2 Questions to think about Why do batters slide their hands up the handle of the bat to lay down a bunt but not to drive the ball? Why might an athletic trainer or physical therapist want to measure the range of motion of a joint?
3 Angular Kinematics Angular motion: all parts of a body move through the same angle Angular kinematics deals with angular motion. Nearly all human movement involves rotation of body segments.
21 Instantaneous Center of Rotation The instantaneous joint center changes throughout any motion of the knee.
22 Measuring Angles An angle is at the intersection of two lines (and planes). Units of measurement Degrees (arbitrary units) Radians (fundamental ratio) Revolutions (one revolution = 360 o ) Circumference = 2πr; therefore, there are 2π radians in 360 o
24 Radians One radian is the angle at the center of a circle described by an arc equal to the length of the radius.
25 1 radian = 57.3 o Converting Angles 1 revolution = 360 o = 2 π radians θ(deg) = (180 / π) θ( rad) Examples: Convert 30 o to radians. Convert 4 radians to degrees.
26 Relative versus Absolute Angles Relative angle: the angle formed between two adjacent body segments (on right) Absolute angle: angular orientation of a single body segment with respect to a fixed line of reference (on left)
27 Absolute Angles Definition of the sagittal view absolute angles of the trunk, thigh, leg, and foot.
28 Rear Foot Angles Definition of the absolute angles of the leg and calcaneus in the frontal plane. These angles are used to constitute the rearfoot angle of the right foot.
29 Standard Reference Terminology Movements Angular - Circular movements around an axis of rotation. Unit of reference --> angle (degrees or radians). Rotation -turning of a bicycle wheel or limb segments around joints Axis of rotation >middle of circle >center of joint Def: imaginary line about which rotation occurs (pivot, hinge) origin
30 Circular Reference Terms Circumference (C=2πr) Radius (r) the distance from the axis of rotation to the perimeter of the circle Diameter (D) the distance between one side of a circle to the opposite going through the axis of rotation Arc A rotary distance between 2 angular positions Arclength curvilinear distance covered on the perimeter of an arc pi (π) =
31 Angular Velocity Angular velocity is the rate of change of angular displacement ω ω ω change in angular position = change in time θ f θi θ = = t t t f i = angular velocity in [ rad / s] θ = angular displacement in [ rad] t = time in  s
32 Example A therapist examines the range of motion of an athlete s knee joint. At full extension, the angle between the leg and thigh is 178 o. At full flexion, the angle between the leg and thigh is 82 o. The leg is moved between these two angles in 1.2 s. What is the angular velocity of the leg?
33 Example Figure skater Michelle Kwan performs a triple twisting jump. She rotates around her longitudinal axis three times while she is in the air. The time it takes to complete the jump from takeoff to landing is 0.8 s. What was Michelle s average angular velocity in twisting for this jump?
34 Angular Acceleration Angular acceleration is the rate of change of angular velocity. change in angular velocity α = change in time ω f ωi ω α = = t t t f i 2 α = angular accleration in [ rad / s ] ω = change in angular velocity in [ rad / s] t = time in  s
35 Example When Josh begins his discus throwing motion, he spins with an angular velocity of 5 rad/s. Just before he releases the discus, Josh s angular velocity is 25 rad/s. If the time from the beginning of the throw to just before release is 1 s, what is Josh s average angular acceleration?
36 Example Randy Johnson is pitching a fastball at a speed of 103 mph. At 0.2 sec into his throw, the angular velocity of the left elbow is 260 /sec. Two frames later, his elbow is extending at 1310 /sec. If the film speed is 30 frames/sec, what is the angular acceleration of the elbow joint?
37 Example Randy Johnson is pitching a fastball at a speed of 103 mph. At 0.2 sec into his throw, the angular velocity of the left elbow is 260 /sec. Two frames later, his elbow is extending at 1310 /sec. If the film speed is 30 frames/sec, what is the angular acceleration of the elbow joint? ω 2 A ω 1
38 Example A golf club is swung with an average angular acceleration of 1.5 rad/s 2. What is the angular velocity of the club when it strikes the ball at the end of a 0.8 s swing?
39 Linear and Angular Displacement s = linear distance = radius of rotation angular displacement s = r θ ( θ must be in radians)
40 Example If the arm segment has length 0.13 m and it rotates about the elbow an angular displacement of 0.23 radians, what is the linear distance traveled by the wrist?
