Data Acquisition. Where am I? Photographs. Video Systems. Not covered in detail he Hamill text, nor in most texts on reserve.
|
|
- Gregory Wells
- 5 years ago
- Views:
Transcription
1 Data Acquisition Not covered in detail he Hamill text, nor in most texts on reserve. The best text to read if the lecture and slides are not clear to you is: Winter, D. Biomechanics of Human Movement. John Wiley & Sons, New York, Photographs Ø If taken in the correct plane photographs can allow for later evaluation of angles and hence for a static kinetic analysis. Ø In dynamic situations how do you know you have the extreme posture? Where am I? Ø The accurate and complete answer to this question is not as simple as it may seem. Video Systems Ø There is a limited amount of quantitative data that can be gleaned from a full-motion video system. Ø Stop frame capability does however allow for a reasonably accurate assessment of posture. Ø 60 frames/sec is more than adequate for most movements but the real problem is identifying joint centres of rotation and calibration. 1
2 Opto-Electronic Systems The location of the joint centres of rotation is entered directly into the computer. Systems usually come with software that will calculate velocity and acceleration. Q-Track and Force Plate Data Q-trac markers Previous Data Acquisition System in Dr. Robinovitch s Lab 2
3 Injury Prevention and Mobility Laboratory Position & Displacement Ø Position defines an object s location in space. Ø Displacement defines the change in position that occurs over a given period of time. Ø Displacement is a vector Ø Distance is a scalar Movements Occur Over Time Speed Knowledge of the temporal patterns of a movement is critical in a kinematic analysis since changes in position occur over time. Speed is a scalar (m/s) Speed = distance Δtime Δ = change in 3
4 Velocity is a vector (m/s) Velocity Velocity = Δposition(displacement) Δtime Velocity is designated by lowercase v Time is designated by lowercase t Dimensions (fundamental units in brackets) Ø Mass (M) Ø Length (L) Ø Time (T) Ø Other fundamental units like temperature is not a focus of Kin 201 Velocity Fundamental units = LT -1 Displacement => Velocity B If we plot our displacement data on a graph we are calculating the slope of the line when we calculate velocity. Displ. A Δt = run Δx = rise Time 4
5 Displacement => Velocity Finite Differentiation v = position final - position initial time at final displ. - time at initial displ. v = x f - x i t f - t i = x f - x i Δt Δx x 1 x 2 x 3 x 4 x 5 Δt As (t f - t i ) is usually constant we just use Δt. t 1 t 2 t 3 t 4 t 5 Displ. Finite Differentiation B (x 2, y 2 ) A (x 1, y 1 ) Time Finite Differentiation Vx Vy x2 " x1 =! t y 2 " y =! t 1 5
6 Sample Data Video Ø Full frame video is 60 Hz (60 frames per second). Ø So strictly speaking ΔT (time interval) is recurring. Ø The values will be acceptable if you use , , , etc. ( ) / = 8.98 Finite Differentiation ( ) / = 4.19 Finite Differentiation Ø But at what time do the velocities on the previous table occur? Ø In other words: What is instantaneous velocity? Ø Clearly the value you get from differentiation is the average velocity of the time period used. There in no such thing as instanaeous velocity when dealing with digital displacement data. 6
7 Finite Differentiation x!1.5! 1.5 y = = x2 " x1! t y 2 " y! t 1 Finite Differentiation What is instantaneous velocity? x 1 x 2 Δt x 3 x 4 x 5 V 2-3 V 3 x 1 x 2 x 3 x 4 x 5 2Δt Finite Differentiation First Central Difference Method! 2 x x " x 3 1 = 2! t You do loose sensitivity in this method, but you can discuss velocities at the same time frame as displacements and acceleration. And if Δt is small enough you will avoid sensitivity problems. Finite Differentiation First central difference method ( ) / =
8 Acceleration Acceleration Acceleration = Δvelocity Δtime Acceleration is designated by lowercase a It is used for both scalar and vector quantities. Ø Again if we are using coordinate systems we use the following convention. Horizontal " acceleration!!! x Vertical " acceleration!!! y Acceleration Ø If my velocity in the x-direction goes from 3 m/s to 2 m/s in 0.05 seconds what would my acceleration be? Ø Answer: -20 m/s 2 Ø Be careful of the term deceleration Ø Deceleration means slowing down (it is in effect a scalar term ). It does not mean negative acceleration (vector). Ø You can have negative acceleration and speed up! 8
9 Sample Problem Time (s) Displ. (m) ! Time Displ.!! 0.0!0.000!! 0.5!0.857!! 1.0!3.160!! 1.5!6.484!! 2.0!10.56!! 2.5!15.21!! 3.0!20.26!! 3.5!25.60!! 4.0!31.130! 4.5!36.77!! 5.0!42.480! Time Displ.! 5.5!48.21!! 6.0!53.95!! 6.5!59.68!! 7.0!65.42!! 7.5!71.16!! 8.0!76.89!! 8.5!82.63!! 9.0!88.37!! 9.5!94.11!! 10.0!99.84!! !! Draw the following graphs (do not use first central difference method du to large Δt) d vs t v vs t a vs t Sampling Theory Winter, 1979 (page 22-39) 9
