEGE OF ENGINEERING AND TECHNOLOGY Pullipalayam,Morur(P.O),Sankari(T.k),Salem(D.T). Two Mark Questions Unit I – Basics 1. What is meant by mechanics? Mechanics is a branch of physical science which deals with the study of a body or bodies such as machines and structures at rest or in motion subjected to external mechanical disturbances such as forces, moments etc. What is meant by Engineering mechanics? Application of the principles of science of mechanics to the practical engineering problems is known as Engineering Mechanics. State the different types of mechanics? Depending upon the nature of the body involved, Mechanics can be classified into two types * Mechanics of Solids * Mechanics of Fluids Define Statics The study of a body which is in motion is known as statics Define Dynamics. The study of a body which is in motion is known as dynamics. Define Kinematics. It is the branch of dynamics which deals with the relationship between displacement, velocity, acceleration and time of a given motion, without considering the forces that cause the motion. Define Kinetics It is the branch of dynamics which deals with the relationship between the forces acting on a body, the mass of the body and the motion of the body. What do you understand from the concept of “Law of dimensional homogeneity”? Law of dimensional homogeneity states that “basic equation representing physical phenomenon must be valid for all systems of units”. State Parallelogram law. It states that...
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...many body parts as possible, so force can be applies over the maximal possible time. The pitcher can increase number of segments by getting side on, whilst also uncocking wrist prior to throw. 5. Follow through is important to prevent deceleration of last segment and safe dissipation of force. This can be seen in the transition from diagram 3 to 4. 6. Ensure all forces are directed towards the batter (the target) b) Spin (6 marks) 1. As the pitcher is throwing a curveball, the type of spin is sidespin. 2. Diagram 3. At the commencement of the throw, an eccentric force is applied to the ball to cause the object to spin. This is an off centre force applied to produce angular motion. 4. Bernoulli’s principle states that velocity is inversely proportional to pressure. 5....
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...DNK201E-Dynamics Instructor: Dr. G.Tansel TAYYAR E-mail Address: tayyargo@itu.edu.tr (use DNK201 title) Text Book: Engineering Mechanics Dynamics (12th Ed.) by R.C.Hibbeler, Prentice Hall Or any other Course Description: This is a 3 credit intermediate level course in dynamics that employs various problem solving methods and the laws of mechanics to analyze and obtain solutions to fundamental problems in engineering and physics. A course in kinematics and kinetics of particles and rigid bodies with applications of Newton's second law and the principles of work-energy and impulse momentum. Course Objectives: * Learn the fundamental concepts of engineering Dynamics. * Learn a sound methodology to solve engineering problems that is applicable to all future courses and work. * Develop in the engineering student the ability to analyze any problem in a simple and logical manner. * Analyze the dynamics of particles and rigid bodies with applications * Appreciate that the governing equations in Dynamics are differential equations. Course Outcomes: * Establish coordinates, sign conventions, variables, and parameters that quantify physical conditions or states. * Draw clear and rigorous Free Body Diagrams that accurately describe physical systems, maintaining consistency with assumptions and quantifiers. * Write equations (in vector form) that govern the behavior physical systems, and check that the equations are well-posed...
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...some basic concepts of rotational dynamics. A fairly realistic analysis of the motion of a flywheel can be made, assuming only that the net frictional torque on a rotating flywheel is constant. In performing this experiment, you will develop understanding of: ! rotational dynamics; ! evaluation of errors in measurements that may be difficult to obtain; ! estimation of a geometrically calculated quantity using simplified models. THEORY The basic equations for angular motion can often be obtained simply from those for linear motion by making the following substitutions: Linear variables Force, F Mass, m Velocity, v Momentum, p Acceleration, a Angular variables Torque, Moment of Inertia, I Angular velocity, Angular Momentum, L Angular acceleration, N.B. The analogy needs to be treated with caution. I is not a constant property of the body, as is mass, since its value depends on the axis around which it is measured. Thus Newton=s Law, F = d p d (m v ) = = m a , becomes: dt dt = dL d (I ) = =I dt dt . In words, the angular acceleration of a body is directly proportional to the torque applied to it and inversely proportional to the moment of inertia of the body about the relevant axis. THE FLYWHEEL -18The moment of inertia, I, is determined by imagining that the body is divided into a number of infinitesimal elements of mass mi each at a distance ri from the axis of rotation. The moment of inertia I about this axis is given by the sum of all the products ( mi ri2 ) calculated...
