Effectiveness of Integral Kinesiology Feedback for Fitness-Based Games
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Rotational Motion (The Dynamics of a Rigid Body)
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Robert Katz Publications Research Papers in Physics and Astronomy 1-1958 Physics, Chapter 11: Rotational Motion (The Dynamics of a Rigid Body) Henry Semat City College of New York Robert Katz University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/physicskatz Part of the Physics Commons Semat, Henry and Katz, Robert, "Physics, Chapter 11: Rotational Motion (The Dynamics of a Rigid Body)" (1958). Robert Katz Publications. 141. https://digitalcommons.unl.edu/physicskatz/141 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Robert Katz Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 11 Rotational Motion (The Dynamics of a Rigid Body) 11-1 Motion about a Fixed Axis The motion of the flywheel of an engine and of a pulley on its axle are examples of an important type of motion of a rigid body, that of the motion of rotation about a fixed axis. Consider the motion of a uniform disk rotat ing about a fixed axis passing through its center of gravity C perpendicular to the face of the disk, as shown in Figure 11-1. The motion of this disk may be de scribed in terms of the motions of each of its individual particles, but a better way to describe the motion is in terms of the angle through which the disk rotates. -
Physics B Topics Overview ∑
Physics 106 Lecture 1 Introduction to Rotation SJ 7th Ed.: Chap. 10.1 to 3 • Course Introduction • Course Rules & Assignment • TiTopics Overv iew • Rotation (rigid body) versus translation (point particle) • Rotation concepts and variables • Rotational kinematic quantities Angular position and displacement Angular velocity & acceleration • Rotation kinematics formulas for constant angular acceleration • Analogy with linear kinematics 1 Physics B Topics Overview PHYSICS A motion of point bodies COVERED: kinematics - translation dynamics ∑Fext = ma conservation laws: energy & momentum motion of “Rigid Bodies” (extended, finite size) PHYSICS B rotation + translation, more complex motions possible COVERS: rigid bodies: fixed size & shape, orientation matters kinematics of rotation dynamics ∑Fext = macm and ∑ Τext = Iα rotational modifications to energy conservation conservation laws: energy & angular momentum TOPICS: 3 weeks: rotation: ▪ angular versions of kinematics & second law ▪ angular momentum ▪ equilibrium 2 weeks: gravitation, oscillations, fluids 1 Angular variables: language for describing rotation Measure angles in radians simple rotation formulas Definition: 360o 180o • 2π radians = full circle 1 radian = = = 57.3o • 1 radian = angle that cuts off arc length s = radius r 2π π s arc length ≡ s = r θ (in radians) θ ≡ rad r r s θ’ θ Example: r = 10 cm, θ = 100 radians Æ s = 1000 cm = 10 m. Rigid body rotation: angular displacement and arc length Angular displacement is the angle an object (rigid body) rotates through during some time interval..... ...also the angle that a reference line fixed in a body sweeps out A rigid body rotates about some rotation axis – a line located somewhere in or near it, pointing in some y direction in space • One polar coordinate θ specifies position of the whole body about this rotation axis. -
Addition Bnewconres Bremodel
8/4/2013 Permit # Permit Date Owner and Contractor PURPOSE TAX_MAP Address TOTALCOST Addition B131575 07/09/2013 QC GENERAL Contractor Removing two walls on rear addition and replace roof and 092342 1321 38 ST $26,000.00 walls to meet current code requirement and build a new deck. Must be built per Lo Milani drawing. MARK N GNATOVICH Owner $26,000.00 B131778 07/29/2013 HARDING BRUCE L/SHEILA Owner ADDITION TO BACK OF HOUSE, KITCHEN REMODEL 104017-20 3520 22 ST $94,142.00 INSTALL NEW SIDING Custom Remodeling by Dean Taylor Inc. Contractor $94,142.00 bnewconres B131645 07/17/2013 Chicago Title Land Trust Contractor Construction 12x16 shed. 192 square feet. Height may not 11328-3 2300 79 AVE W $1,500.00 exceed 15'. Must be located in back yard. Becky Barnes Owner $1,500.00 B131697 07/19/2013 Jeffrey C Conover Owner Build a new 26'x38' garage. 101816-B 2801 44 ST $22,500.00 Sandy E Lamar Owner $22,500.00 B131741 07/25/2013 Timothy J Knanishu Owner 24 x 24 garage 103314-C 3933 31 AVE $14,000.00 Taylor Garages Inc. Contractor $14,000.00 B131742 07/25/2013 Taylor Garages Inc. Contractor 24 x 30 garage 111423-10-A 1914 65 AVE W $17,000.00 TIMOTHY J MILLER Owner $17,000.00 B131744 07/25/2013 Eagle's Nest of Q.C., LLC Contractor Secondary Stairwell 096471 1721 3 AVE $165,000.00 Eagle's Nest LLC Contractor $165,000.00 Eagle's Nest of Q.C., LLC Contractor 1713 3 AV $165,000.00 Eagle's Nest LLC Contractor $165,000.00 bremodel B131495 07/01/2013 First United Methodist Church Contractor Move wall and change stage and chair lift. -
Hydraulophone Design Considerations: Absement, Displacement, and Velocity-Sensitive Music Keyboard in Which Each Key Is a Water Jet