10 Instantaneous Velocity How small should Δt be? Tangent Displ. Δt => 0 This line would be a poor estimate of the tangent for this section of the curve. Time Δt Analogue to Digital Ø Obviously the smaller Δt is the more accurate you estimate of instantaneous velocity. Ø However, the smaller you try to get Δt the more expensive it is going to be! Ø Regular video at 60 frames/sec is good for most applications. 10
11 Synchronization (A to D) Ø If you have force platform, video and EMG data there can be a problem in synchronizing the data. Ø This is not a problem if all data is collected by computer. However, if some data is collected on video and some on the computer how do you know the time frames on the video match those collected by the computer? Ø One possibility is to turn a light on in the video view once the computer starts data collection. Signal 2 Aliasing Error (Δt is too large to sample signal 2) Signal 1 Aliasing Error Proper sampling rate Sampling rate too low Error (Noise) Ø In one study researchers actually drilled markers into bone. Ø However, markers are almost always placed on the skin and are therefore vulnerable to movement that is not due to movement of the skeleton. Ø When landing from a jump or the impact of foot strike the markers will vibrate. Ø If not very well isolated the sensors will also vibrate. Ø The 60 Hz AC electrical current could also affect the recorded data. Ø Any source of error like these is referred to as noise. Filtering Raw Data Sampling Theory Filtering attenuates (reduces) noise 11
12 Differentiation is Sensitive to Noise Signal vs Noise The differentials (slopes) calculated between these markers is much larger than the difference in their locations. Red stars = true location of bony landmark Yellow stars = location of marker due to noise Integration Ø Differentiating positional data to get velocity and acceleration has been covered. Ø However, acceleration may be collected in a biomechanical analysis. Ø In this case, you may want to calculate velocity and displacement data. Ø This is the opposite of differentiation and is known as integration. Accelerometer 12
13 Tri-Axial Accelerometers Ø Accelerometers vary considerably in resolution and max. acceleration. Ø Must be sure of planar acceleration if using uniaxial accelerometers. Ø Tri-axial accelerometers are bulkier and much more expensive. Ø These can be rented rather than purchased. Vibration (seat pan accelerometer) Ø Vibration is measured using accelerometers and then various mathematical and statistical techniques are used to quantify and interpret the signal. Force Platform Data If you have force and obviously F = ma, then you can easily calculate the acceleration of the body s centre of gravity. Finite Integration Ø We have seen that finite differentiation methods are used with digital data. Ø Similarly, finite integration methods are used with digital data. Ø We saw that with finite differentiation you are calculating the slope of the curve. Ø Finite integration calculates the area under the curve. Ø Most often used with force-time curves area under the curve is mechanical impulse (Ft = Δmv) Ø Integration of an acceleration curve (from force plate data divided by body mass) will allow you to calculate velocity of the body s centre of gravity. Ø Integration again will calculate displacement of the whole body centre of gravity. 13
14 7 acc. 3 A Example B Time Ø Area A equals 3m/s 2 x 6s = 18 m/s Ø Units! LT -2 x T = LT -1 Ø This is change in velocity from 0-6 s. Ø Area B is 14 m/s. Ø Total change in velocity from 0-8 s is 32 m/s. If :" a = #v #t Then :" #v = a#t Finite Integration Acceleration Hence area under curve = a"t Δt # Approximated as = a 1 + a & 2 % ("t $ 2 ' Time a 1 a a 2 Riemann Sum Ø Finite integration approximates the area under curves as a series of rectangles Ø This is called the Riemann sum (see equation opposite) Ø If Δt is small enough this is an accurate approximation t30 vxi! dt t1 ds = 30 " i= 1 = ds (v xi *dt) Example above: Horizontal velocity time curve with 30 time intervals. Integral equals change in displacement. Integration is less sensitive to errors due to noise High frequency noise present A B The slope of curve A varies greatly but the area under the curve is not that different from curve B. 14