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...Alpha School of Academic Propensity Engineering Science Angular Motion Call 0977 127 054 or 0968226870 or 0950868535 Email: - ddk2012@gmail.com Box 71528.Ndola 1.0 Definition: Motion will ever be motion except the point to be established is, what is being covered during that motion, in case of linear motion which we are all familiar with at this time what is being covered is distance (in meters or kilometers) whilst in angular motion what is being covered are angles (in degrees, radians or revolutions) hence the name angular motion. This is motion in which an angle (θ in radians) is swept through a time (t in seconds) see fig 1. As a particle moves from point P to point Q it covers a distance s and as it sweeps an angle θ, through a time t seconds. 2.0 Units The radian is defined as the angle subtended by an arc whose length is equal to the radius of the circle. Q sr 1r O r P 3. Relationship between the degree and the radian Taking ratios of similar shapes, Arc length PQ ( s r ) Angle POQ Circumference of circle Total angle in acircle r 1 radian i.e. 2r 360o 2 radians 360o Half revolution is radians 180o and 90o 2 1 radian 57.2958o 57.3o one right angle is 4.0 Arc length: Let s be the arc length subtending an angle θ radians at the centre of a circle Then arc length s radians Circumference Totalangle in a circle i.e. s 2r radians 2 radians {s s r ( in radians) 360 o 2r...
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...Chapter 5. A physical quantity that is completely speci®ed, in appropriate units, by a single number (called its magnitude) such as volume, mass, and temperature is called a scalar. Scalar quantities are treated as ordinary real numbers. They obey all the regular rules of algebraic addition, subtraction, multiplication, division, and so on. There are also physical quantities which require a magnitude and a direction for their complete speci®cation. These are called vectors if their combination with each other is commutative (that is the order of addition may be changed without aecting the result). Thus not all quantities possessing magnitude and direction are vectors. Angular displacement, for example, may be characterised by magnitude and direction but is not a vector, for the addition of two or more angular displacements is not, in general, commutative (Fig. 1.1). In print, we shall denote vectors by boldface letters (such as A) and use ordinary italic letters (such as A) for their magnitudes; in writing, vectors are usually ~ ~ represented by a letter with an arrow above it such as A. A given vector A (or A) can be written as ^ A AA; 1:1 ^ where A is the magnitude of vector A and so it has unit and dimension, and A is a dimensionless unit vector with a unity magnitude having the direction of A. Thus ^ A A=A. 1 © Cambridge University Press www.cambridge.org Cambridge...
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...Introductory Physics I Elementary Mechanics by Robert G. Brown Duke University Physics Department Durham, NC 27708-0305 rgb@phy.duke.edu Copyright Notice Copyright Robert G. Brown 1993, 2007, 2013 Notice This physics textbook is designed to support my personal teaching activities at Duke University, in particular teaching its Physics 141/142, 151/152, or 161/162 series (Introductory Physics for life science majors, engineers, or potential physics majors, respectively). It is freely available in its entirety in a downloadable PDF form or to be read online at: http://www.phy.duke.edu/∼rgb/Class/intro physics 1.php It is also available in an inexpensive (really!) print version via Lulu press here: http://www.lulu.com/shop/product-21186588.html where readers/users can voluntarily help support or reward the author by purchasing either this paper copy or one of the even more inexpensive electronic copies. By making the book available in these various media at a cost ranging from free to cheap, I enable the text can be used by students all over the world where each student can pay (or not) according to their means. Nevertheless, I am hoping that students who truly find this work useful will purchase a copy through Lulu or a bookseller (when the latter option becomes available), if only to help subsidize me while I continue to write inexpensive textbooks in physics or other subjects. This textbook is organized for ease of presentation and ease of learning. In particular, they are...
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...! ! ! ! ! ! ! ! ! A Boxer’s Punch A Senior Project presented to the Faculty of the Physics Department California Polytechnic State University, San Luis Obispo ! ! ! In Partial Fulfillment of the Requirements for the Degree Bachelor of Science, Physics ! ! by ! ! ! Jacob A. Ekegren ! April 2014 ! ! Advised by Dr. Matthew Moelter ! © 2014 Jacob A. Ekegren ! ! Table of Contents ! Pg. # Introduction and Setup 3 Theory Applied 4 Experimental Procedure 5 Results and Analysis 5 Conclusion! 10 References 11 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! 2 Introduction and Setup For over a year now, I have been interested in the sport of boxing. This fascination led me to explore what occurs to a human head upon impact from a boxer’s punch. It is known that a knockout occurs when blood circulation to the brain is compressed. This compression results from the sudden acceleration and deceleration of the head[1]. Therefore, the primary focus of this experiment explores the relative effort necessary to cause significant movement to a head about a neck. Figure 1 - Picture of modeled head and spine secured to a table ! To achieve this, a simplistic mechanical model of a human head, a socket, and a spine was built. A volleyball was used to simulate a head. A garage door spring with a diameter of 4.0 ± .05cm was used as a spine. Lastly, a small wooden...
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