...(2006). Serway’s College Physics. Thomson Brooks/Cole Course Requirements ● Attendance + Discussion + Homework: 15% ● Assignment: 15% ● Mid-term exam: 30% ● Final: 40% Preparation for each class ● Read text ahead of time ● Finish homework Chapter 1 Bases of Kinematics Chapter 2 Force and Motion (Newton’s Laws) Chapter 3 Work and Mechanical Energy Midterm exam after Lecture 6 Chapter 4 Linear Momentum and Collisions Part A Dynamics of Mass Point Part B Laws of Conservation Chapter 5 Rotation of a Rigid Body About a Fixed Axis Assignment given in Lecture 11 Chapter 6 Equilibrium and Elasticity Chapter 7 Gravitation Final exam after Lecture 12 Part C Dynamics and Statics of Rigid Body Chapter 1 Bases of Kinematics 1. 1. Motion in One Dimension Part A Dynamics of Mass Point 1.1.1. Position, Velocity, and Acceleration 1.1.2. One-Dimensional Motion with Constant Acceleration 1.1.3. Freely Falling Objects 1. 2. Motion in Two Dimensions 1.2.1. The Position, Velocity, and Acceleration Vectors 1.2.2. Two-Dimensional Motion with Constant Acceleration. Projectile Motion 1.2.3. Circular Motion. Tangential and Radial Acceleration 1.2.4. Relative Velocity and Relative Acceleration Measurements ● Use laws of Physics to describe our understanding of nature ● Test laws by experiments ● Need Units to measure...
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...Lecture 3 Kinematics Copyright © 2010 Pearson Education, Inc. Units of Lecture 3 Position, Distance, and Displacement, Average Speed and Velocity, Acceleration Motion with Constant Acceleration Freely Falling Objects Motion in Two Dimensions Relative Velocity Copyright © 2010 Pearson Education, Inc. Position, Distance, and Displacement Before describing motion, you must set up a coordinate system – define an origin and a positive direction. Copyright © 2010 Pearson Education, Inc. Position, Distance, and Displacement The distance is the total length of travel; (Example - if you drive from your house to the grocery store and back, you have covered a distance of 8.6 mi). Displacement is the change in position. (Example - If you drive from your house to the grocery store and then to your friend’s house, your displacement is 2.1 mi and the distance you have traveled is 10.7 mi). Copyright © 2010 Pearson Education, Inc. Distance is the length of Displacement is the the actual path taken by an object. straight-line separation of two points in a specified direction. Distance, s is a scalar Displacement, D is a quantity (no direction) Contains magnitude only and consists of a number and a unit. Example: (20 m, 40 mi/h) vector quantity Contains magnitude AND direction, a number, unit & angle. Example: (12 m, 300; 8 km/h) Consider travel from point A to point B in diagram below: Consider travel from point...
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...How to Succeed in Physics (and reduce your workload) Kyle Thomas, Lead Author Luke Bruneaux, Supporting Author Veritas Tutors, LLC How To Succeed in Physics | 2 About the Authors Kyle Thomas Kyle is currently a PhD candidate in the Psychology Department at Harvard University where he studies evolutionary social psychology and serves as a teaching fellow for graduate and undergraduate courses. Kyle has primarily tutored and taught Physics and Organic Chemistry through the UC Santa Cruz peer tutoring program where he became a program administrator. About Veritas Tutors Founded by two Harvard graduates in 2005, Veritas Tutors (www. veritutors.com) is the premiere provider of educational services and products in the Boston area. Offering subject tutoring, standardized test preparation, and admissions consulting, Veritas Tutors is dedicated to providing the best possible instruction to each of its students. Working with educators and consultants from Harvard, Yale, Columbia, MIT, and other elite academic institutions, our students all receive personalized guidance to achieve their goals in and out of the classroom. If you Luke Bruneaux have any questions, comments, or concerns, please contact us at info@ Luke holds a BA Summa Cum Laude from the University of Pennsylvania, veritutors.com or 1-877-265-6582. an MS from the University of Chicago and is working towards a PhD in physics at Harvard University. Luke was awarded a 2011 Derek Bok ...