15 Stride Rate vs Stride Length Kinematics of Running Reserve text: Hamill & Knutzen, Chapter 8 (pages ) Running Kinematics Ø Stride length (SL) and stride frequency (SF) are very commonly studied kinematic parameters. Ø Both SR & SL increase linearly (approx.) from a slow jog up until 7 m/s. Ø After this SR increases much more than SL. Ø Support and non-support phases are also of interest. Ø Support Phase: Jogging 68%, moderate sprint 54%, full-sprint 47% Mechanical Efficiency (Figure 8-27) 0 2 consumption PSF = preferred stride frequency -20% -10% PSF +10% +20% 15
16 Displacement - Time Answer to Running Kinematics Problem Displacement-Time Graph Answer to Running Velocity - Kinematics Time Problem Velocity-Time Graph Displ. (m) Time (s) Vel. (m/s) Female high school sprinters reached max. speed between m. Lost an average of 7.3% during final 10 m. Chow, Time (s) Ø The world record for the 100m is? Ø The world record for the 200m is? 100 m vs 200 m Accel. (m/s2) Answer to Running Acceleration Kinematics - Time Problem Acceleration-Time Graph Time (s) 16
Kinesiology 201 Solutions Kinematics
Kinesiology 201 Solutions Kinematics Tony Leyland School of Kinesiology Simon Fraser University 1. a) Vertical ocity = 10 sin20 = 3.42 m/s Horizontal ocity = 10 cos20 = 9.4 m/s B Vertical A-B (start to
More informationChapter 2. Motion in One Dimension. Professor Wa el Salah
Chapter 2 Motion in One Dimension Kinematics Describes motion while ignoring the external agents that might have caused or modified the motion For now, will consider motion in one dimension Along a straight
More informationPhysics 101 Lecture 3 Motion in 1D Dr. Ali ÖVGÜN
Physics 101 Lecture 3 Motion in 1D Dr. Ali ÖVGÜN EMU Physics Department Motion along a straight line q Motion q Position and displacement q Average velocity and average speed q Instantaneous velocity and
More informationMotion along a straight line. Physics 11a. 4 Basic Quantities in Kinematics. Motion
Physics 11a Motion along a straight line Motion Position and Average velocity and average speed Instantaneous velocity and speed Acceleration Constant acceleration: A special case Free fall acceleration
More informationVelocity. UF PHY2053, Lecture 3: Motion in One Dimension
Velocity 1 Average Velocity vs Average Speed Average Velocity is the change in position during a time interval vav,x Δx Δt x f - xi tf - ti Average Speed is the distance traveled during a time interval
More informationKINEMATICS OF A PARTICLE. Prepared by Engr. John Paul Timola
KINEMATICS OF A PARTICLE Prepared by Engr. John Paul Timola Particle has a mass but negligible size and shape. bodies of finite size, such as rockets, projectiles, or vehicles. objects can be considered
More informationChapter 2 Describing Motion: Kinematics in One Dimension
Chapter 2 Describing Motion: Kinematics in One Dimension Units of Chapter 2 Reference Frames and Displacement Average Velocity Instantaneous Velocity Acceleration Motion at Constant Acceleration Solving
More informationIn this lesson about Displacement, Velocity and Time, you will:
Slide 1 Module 3, Lesson 2 - Objectives & Standards In this lesson about Displacement, Velocity and Time, you will: Pb: Demonstrate an understanding of the principles of force and motionand relationships
More informationDistance vs. Displacement, Speed vs. Velocity, Acceleration, Free-fall, Average vs. Instantaneous quantities, Motion diagrams, Motion graphs,
Distance vs. Displacement, Speed vs. Velocity, Acceleration, Free-fall, Average vs. Instantaneous quantities, Motion diagrams, Motion graphs, Kinematic formulas. A Distance Tells how far an object is from
More informationFigure 2.1 The Inclined Plane
PHYS-101 LAB-02 One and Two Dimensional Motion 1. Objectives The objectives of this experiment are: to measure the acceleration due to gravity using one-dimensional motion, i.e. the motion of an object
More informationChapter 2. Motion in One Dimension
Chapter 2 Motion in One Dimension Types of Motion Translational An example is a car traveling on a highway. Rotational An example is the Earth s spin on its axis. Vibrational An example is the back-and-forth
More informationKinematics. Kinetics. Frames of Reference. Role of Kinematic Analysis in Biomechanics. Frames of Reference. Frames of Reference
Kinematics Kinematics theory Kinematics Mechanics Physics Other areas of physics Processing techniques Statics Dynamics Measurement techniques Introduction to 3D kinematics Kinematics Kinetics Kinematics:
More informationAcceleration. 3. Changing Direction occurs when the velocity and acceleration are neither parallel nor anti-parallel
Acceleration When the velocity of an object changes, we say that the object is accelerating. This acceleration can take one of three forms: 1. Speeding Up occurs when the object s velocity and acceleration
More informationPhysics 2A. Lecture 2A. "You must learn from the mistakes of others. You can't possibly live long enough to make them all yourself.