Hydraulophone Design Considerations: Absement, Displacement, and Velocity-Sensitive Music Keyboard in which each key is a Water Jet Steve Mann, Ryan Janzen, Mark Post University of Toronto, Dept. of Electrical and Computer Engineering, Toronto, Ontario, Canada For more information, see http://funtain.ca ABSTRACT General Terms We present a musical keyboard that is not only velocity- Measurement, Performance, Design, Experimentation, Hu- sensitive, but in fact responds to absement (presement), dis- man Factors, Theory placement (placement), velocity, acceleration, jerk, jounce, etc. (i.e. to all the derivatives, as well as the integral, of Keywords displacement). Fluid-user-interface, tangible user interface, direct user in- Moreover, unlike a piano keyboard in which the keys reach terface, water-based immersive multimedia, FUNtain, hy- a point of maximal displacement, our keys are essentially draulophone, pneumatophone, underwater musical instru- infinite in length, and thus never reach an end to their key ment, harmelodica, harmelotron (harmellotron), duringtouch, travel. Our infinite length keys are achieved by using water haptic surface, hydraulic-action, tracker-action jet streams that continue to flow past the fingers of a per- son playing the instrument. The instrument takes the form 1. INTRODUCTION: VELOCITY SENSING of a pipe with a row of holes, in which water flows out of KEYBOARDS each hole, while a user is invited to play the instrument by High quality music keyboards are typically velocity-sensing, interfering with the flow of water coming out of the holes. i.e. the notes sound louder when the keys are hit faster. The instrument resembles a large flute, but, unlike a flute, Velocity-sensing is ideal for instruments like the piano, there is no complicated fingering pattern. -
Chapter 24 Physical Pendulum
Chapter 24 Physical Pendulum 24.1 Introduction ........................................................................................................... 1 24.1.1 Simple Pendulum: Torque Approach .......................................................... 1 24.2 Physical Pendulum ................................................................................................ 2 24.3 Worked Examples ................................................................................................. 4 Example 24.1 Oscillating Rod .................................................................................. 4 Example 24.3 Torsional Oscillator .......................................................................... 7 Example 24.4 Compound Physical Pendulum ........................................................ 9 Appendix 24A Higher-Order Corrections to the Period for Larger Amplitudes of a Simple Pendulum ..................................................................................................... 12 Chapter 24 Physical Pendulum …. I had along with me….the Descriptions, with some Drawings of the principal Parts of the Pendulum-Clock which I had made, and as also of them of my then intended Timekeeper for the Longitude at Sea.1 John Harrison 24.1 Introduction We have already used Newton’s Second Law or Conservation of Energy to analyze systems like the spring-object system that oscillate. We shall now use torque and the rotational equation of motion to study oscillating systems like pendulums and torsional springs. 24.1.1 Simple -
Rotation: Kinematics
Rotation: Kinematics Rotation refers to the turning of an object about a fixed axis and is very commonly encountered in day to day life. The motion of a fan, the turning of a door knob and the opening of a bottle cap are a few examples of rotation. Rotation is also commonly observed as a component of more complex motions that result as a combination of both rotation and translation. The motion of a wheel of a moving bicycle, the motion of a blade of a moving helicopter and the motion of a curveball are a few examples of combined rotation and translation. This module focuses on the kinematics of pure rotation. This module begins by defining the angular variables and then proceeds to describe the relation between these variables and the variables of linear motion. Angular Variables Angular Position Consider an object rotating about a fixed axis. Let us define a coordinate system such that the axis of rotation passes through the origin and is perpendicular to the x- and y- axes. Fig. 1 shows a view of the x-y plane. If a reference line is drawn through the origin and a fixed point in the object, the angle between this line and a fixed direction is used to define the angular position of the object. In Fig. 1, the angular position is measured from the positive x-direction. Fig. 1: Rotating object - Angular position. Also, from geometry, the angular position can be written as the ratio of the length of the path traveled by any point on the reference line measured from the fixed direction to the radius of the path, ...Eq. -
CHAPTER 9: Rotation of a Rigid Body About a Fixed Axis up Until Know