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...KINEMATICS 1. INTRODUCTION TO KINEMATICS Dynamics is the study of moving objects. The subject is divided into kinematics and kinetics. Kinematics is the study of a body’s motion independent of the forces on the body. It is the study of the geometry of motion without consideration of the causes of motion. Kinematics deals only with relationships among the position, velocity, acceleration, and time. Kinetics deals with both forces and motion. 2. PARTICLES AND RIGID BODIES Bodies in motion can be considered particles if rotation is absent or insignificant. Particles do not possess rotational kinetic energy. All parts of a particle have the same instantaneous displacement, velocity, and acceleration. A rigid body does not deform when loaded and can be considered as a combination of two or more particles that remain at a fixed, finite distance from each other. 3. COORDINATE SYSTEMS The position of a particle is specified with reference to a coordinate system. A coordinate can represent a position along an axis, as in the rectangular coordinate system or it can represent an angle, as in the polar, cylindrical, and spherical coordinate systems. In general, the number of degrees of freedom is equal to the number of coordinates required to completely specify the state of an object. If each of the coordinates is independent of the others, the coordinates are shown as holonomic coordinates. 4. CONVENTIONS OF REPRESENTATION ...
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...sketch and test acceleration vs. time kinematics graphs To review predicting and sketching distance vs. time and velocity vs. time kinematics graphs PROCEDURE: Begin by making charts like the one below for each of the following a-d a. The man walks slowly to the house from the origin. Position –Time Graph The moving man starts at a position of -8 meters and is accelerating at 1 m/s 2. He starts with a velocity of 0 m/s. After 1 second, he will be going 1 m/s (remember acceleration is 1 m/s per s so velocity will change by +1 m/s with each second that elapses). So after 2 seconds, he will be going 2 m/s, etc. If you carry this motion out with moving man, you see it will take him 4 seconds to get to the origin (a position of 0 meters), or equivalently to move +8 meters from where he started. At 4 seconds, he will have a velocity of 4 m/s On the Position-Time graph, the line is a positive consistent rise. This is because his position is going in a positive direction as well as the time is going in a consistent positive direction. Explanation for graph’s appearance –after actually performing the activity. Velocity-Time Graph On the Velocity-Time graph, the line is straight across at 2 m/s because the velocity does not change because of the consistent speed of the man walking to the house. Since the velocity is constant the acceleration is zero. Explanation for graph’s appearance - after actually performing the activity. Acceleration –Time Graph On the Acceleration-Time graph, the...
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...Copyrighted Material Copyrighted Material Copyrighted Material 4-2 CATIA V5 Tutorials in Mechanism Design and Animation Introduction In this tutorial you create a slider crank mechanism using a combination of revolute and cylindrical joints. You will also experiment with additional plotting utilities in CATIA. 1 Problem Statement A slider crank mechanism, sometimes referred to as a three-bar-linkage, can be thought of as a four bar linkage where one of the links is made infinite in length. The piston based internal combustion is based off of this mechanism. The analytical solution to the kinematics of a slider crank can be found in elementary dynamics textbooks. In this tutorial, we aim to simulate the slider crank mechanism shown below for constant crank rotation and to generate plots of some of the results, including position, velocity, and acceleration of the slider. The mechanism is constructed by assembling four parts as described later in the tutorial. In CATIA, the number and type of mechanism joints will be determined by the nature of the assembly constraints applied. There are several valid combinations of joints which would produce a kinematically correct simulation of the slider crank mechanism. The most intuitive combination would be three revolute joints and a prismatic joint. From a degrees of freedom standpoint, using three revolute joints and a prismatic joint redundantly constrains the system, although the redundancy does not create a problem...
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...Acceleration, in physics, is the rate at which the velocity of an object changes over time. An object's acceleration is the net result of any and all forces acting on the object, as described by Newton's Second Law. [1] The SI unit for acceleration is the metre per second squared (m/s2). Accelerations are vector quantities (they have magnitude and direction) and add according to the parallelogram law.[2][3] As a vector, the calculated net force is equal to the product of the object's mass (a scalar quantity) and the acceleration. For example, when a car starts from a standstill (zero relative velocity) and travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the car changes direction there is an acceleration toward the new direction. When accelerating forward, passengers in the car experience a force pushing them back into their seats. They experience sideways forces when changing direction. If the speed of the car decreases, this is acceleration in the opposite direction, sometimes called deceleration.[4]Mathematically, there is no separate formula for deceleration, as both are changes in velocity. In everyday use and in kinematics, the speed of an object is the magnitude of its velocity (the rate of change of its position); it is thus a scalar quantity.[1] The average speed of an object in an interval of time is the distance travelled by the object divided by theduration of the interval;[2] the instantaneous speed is the limit of...