Physics 2A Lecture 2A "You must learn from the mistakes of others. You can't possibly live long enough to make them all yourself." --Sam Levenson 1 Motion Chapter 2 will focus on motion in one dimension.
More informationMarble Launch Experiment
Marble Launch Experiment Purpose The intent of this experiment is to numerically trace the path of a marble launched into the air at an angle in order to observe the parabolic nature of the trajectory.
More informationDemo: x-t, v-t and a-t of a falling basket ball.
Demo: x-t, v-t and a-t of a falling basket ball. I-clicker question 3-1: A particle moves with the position-versus-time graph shown. Which graph best illustrates the velocity of the particle as a function
More informationChapter 2. Motion in One Dimension. AIT AP Physics C
Chapter 2 Motion in One Dimension Kinematics Describes motion while ignoring the agents that caused the motion For now, will consider motion in one dimension Along a straight line Will use the particle
More informationWhat does the lab partner observe during the instant the student pushes off?
Motion Unit Review State Test Questions 1. To create real-time graphs of an object s displacement versus time and velocity versus time, a student would need to use a A motion sensor.b low- g accelerometer.
More information5. KINEMATICS. Figure 5.1 Types of planar motions
5. KINEMATICS Suddenly there is no more acceleration and no more pressure on my body. It is like being at the top of a roller coaster and my whole body is in free-fall. Roberta Bondar, Touching the Earth.
More informationCHAPTER 2 DESCRIBING MOTION: KINEMATICS IN ONE DIMENSION
CHAPTER 2 DESCRIBING MOTION: KINEMATICS IN ONE DIMENSION OBJECTIVES After studying the material of this chapter, the student should be able to: state from memory the meaning of the key terms and phrases
More informationLECTURE 2. Mechanics is constituted by two main part: Kinematics and Dynamics
LECTURE 2 KINEMATICS, YNAMICS AN STATIC Mechanics is constituted by two main part: Kinematics and ynamics -Kinematics is that part of mechanics that describes the movement of objects without paying attention
More informationChapter 2 Describing Motion: Kinematics in One Dimension
Chapter 2 Describing Motion: Kinematics in One Dimension 2-1 Reference Frames and Displacement Any measurement of position, distance, or speed must be made with respect to a reference frame. For example,
More informationKinematics Unit. Measurement
Kinematics Unit Measurement The Nature of Science Observation: important first step toward scientific theory; requires imagination to tell what is important. Theories: created to explain observations;
More informationChapter 2. Kinematic Equations. Problem 1. Kinematic Equations, specific. Motion in One Dimension
Kinematic Equations Chapter Motion in One Dimension The kinematic equations may be used to solve any problem involving one-dimensional motion with a constant You may need to use two of the equations to
More information1.1 Graphing Motion. IB Physics 11 Kinematics
IB Physics 11 Kinematics 1.1 Graphing Motion Kinematics is the study of motion without reference to forces and masses. We will need to learn some definitions: A Scalar quantity is a measurement that has
More informationBIOMECHANICS AND MOTOR CONTROL OF HUMAN MOVEMENT
BIOMECHANICS AND MOTOR CONTROL OF HUMAN MOVEMENT Third Edition DAVID Α. WINTER University of Waterloo Waterloo, Ontario, Canada WILEY JOHN WILEY & SONS, INC. CONTENTS Preface to the Third Edition xv 1
More informationLab I. 2D Motion. 1 Introduction. 2 Theory. 2.1 scalars and vectors LAB I. 2D MOTION 15
LAB I. 2D MOTION 15 Lab I 2D Motion 1 Introduction In this lab we will examine simple two-dimensional motion without acceleration. Motion in two dimensions can often be broken up into two separate one-dimensional
More informationNewton s Second Law. Computer with Capstone software, motion detector, PVC pipe, low friction cart, track, meter stick.
F = m a F = m a Newton s Second Law 1 Object To investigate, understand and verify the relationship between an object s acceleration and the net force acting on that object as well as further understand
More informationChapter 3. Motion in One Dimension
Chapter 3 Motion in One Dimension Outline 3.1 Position, Velocity and Speed 3.2 Instantaneous Velocity and Speed 3.3 Acceleration 3.4 Motion Diagrams 3.5 One-Dimensional Motion with Constant Acceleration
More informationChapter 2. Kinematics in One Dimension. continued
Chapter 2 Kinematics in One Dimension continued 2.4 Equations of Kinematics for Constant Acceleration vx0 = 0m s ax = +31 m s 2 Δx vx = 62m s Example: Catapulting a Jet Find its displacement. vx0 = 0m
More informationFour Types of Motion We ll Study
Four Types of Motion We ll Study The branch of mechanics that studies the motion of a body without caring about what caused the motion. Kinematics definitions Kinematics branch of physics; study of motion
More informationPH 1110 Summary Homework 1
PH 111 Summary Homework 1 Name Section Number These exercises assess your readiness for Exam 1. Solutions will be available on line. 1a. During orientation a new student is given instructions for a treasure
More informationWelcome Back to Physics 211!