Lecture 13: Reviews of Rotational Kinematics and Dynamics 1 CHAPTER 9: Rotation of a Rigid Body about a Fixed Axis Up until know we have always been looking at \point particles" or the motion of the center{of{mass of extended objects. In this chapter we begin the study of rotations of an extended object about a ¯xed axis. Such objects are called rigid bodies because when they rotate they maintain their overall shape. It is just their orientation in space which is changing. Angular Variables: , !, ® The variables used to described the motion of \point particles" are displacement, velocity, and acceleration. For a rotating rigid body, there are three completely analogous variables: angular displacement, angular velocity, and angular acceler- ation. These angular variables are very useful because the they can be assigned to every point on the rigid body as it rotates about a ¯xed axis. The ordi- nary displacement, velocity, and acceleration can be calculated at a given point from the angular displacement, angular velocity, and angular acceleration just by multiplying by the distance r of that point from the axis of rotation. Equations of motion with constant angular acceleration ®: For every equation which you have learned to describe the linear motion of a point particle, there is an exactly analogous equation to describe the rotational motion ((t) and !(t)) about a ¯xed axis. 1 2 1 2 Position with time: x(t) = x0 +v0t+ at corresponds to (t) = 0 +!0t+ ®t 2 2 Speed with time: v(t) = v0 + at corresponds to !(t) = !0 + ®t 2 2 2 2 Speed with distance: v (x) = v0+2a(x¡x0) corresponds to ! () = !0+2®(¡0) Relating linear kinematics with angular kinematics For a purely rotating body, all points on the body move in circles about the axis of rotation. -
UC Irvine UC Irvine Electronic Theses and Dissertations
UC Irvine UC Irvine Electronic Theses and Dissertations Title Microscopic Car Following Models Simulation Study Permalink https://escholarship.org/uc/item/8tx731bq Author Luong, Elaine Publication Date 2018 License https://creativecommons.org/licenses/by/4.0/ 4.0 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA, IRVINE Microscopic Car Following Models Simulation Study THESIS submitted in partial satisfaction of the requirements for the degree of MASTER OF SCIENCE in Civil Engineering by Elaine Luong Thesis Committee: Professor Wenlong Jin, Chair Professor R. Jayakrishnan Professor Stephen Ritchie 2018 © 2018 Elaine Luong DEDICATION To my parents for their guidance, patience, and support ii TABLE OF CONTENTS Page LIST OF FIGURES iv LIST OF TABLES v ACKNOWLEDGMENTS vi ABSTRACT OF THE THESIS vii CHAPTER 1: Introduction 1 1.1 Background 1 1.2 Motivation for Study 3 1.3 Thesis Outline 5 CHAPTER 2: Literature Study 7 2.1 Notation 7 2.2 Safe Distance Models 8 2.3 Optimal Velocity Models 10 2.4 Linear Models 12 2.5 Non-linear Models 15 2.6 Fritzsche Model 18 CHAPTER 3: Model Development 20 3.1 Model parameters and conditions 20 3.2 Procedure 21 CHAPTER 4: Simulation Results 24 4.1 Safe Distance Models 25 4.2 Optimal Velocity Models 27 4.3 Linear Models 29 4.4 Non-linear Models 32 4.5 Fritzsche Model 36 4.6 Overall Comparisons 36 CHAPTER 5: Summary and Conclusions 38 5.1 Limitations 39 5.2 Suggestions for Future Research 40 REFERENCES 42 iii LIST OF FIGURES -
Angular, Or Rotational Motion
Chapter 8 Angular, or Rotational Motion The radian There are 2 types of pure unmixed motion: n Translational - linear motion n Rotational - motion involving a rotation or revolution around a fixed chosen axis (an axis which does not move). We need a system that defines BOTH types of motion working together on a system. Rotational quantities are usually defined with units involving a radian measure. If we take the radius of a circle and LAY IT DOWN on the circumference, it will create an angle whose arc length is equal to R. In other words, one radian angle subtends an arc length Ds equal to the radius of the circle (R) Angular Quantities In purely rotational motion, all points on the object move in circles around the axis of rotation (“O”). The radius of the circle is r. Note that all points on a straight line drawn through the axis move through the same angle in the same time. s The angle θ is 1 radian if the arc length is equal to the radius. Therefore, The radian Half a radian would subtend an arc length, s, equal to half the radius, and 2 radians would subtend an arc length equal to two times the radius. A general Radian Angle (Dq) subtends an arc length (Ds) equal to R. The theta in this case represents ANGULAR DISPLACEMENT. Angular Velocity Since velocity is defined as the rate of change of displacement, ANGULAR VELOCITY is defined as the rate of change of ANGULAR DISPLACEMENT. Angular Acceleration Once again, following the same lines of logic… Since acceleration is defined as the rate of change of velocity, we can say the ANGULAR ACCELERATION is defined as the rate of change of the angular velocity. -
Circular Motion