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...A REPORT ON “Newton Euler Strategy for the Dynamic Analysis of 3-DOF Parallel UPU Manipulator” Abstract This projects aims to describe the dynamic analysis of the 3-DOF Parallel UPU manipulator. The 3 DOF UPU is a parallel manipulator in which the U and P notations are for universal and prismatic pairs respectively, is a well-known manipulator that provides the platform with three degrees of freedom of pure translation, pure rotation or mixed translation and rotation with respect to the base, according to the relative directions of the revolute pair axes. The pure translational parallel 3-UPU manipulators have received a great lot of attention. Over the years many studies have been reported in the literature on the kinematic analysis, workspace optimization, singularities and joint clearance influence on the platform accuracy of this manipulator. However, the evaluation of the dynamic modelling of the parallel manipulators based on the two most famous methods i.e. Newton- Euler and Lagrange’s method have not been clearly discussed so far. Therefore, this project tries to throw light on this area and covers the Newton Euler Strategy for the calculation of the dynamic model of the 3 DOF UPU Parallel Manipulator. 1. Introduction Over the last few decades the parallel manipulators have attracted the attention of lot of researchers because of their complementary characteristic with serial manipulator. The word 'Parallel’ which is used here is to point out is not...
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...Experiment #6-FREE FALL FALLING BODIES OBJECTIVES: 1.To describe how the velocity and acceleration of an object change over time when falling under the influence of gravity and to explain why such changes are observed. 2. To determine gravitational acceleration by studying the velocity of a falling object as a function of time. INTRODUCTION: Everything on Earth is under the influence of it’s gravitational field keeping us from jumping of respected measure high.Along with this things that are on Earth,there are objects that are soon to be on Earth’s surface,falling objects have certain interactions with Earth’s gravity.Air resistance is a factor of free-falling objects.Since Earth has an atmosphere,the speed of which objects fall at are not constant. While you are falling, you will probably feel as if you are floating—or not even moving at all. Falling is relational—if there is nothing to fall toward, you may not even be aware that you’re falling. If there is no ground, gravity might be low and you’ll feel weightless. Objects will stay suspended if you let go of them. Whole societies around you may be falling just as you are. And it may actually feel like perfect stasis—as if history and time have ended and you can’t even remember that time ever moved forward. A free falling object is an object that is falling under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. ...
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...reactions. We used stopwatches, to measure the total amount of time that the rocket is in the air. Next, we use the three kinematics equations to determine the initial velocity and displacement height of the rocket. To do the experiment each group received a stomp rocket/launcher and a stopwatch. The main goal of the lab is to figure out the initial velocity and displacement height of the rocket. Kinematics equations were used throughout the whole lab to determine...
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...* 000000 Motion * Acceleration * Velocity Keywords * Motion * Acceleration * Velocity * Circular Motion * Vectors * Harmonic Motion * Kinematics * Rotational Motion * Linear Motion Sample Learning Goals * Is the velocity vector blue or green? How can you tell? * Is the acceleration vector blue or green? How can you tell? * Explain why the velocity and acceleration vectors behave as they do for the preset motions (linear acceleration I, II, circular motion, & harmonic motion). Tips for Teachers The teacher's guide (pdf) contains tips created by the PhET team. Teaching Ideas Title | Authors | Level | Type | Updated | 2D Motion | Patrick Foley | HS | Lab | 9/20/12 | Rotational Motion | Sarah Stanhope | HS | Lab | 1/27/11 | 1 Dimensional Motion - Kinematics and Graphing | Sarah Stanhope | HS | Lab | 1/27/11 | Introduction to rotational motion | Sarah Stanhope | HS UG-Intro | CQs | 2/24/10 | 2D Motion Activity | Drew Isola | HS | CQs | 1/11/09 | Vectors Phet Lab | Chris Bires | HS | Lab | 8/4/10 | Modeling a linear simple harmonic oscillator | Mark Kelly | UG-Intro | Lab | 4/7/08 | Motion in Two Dimensions | Gretchen Swanson | HS | Lab | 9/18/07 | You can submit your own ideas and activities. Translated Versions: Language | Language (Translated) | Simulation Title | | | Arabic | العربية | الحركة في بعدين | Run Now | Download | Arabic, Saudi Arabia | العربية (السعودية) | الحركة...