Welcome Back to Physics 211! (General Physics I) Thurs. Aug 30 th, 2012 Physics 211 -Fall 2014 Lecture01-2 1 Last time: Syllabus, mechanics survey Unit conversions Today: Using your clicker 1D displacement,
More informationExperiment 3. d s = 3-2 t ANALYSIS OF ONE DIMENSIONAL MOTION
Experiment 3 ANALYSIS OF ONE DIMENSIONAL MOTION Objectives 1. To establish a mathematical relationship between the position and the velocity of an object in motion. 2. To define the velocity as the change
More informationLab I. 2D Motion. 1 Introduction. 2 Theory. 2.1 scalars and vectors LAB I. 2D MOTION 15
LAB I. 2D MOTION 15 Lab I 2D Motion 1 Introduction In this lab we will examine simple two-dimensional motion without acceleration. Motion in two dimensions can often be broken up into two separate one-dimensional
More informationDefinitions. Mechanics: The study of motion. Kinematics: The mathematical description of motion in 1-D and 2-D motion.
Lecture 2 Definitions Mechanics: The study of motion. Kinematics: The mathematical description of motion in 1-D and 2-D motion. Dynamics: The study of the forces that cause motion. Chapter Outline Consider
More informationKinematics. Chapter 2. Position-Time Graph. Position
Kinematics Chapter 2 Motion in One Dimension Describes motion while ignoring the agents that caused the motion For now, will consider motion in one dimension Along a straight line Will use the particle
More informationMathematical review trigonometry vectors Motion in one dimension
Mathematical review trigonometry vectors Motion in one dimension Used to describe the position of a point in space Coordinate system (frame) consists of a fixed reference point called the origin specific
More informationPhysics. Chapter 3 Linear Motion
Physics Chapter 3 Linear Motion Motion is Relative How fast are you moving? We can only speak of how fast in relation to some other thing. Unless otherwise specified, we will assume motion relative to
More informationIntroduction to 1-D Motion Distance versus Displacement
Introduction to 1-D Motion Distance versus Displacement Kinematics! Kinematics is the branch of mechanics that describes the motion of objects without necessarily discussing what causes the motion.! 1-Dimensional
More informationDisplacement, Velocity, and Acceleration AP style
Displacement, Velocity, and Acceleration AP style Linear Motion Position- the location of an object relative to a reference point. IF the position is one-dimension only, we often use the letter x to represent
More informationChapter 2 Kinematics in One Dimension:
Chapter 2 Kinematics in One Dimension: Vector / Scaler Quantities Displacement, Velocity, Acceleration Graphing Motion Distance vs Time Graphs Velocity vs Time Graphs Solving Problems Free Falling Objects
More informationPresenter: Siu Ho (4 th year, Doctor of Engineering) Other authors: Dr Andy Kerr, Dr Avril Thomson
The development and evaluation of a sensor-fusion and adaptive algorithm for detecting real-time upper-trunk kinematics, phases and timing of the sit-to-stand movements in stroke survivors Presenter: Siu
More informationConstant Acceleration
Constant Acceleration Ch. in your text book Objectives Students will be able to: ) Write the definition of acceleration, either in words or as an equation ) Create an equation for the movement of an object
More informationSpeed how fast an object is moving (also, the magnitude of the velocity) scalar
Mechanics Recall Mechanics Kinematics Dynamics Kinematics The description of motion without reference to forces. Terminology Distance total length of a journey scalar Time instant when an event occurs
More informationImpulse, Momentum, and Energy
Impulse, Momentum, and Energy Impulse, Momentum, and Energy 5-1 INTRODUCTION Newton expressed what we now call his second law of motion, 1 not as F = m a, but in terms of the rate of change of momentum
More information2008 FXA. DISPLACEMENT (s) / metre (m) 1. Candidates should be able to : The distance moved by a body in a specified direction.
DISPLACEMENT (s) / metre (m) 1 Candidates should be able to : Define displacement, instantaneous speed, average speed, velocity and acceleration. Select and use the relationships : average speed = distance
More informationLecture 3. (sections )
Lecture 3 PHYSICS 201 (sections 521-525) Instructor: Hans Schuessler Temporary: Alexandre e Kolomenski o http://sibor.physics.tamu.edu/teaching/phys201/ Average velocity v Δx Δt Instantaneous velocity
More informationChapter 2 One-Dimensional Kinematics. Copyright 2010 Pearson Education, Inc.