Lecture 6 Circular Motion Pre-reading: KJF §6.1 and 6.2 Please log in to Socrative, room HMJPHYS1002 CIRCULAR MOTION KJF §6.1–6.4 Angular position If an object moves in a circle of radius r, then after travelling a distance s it has moved an angular displacement θ: s θ = r θ is measured in radians (2π radians = 360°) KJF §3.8 3 Tangential velocity If motion is uniform and object takes time t to execute motion, then it has tangential velocity of magnitude v given by s v = t Period of motion T = time to complete one revolution (units: s) Frequency f = number of revolutions per second (units: s–1 or Hz) 1 f = T 4 Angular velocity Define an angular velocity ω angular displacement θ ω = = time interval t Uniform circular motion is when ω is constant. Combining last 3 equations: v = rω 2π T = period ω KJF §6.1 5 Question You place a beetle on a uniformly rotating record (a) Is the beetle's tangential velocity different or the same at different radial positions? (b)Is the beetle's angular velocity different or the same at the different radial positions? Remember; all points on a rigid rotating object will experience the same angular velocity 6 Consider an object is moving in uniform circular motion – tangential speed is constant. Is the object accelerating? Velocity is a vector ∴ changing direction ⇒ acceleration ⇒ net force 7 The change in velocity Δv = v2 – v1 and Δv points towards the centre of the circle Angle between velocity vectors is θ so Δv = vθ and so ∆v vθ v2 a = = = ∆t rθ/v r KJF §3.8 8 Centripetal acceleration Acceleration points towards centre – centripetal acceleration ac v2 a = = ω2r c r Since the object is accelerating, there must be a force to keep it moving in a circle mv2 F = = mω2r c r This centripetal force may be provided by friction, tension in a string, gravity etc. -
Open JDHPHD.Pdf
The Pennsylvania State University The Graduate School College of Health and Human Development A KINEMATIC AND KINETIC ANALYSIS OF POSTURAL PERTURBATION A Thesis in Exercise and Sport Science by John D. Henley Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy May 2002 We approve the thesis of John D. Henley. Date of Signature Peter R. Cavanagh Distinguished Professor of Locomotion Studies, Medicine, Orthopedics and Rehabilitation, and Biobehavioral Health Thesis Advisor Chair of Committee R. Scott Kretchmar Professor of Exercise and Sport Science Interim Head of the Department of Kinesiology Karl M. Newell Professor of Kinesiology and Biobehavioral Health H. Joseph Sommer III Professor of Mechanical Engineering Vladimir Zatsiorsky Professor of Kinesiology iii Abstract This study was designed to quantify postural reaction to a sudden toe-up rotational perturbation by twenty-two healthy young adults (eleven males, eleven females, average age of 26 years, height of 1.72 m, and weight of 649.62 N) with no physical or physiological conditions that would compromise their ability to react to the perturbation. The goal was to achieve an understanding of the mechanical requirements necessary for maintenance of balance and stance. The human body was modeled as a system of five rigid segments. The act of reacting to a movement of the ground that suddenly dorsiflexed the ankle was monitored by a video analysis system operating at 60 Hz. Special care was taken to maximize marker resolution by covering the action with several cameras each zoomed in on part of the body. Segmental kinematics and kinetics were calculated after numerically filtering at 6 Hz and differentiating the digitized location of retroreflective markers attached to the subjects’ skin. -
Green Infrastructure
Cities Alive 12th Annual Green Roof & Wall Conference Rethinking Green Infrastructure Brad Bass Great Lakes Issues & Management Reporting Section Environment Canada PresencePresence ofof algalalgal bloomsblooms andand hypoxichypoxic eventsevents havehave renewedrenewed interestinterest inin quantifyingquantifying phosphorousphosphorous loadsloads andand dynamicsdynamics inin thethe LakeLake ErieErie basinbasin Actual LID Installed Comparison of Green Infrastructure Usage Established Urban forests Interest in Sustainable municipal Permeable Rai n Downspout / wetlands / learning more Infiltration Tree City Green roof Rain gardens Bi oswales street Bioretention programs and pavement barrels disconnection natural space about green planters cover design funding protection infrastructure Canada Toronto London St. Catherines Niagara Falls Hamilton Owen Sound Kingston Guel ph Windsor Waterloo Uni ted States Portland, Oregon Chicago, Illinois New York City, New York Observations of Green Infrastructure Percentage Removal Efficiency of Phosphorus, Apex NC International Stormwater Best Management Practices (BMP) Database Pollutant Category Summary: Nutrients. International Stormwater BMP Database, www.bmpdatabase.org. Observations of Green Infrastructure McElmurray, S.P., Confessor, R., and Richards, R.P. (2013). Reducing Phosphorus Loads to Lake Erie: Best Management Practices Literature Review. Prepared for the International Joint Commission. Total P removal Total P removal was observed in was observed in <15% of 55% of detention