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...Assignment Week 2 Due: 11:59pm on Sunday, January 18, 2015 You will receive no credit for items you complete after the assignment is due. Grading Policy A message from your instructor... The next seven problems are for practice. Item 1 Learning Goal: To understand that adding vectors by using geometry and by using components gives the same result, and that manipulating vectors with components is much easier. Vectors may be manipulated either geometrically or using components. In this problem we consider the addition of two vectors using both of these two methods. The vectors and have lengths and , respectively, and makes an angle from the direction of . ⃗ ⃗ ⃗ ⃗ Vector addition using geometry Vector addition using geometry is accomplished by putting the tail of one vector (in this case ) on the tip of the other ( ) and using the laws of plane geometry to find ⃗ ⃗ ⃗ ⃗ : , √ 1. ⃗ the length , and angle , of the resultant (or sum) vector, 2. Vector addition using components Vector addition using components requires the choice of a coordinate system. In this problem, the x axis is chosen along the direction of . Then the x and y ⃗ components of are and respectively. This means that the x and y components of are given by ⃗ 3. 4. , . Part A Which of the following sets of conditions, if true, would show that the expressions 1 and 2 above define the same vector as expressions 3 and 4...
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...by a multitude of independent kinematic chains. Generally it comprises two platforms which are connected by joints or legs acting in parallel. In recent years, parallel kinematic mechanisms have attracted a lot of attention from the academic and industrial communities due to their potential applications not only as robot manipulators but also as machine tools. The dream of all developers in Machine Tools has always been to combine the flexibility and envelope of the robots with the accuracy and stiffness of traditional Machine Tools. In the last 20 years the focus of this development has been Parallel Kinematics Machines so called PKM. This technology means that the motions in X, Y and Z are performed by three or more parallel axis that gives an outstanding stiffness and accuracy with a maintained flexibility and envelope. Generally, the criteria used to compare the performance of traditional serial robots and parallel robots are the workspace, the ratio between the payload and the robot mass, accuracy, and dynamic behavior. In addition to the reduced coupling effect between joints, parallel robots bring the benefits of much higher payload-robot mass ratios, superior accuracy and greater stiffness; qualities which lead to better dynamic performance. The main drawback with parallel robots is the relatively small workspace. 1.2 OUTLAY OF PROJECT REPORT Objective of our major project is to model, design and fabricate a 2-axis Parallel Kinematic Machine and to test the same...
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...Kellis, E., & Katis, A. (2007). Biomechanical Characteristics and Determinants of Instep Soccer Kick. Journal of Sports Science and Medicine, 6, 154-165. The purpose of this review in the Journal of Sports Science and Medicine was to examine the latest research findings on biomechanics of soccer kick performance and identify weaknesses of present research which justify further research in the future. A soccer kick is regarded as motions of the lower limb sections of the player’s dominant kicking leg. Angular velocity is maximized first by the thigh, then through the leg limb, and finally by the foot. This is accomplished by both segmental and joint movements on multiple surfaces. During the backswing, the thigh reduces speed mainly due...
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...revolutions, or radians. A radian is the measure of the angle subtended by an arc that is the length of the given radius. 2 rad is equal to 360. Therefore, 1 rad is equal to 57.3. Section 8.2 discusses angular velocity . Average angular velocity is derived in a similar way to the average linear velocity we have already discussed. It is simply the angular displacement divided by the elapsed time, and it is usually measured in radians per second. This section also deals with the difference between instantaneous and average angular velocity. This is also analogous to what has already been discussed with linear velocity. Also similar to the concepts we have already dealt with in linear motion is the concept of angular acceleration (), which is simply a change in the angular velocity. Section 8.3 clarifies the equations (similar to those used in linear motion study) that are necessary to work problems dealing with angular motion. These are the equations of rotational kinematics for constant angular acceleration: = 0 + t = ½ (0 + )t = 0t + ½ t2 2 = 02 + 2 Also in this section is a useful table of symbols: Quantity Rotational Motion Linear Motion Displacement X Initial Velocity 0 v0 Final Velocity V Acceleration A Time t T This section closes with a list of reasoning strategies for applying these equations. 1. Make a drawing 2. Decide on a positive and negative direction 3. Write down values for the variables 4. Make...
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