Chapter One-Dimensional Kinematics Units of Chapter Position, Distance, and Displacement Average Speed and Velocity Instantaneous Velocity Acceleration Motion with Constant Acceleration Applications of
More information12/06/2010. Chapter 2 Describing Motion: Kinematics in One Dimension. 2-1 Reference Frames and Displacement. 2-1 Reference Frames and Displacement
Chapter 2 Describing Motion: Kinematics in One Dimension 2-1 Reference Frames and Displacement Any measurement of position, distance, or speed must be made with respect to a reference frame. For example,
More informationLecture 2. 1D motion with Constant Acceleration. Vertical Motion.
Lecture 2 1D motion with Constant Acceleration. Vertical Motion. Types of motion Trajectory is the line drawn to track the position of an abject in coordinates space (no time axis). y 1D motion: Trajectory
More informationHW Chapter 3 Q 14,15 P 2,7,812,18,24,25. Chapter 3. Motion in the Universe. Dr. Armen Kocharian
HW Chapter 3 Q 14,15 P 2,7,812,18,24,25 Chapter 3 Motion in the Universe Dr. Armen Kocharian Predictability The universe is predictable and quantifiable Motion of planets and stars description of motion
More informationMotion Unit Review 1. To create real-time graphs of an object s displacement versus time and velocity versus time, a student would need to use a
Motion Unit Review 1. To create real-time graphs of an object s displacement versus time and velocity versus time, a student would need to use a A motion sensor.b low- g accelerometer. C potential difference
More informationRigid Body Kinetics :: Force/Mass/Acc
Rigid Body Kinetics :: Force/Mass/Acc General Equations of Motion G is the mass center of the body Action Dynamic Response 1 Rigid Body Kinetics :: Force/Mass/Acc Fixed Axis Rotation All points in body
More informationQ1. For the two physical quantities, impulse and force, which one of the following is correct?
PhysicsndMathsTutor.com 1 Q1. For the two physical quantities, impulse and force, which one of the following is correct? B C D Impulse is a scalar and force is a scalar. Impulse is a scalar and force is
More informationChapter 3. Accelerated Motion
Chapter 3 Accelerated Motion Chapter 3 Accelerated Motion In this chapter you will: Develop descriptions of accelerated motions. Use graphs and equations to solve problems involving moving objects. Describe
More informationKinematics 1D Kinematics 2D Dynamics Work and Energy
Kinematics 1D Kinematics 2D Dynamics Work and Energy Kinematics 1 Dimension Kinematics 1 Dimension All about motion problems Frame of Reference orientation of an object s motion Used to anchor coordinate
More informationMatthew W. Milligan. Kinematics. What do you remember?
Kinematics What do you remember? Kinematics Unit Outline I. Six Definitions: Distance, Position, Displacement, Speed, Velocity, Acceleration II. Graphical Interpretations III. Constant acceleration model
More informationSpring 2015, Math 111 Lab 4: Kinematics of Linear Motion
Spring 2015, Math 111 Lab 4: William and Mary February 24, 2015 Spring 2015, Math 111 Lab 4: Learning Objectives Today, we will be looking at applications of derivatives in the field of kinematics. Learning
More informationτ = F d Angular Kinetics Components of Torque (review from Systems FBD lecture Muscles Create Torques Torque is a Vector Work versus Torque
Components of Torque (review from Systems FBD lecture Angular Kinetics Hamill & Knutzen (Ch 11) Hay (Ch. 6), Hay & Ried (Ch. 12), Kreighbaum & Barthels (Module I & J) or Hall (Ch. 13 & 14) axis of rotation
More informationLecture PowerPoints. Chapter 2 Physics: Principles with Applications, 6 th edition Giancoli
Lecture PowerPoints Chapter 2 Physics: Principles with Applications, 6 th edition Giancoli 2005 Pearson Prentice Hall This work is protected by United States copyright laws and is provided solely for the
More informationDerivation of Kinematic Equations. View this after Motion on an Incline Lab
Derivation of Kinematic Equations View this after Motion on an Incline Lab Constant velocity Average velocity equals the slope of a position vs time graph when an object travels at constant velocity. v
More informationStatic and Kinetic Friction
Static and Kinetic Friction If you try to slide a heavy box resting on the floor, you may find it difficult to get the box moving. Static friction is the force that is counters your force on the box. If
More informationChapter 3 Acceleration
Chapter 3 Acceleration Slide 3-1 Chapter 3: Acceleration Chapter Goal: To extend the description of motion in one dimension to include changes in velocity. This type of motion is called acceleration. Slide
More informationChapter 2. Kinematics in one dimension
Chapter 2 Kinematics in one dimension Galileo - the first modern kinematics 1) In a medium totally devoid of resistance all bodies will fall at the same speed 2) During equal intervals of time, a falling
More informationCh 2. Describing Motion: Kinematics in 1-D.
Ch 2. Describing Motion: Kinematics in 1-D. Introduction Kinematic Equations are mathematic equations that describe the behavior of an object in terms of its motion as a function of time. Kinematics is
More informationStatic and Kinetic Friction
Experiment Static and Kinetic Friction Prelab Questions 1. Examine the Force vs. time graph and the Position vs. time graph below. The horizontal time scales are the same. In Region I, explain how an object
More informationIntroduction to Physics Physics 114 Eyres
What is Physics? Introduction to Physics Collecting and analyzing experimental data Making explanations and experimentally testing them Creating different representations of physical processes Finding
More informationDEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS
DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS LSN 2-1A, KINEMATICS Questions From Reading Activity? Essential idea Motion may be described and analyzed by the use of graphs and equations. Nature
More informationStatic and Kinetic Friction
Experiment 12 If you try to slide a heavy box resting on the floor, you may find it difficult to get the box moving. Static friction is the force that is acting against the box. If you apply a light horizontal
More informationMotion in Two Dimensions. 1.The Position, Velocity, and Acceleration Vectors 2.Two-Dimensional Motion with Constant Acceleration 3.
Motion in Two Dimensions 1.The Position, Velocity, and Acceleration Vectors 2.Two-Dimensional Motion with Constant Acceleration 3.Projectile Motion The position of an object is described by its position
More informationStudy Guide Solutions
Study Guide Solutions Table of Contents Chapter 1 A Physics Toolkit... 3 Vocabulary Review... 3 Section 1.1: Mathematics and Physics... 3 Section 1.2: Measurement... 3 Section 1.3: Graphing Data... 4 Chapter
More informationProjectile Motion B D B D A E A E
Projectile Motion Projectile motion is motion under a constant unbalanced force. A projectile is a body that has been thrown or projected. No consideration is given to the force projecting the body, nor
More informationONE-DIMENSIONAL KINEMATICS
ONE-DIMENSIONAL KINEMATICS Chapter 2 Units of Chapter 2 Position, Distance, and Displacement Average Speed and Velocity Instantaneous Velocity Acceleration Motion with Constant Acceleration Applications
More informationKinematics. Become comfortable with the data aquisition hardware and software used in the physics lab.
Kinematics Objective Upon completing this experiment you should Become comfortable with the data aquisition hardware and software used in the physics lab. Have a better understanding of the graphical analysis
More informationComment: Unlike distance, displacement takes into consideration the direction of motion from the point of origin (where the object starts to move).
Chapter 3 Kinematics (A) Distance Vs Displacement 1. Compare distance and displacement in terms of: (a) definition Distance is the total length of travel, irrespective of direction. Displacement is the
More informationPhysics 101 Prof. Ekey. Chapter 2
Physics 11 Prof. Ekey Chapter 2 Kinematics in one dimension Uniform motion, s vs t, v vs t, a vs t, kinematic equations fun. In this chapter, you will learn how to solve problems about motion along a straight
More information2/18/2019. Position-versus-Time Graphs. Below is a motion diagram, made at 1 frame per minute, of a student walking to school.
Position-versus-Time Graphs Below is a motion diagram, made at 1 frame per minute, of a student walking to school. A motion diagram is one way to represent the student s motion. Another way is to make
More informationChapter 2. Motion along a straight line. We find moving objects all around us. The study of motion is called kinematics.
Chapter 2 Motion along a straight line 2.2 Motion We find moving objects all around us. The study of motion is called kinematics. Examples: The Earth orbits around the Sun A roadway moves with Earth s
More informationMAKING MEASUREMENTS. I walk at a rate of paces per...or...my pace =
MAKING MEASUREMENTS TIME: The times that are required to work out the problems can be measured using a digital watch with a stopwatch mode or a watch with a second hand. When measuring the period of a
More informationLook over: Chapter 2 Sections 1-9 Sample Problems 1, 2, 5, 7. Look over: Chapter 2 Sections 1-7 Examples 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 PHYS 2211
PHYS 2211 Look over: Chapter 2 Sections 1-9 Sample Problems 1, 2, 5, 7 PHYS 1111 Look over: Chapter 2 Sections 1-7 Examples 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 Topics Covered 1) Average Speed 2) Average Velocity
More informationTrigonometry I. Pythagorean theorem: WEST VIRGINIA UNIVERSITY Physics
Trigonometry I Pythagorean theorem: Trigonometry II 90 180 270 360 450 540 630 720 sin(x) and cos(x) are mathematical functions that describe oscillations. This will be important later, when we talk about
More informationChapter 3: Introduction to Kinematics
Chapter 3: Introduction to Kinematics Kari Eloranta 2018 Jyväskylän Lyseon lukio Pre Diploma Program Year October 11, 2017 1 / 17 3.1 Displacement Definition of Displacement Displacement is the change
More informationWelcome Back to Physics 211!
Welcome Back to Physics 211! (General Physics I) Thurs. Aug 30 th, 2012 Physics 211 -Fall 2012 Lecture01-2 1 Last time: Syllabus, mechanics survey Particle model Today: Using your clicker 1D displacement,
More informationChapter 4. Forces and the Laws of Motion. CH 4 Forces and the Laws of Motion.notebook. April 09, Changes in Motion. A. Force
CH 4 Forces and the Laws of Motion.notebook Chapter 4 A. Force April 09, 2015 Changes in Motion Forces and the Laws of Motion 1. Defined as the cause of an acceleration, or the change in an object s motion,
More informationPHYSICS Kinematics in One Dimension
PHYSICS Kinematics in One Dimension August 13, 2012 www.njctl.org 1 Motion in One Dimension Return to Table of Contents 2 Distance We all know what the distance between two objects is... So what is it?
More informationConstant velocity and constant acceleration
Constant velocity and constant acceleration Physics 110 Laboratory Introduction In this experiment we will investigate two rather simple forms of motion (kinematics): motion with uniform (non-changing)
More informationPHY 221 Lab 3 Vectors and Motion in 1 and 2 Dimensions
PHY 221 Lab 3 Vectors and Motion in 1 and 2 Dimensions Print Your Name Print Your Partners' Names Instructions Before lab, read the Introduction, and answer the Pre-Lab Questions on the last page of this
More informationLecture PowerPoints. Chapter 2 Physics: Principles with Applications, 7 th edition Giancoli
Lecture PowerPoints Chapter 2 Physics: Principles with Applications, 7 th edition Giancoli This work is protected by United States copyright laws and is provided solely for the use of instructors in teaching
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Two Dimensions; Vectors Vectors and Scalars Units of Chapter 3 Addition of Vectors Graphical Methods Subtraction of Vectors, and Multiplication of a Vector by a Scalar Adding Vectors
More informationTo conduct the experiment, each person in your group should be given a role:
Varying Motion NAME In this activity, your group of 3 will collect data based on one person s motion. From this data, you will create graphs comparing displacement, velocity, and acceleration to time.
More informationChapter 3 Acceleration
Chapter 3 Acceleration Slide 3-1 Chapter 3: Acceleration Chapter Goal: To extend the description of motion in one dimension to include changes in velocity. This type of motion is called acceleration. Slide
More informationEnergy and Power in (Sports) Biomechanics. Objectives. Contents
Energy and Power in (Sports) Biomechanics Department Center of for Sport Sensory-Motor and Exercise Interaction Science SPORTSCI 306 Technique Anvendt Assessment Biomekanik Uwe Uwe Kersting Kersting MiniModule
More informationEXPERIMENT 3 Analysis of a freely falling body Dependence of speed and position on time Objectives
EXPERIMENT 3 Analysis of a freely falling body Dependence of speed and position on time Objectives to verify how the distance of a freely-falling body varies with time to investigate whether the velocity
More informationUnit 2 - Linear Motion and Graphical Analysis
Unit 2 - Linear Motion and Graphical Analysis Motion in one dimension is particularly easy to deal with because all the information about it can be encapsulated in two variables: x, the position of the
More informationLecture 2. 1D motion with Constant Acceleration. Vertical Motion.
Lecture 2 1D motion with Constant Acceleration. Vertical Motion. Types of motion Trajectory is the line drawn to track the position of an abject in coordinates space (no time axis). y 1D motion: Trajectory
More informationINTRODUCTION & RECTILINEAR KINEMATICS: CONTINUOUS MOTION
INTRODUCTION & RECTILINEAR KINEMATICS: CONTINUOUS MOTION (Sections 12.1-12.2) Today s Objectives: Students will be able to find the kinematic quantities (position, displacement, velocity, and acceleration)
More informationWhat is a Vector? A vector is a mathematical object which describes magnitude and direction
What is a Vector? A vector is a mathematical object which describes magnitude and direction We frequently use vectors when solving problems in Physics Example: Change in position (displacement) Velocity
More informationGeneral Physics (PHY 170) Chap 2. Acceleration motion with constant acceleration. Tuesday, January 15, 13
General Physics (PHY 170) Chap 2 Acceleration motion with constant acceleration 1 Average Acceleration Changing velocity (non-uniform) means an acceleration is present Average acceleration is the rate
More informationSection Distance and displacment
Chapter 11 Motion Section 11.1 Distance and displacment Choosing a Frame of Reference What is needed to describe motion completely? A frame of reference is a system of objects that are not moving with
More information