41 Linear and Angular Velocity v = linear velocity = radius of rotation angular velocity v = r ω ( m / s) = ( m) ( rad / s)
42 Example Two baseballs are consecutively hit by a bat. The first ball is hit 25 cm from the bat s axis of rotation, and the second ball is hit 45 cm from the bat s axis of rotation. If the angular velocity of the bat was 35 rad/s at the instant that both balls were contacted, what was the linear velocity of the bat at the two contact points?
43 Example A tennis racket swung with an angular velocity of 12 rad/s strikes a motionless ball at a distance of 0.5 m from the axis of rotation. What is the linear velocity of the racket at the point of contact with the ball?
44 Linear and Angular Acceleration a = linear acceleration = radius of rotation angular acceleration a = r α m s = m rad s 2 2 ( / ) ( ) ( / )
45 Radial Acceleration Since linear velocity is a vector its direction will change even if the angular speed of an object is constant. The acceleration associated with the changing direction of the velocity vector is called radial acceleration or centripetal acceleration. a r 2 ( linear velocity) = radial acceleration = radius of rotation a r v = ( m/ s ) = r ( m/ s) m 2 2 2
46 Tangential and Centripetal Acceleration linear acceleration=tangential acceleration=a T radial acceleration=centripetal acceleration=a C
47 Example An individual is running around a turn with an 11 m radius at 3.75 m/s. What is the runner s centripetal acceleration?
48 Example A hammer thrower spins with an angular velocity of 1700 o /s. The distance from her axis of rotation to the hammer head is 1.2 m. a) What is the linear velocity of the hammer head? b) What is the centripetal acceleration of the hammer head? c) If the distance to the hammer head changes to 1.0 m does the centripetal acceleration increase or decrease?
Linear and Angular Kinematics (continued) 17 Relationship Between Linear and Angular Motion A very important feature of human motion... Segment rotations combine to produce linear motion of the whole body
Read a chapter on Angular Kinematics Angular Kinematics Hamill & Knutzen (Ch 9) Hay (Ch. 4), Hay & Ried (Ch. 10), Kreighbaum & Barthels (Module Ι) or Hall (Ch. 11) Reporting Angles Measurement of Angles
Linear and angular kinematics How far? Describing change in linear or angular position Distance (scalar): length of path Displacement (vector): difference between starting and finishing positions; independent
Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle
Relationships between linear and angular motion Body segment rotations combine to produce linear motion of the whole body or of a specific point on a body segment or implement Joint rotations create forces
Physics 1A Homework 9 Chapter 1 (part 1) 1.1) The following angles are given in degrees. Convert them to radians. 1. Picture the Problem: This is a units conversion problem. π radians Strategy: Multiply
Lecture 14 More on rotation Rotational Kinematics Rolling Motion Torque Cutnell+Johnson: 8.1-8.6, 9.1 More on rotation We ve done a little on rotation, discussing objects moving in a circle at constant
Lecture Presentation Chapter 7 Rotational Motion Suggested Videos for Chapter 7 Prelecture Videos Describing Rotational Motion Moment of Inertia and Center of Gravity Newton s Second Law for Rotation Class
Angular velocity Angular velocity measures how quickly the object is rotating. Average angular velocity Instantaneous angular velocity Two coins rotate on a turntable. Coin B is twice as far from the axis
PSI AP Physics I Rotational Motion Multiple-Choice questions 1. Which of the following is the unit for angular displacement? A. meters B. seconds C. radians D. radians per second 2. An object moves from
11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational
Week 7 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 7-0 Linear and Circular Motion Compared Slide 7- Linear and Circular Kinematics Compared Slide 7-
Section 6.1 Angle Measure An angle AOB consists of two rays R 1 and R 2 with a common vertex O (see the Figures below. We often interpret an angle as a rotation of the ray R 1 onto R 2. In this case, R
Circular Motion I. Circular Motion and Polar Coordinates A. Consider the motion of ball on a circle from point A to point B as shown below. We could describe the path of the ball in Cartesian coordinates
SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS This work covers elements of the syllabus for the Engineering Council exams C105 Mechanical and Structural Engineering
Mechanics of swinging a bat Rod Cross a Department of Physics, University of Sydney, Sydney NSW 26, Australia Received 3 June 28; accepted 27 August 28 Measurements on the swing of a baseball bat are analyzed
1206 - Concepts of Physics Wednesday, October 7th Center of mass Last class, we talked about collision - in many cases objects were interacting with each other - for examples two skaters pushing off. In
KINEMTICS OF PRTICLES RELTIVE MOTION WITH RESPECT TO TRNSLTING XES In the previous articles, we have described particle motion using coordinates with respect to fixed reference axes. The displacements,
Physics 111 Lecture 0 (Walker: 10.1-3) Rotational Motion Oct.19, 009 Rotational Motion Study rotational motion of solid object with fixed axis of rotation (axle) Have angular versions of the quantities
Q9.1 The graph shows the angular velocity and angular acceleration versus time for a rotating body. At which of the following times is the rotation speeding up at the greatest rate? A. t = 1 s B. t = 2
Basic Biomechanics the body as a living machine for locomotion What is Kinesiology? Kinesis: To move -ology: to study: The study of movement What the heck does that mean? Why do we need Kinesiology? As
Name: 1 Assessment of the basic motor skills Developmental change is observed for most skills in terms of the developmental steps or levels for each body component. The ability to assess the maturity of
Rotational Kinematics and Dynamics Name : Date : Level : Physics I Teacher : Kim Angular Displacement, Velocity, and Acceleration Review - A rigid object rotating about a fixed axis through O perpendicular
Hand Held Centripetal Force Kit PH110152 Experiment Guide Hand Held Centripetal Force Kit INTRODUCTION: This elegantly simple kit provides the necessary tools to discover properties of rotational dynamics.
ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION This tutorial covers pre-requisite material and should be skipped if you are
Centripetal Force 1 Introduction In classical mechanics, the dynamics of a point particle are described by Newton s 2nd law, F = m a, where F is the net force, m is the mass, and a is the acceleration.
Rotational Dynamics 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. All points on a straight line
November 5, 2007 Physics 1111 Quiz 8 Name SOLUTION 1. Express 27.5 o angle in radians. (27.5 o ) /(180 o ) = 0.480 rad 2. As the wind dies, a windmill that was rotating at 3.60 rad/s comes to a full stop
Ch 9 Rotation 9.1 Rotational Kinematics: Angular Velocity and Angular Acceleration Q: What is angular velocity? Angular speed? What symbols are used to denote each? What units are used? Q: What is linear
Linear Motion vs. Rotational Motion Linear motion involves an object moving from one point to another in a straight line. Rotational motion involves an object rotating about an axis. Examples include a
1. Two points, A and B, are on a disk that rotates about an axis. Point A is closer to the axis than point B. Which of the following is not true? A) Point B has the greater speed. B) Point A has the lesser
SOLID MECHANICS DYNAMICS TUTOIAL MOMENT OF INETIA This work covers elements of the following syllabi. Parts of the Engineering Council Graduate Diploma Exam D5 Dynamics of Mechanical Systems Parts of the
HW 7 Q 14,20,20,23 P 3,4,8,6,8 Chapter 7 Rotational Motion of the Object Dr. Armen Kocharian Axis of Rotation The radian is a unit of angular measure The radian can be defined as the arc length s along
Lesson 5 Rotational and Projectile Motion Introduction: Connecting Your Learning The previous lesson discussed momentum and energy. This lesson explores rotational and circular motion as well as the particular
Section.1 Radian Measure Another way of measuring angles is with radians. This allows us to write the trigonometric functions as functions of a real number, not just degrees. A central angle is an angle
physics 111N rotational motion rotations of a rigid body! suppose we have a body which rotates about some axis! we can define its orientation at any moment by an angle, θ (any point P will do) θ P physics
Acceleration Introduction: Acceleration is defined as the rate of change of velocity with respect to time, thus the concepts of velocity also apply to acceleration. In the velocity-time graph, acceleration
Chapter 4 Dynamics: Newton s Laws of Motion Units of Chapter 4 Force Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the NormalForce
5 ANGULAR MOTION 5.2 Rotational Kinematics, Moment of Inertia Name: 5.2 Rotational Kinematics, Moment of Inertia 5.2.1 Rotational Kinematics In (translational) kinematics, we started out with the position
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA FURTHER MECHANICAL PRINCIPLES AND APPLICATIONS UNIT 11 - NQF LEVEL 3 OUTCOME 3 - ROTATING SYSTEMS TUTORIAL 1 - ANGULAR MOTION CONTENT Be able to determine the characteristics
Chapter 9 Rotation of Rigid Bodies 1 Angular Velocity and Acceleration θ = s r (angular displacement) The natural units of θ is radians. Angular Velocity 1 rad = 360o 2π = 57.3o Usually we pick the z-axis
Math Review: Circular Motion 8.01 Position and Displacement r ( t) : position vector of an object moving in a circular orbit of radius R Δr ( t) : change in position between time t and time t+δt Position
1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always
CHAPTER 8 THE CIRCLE AND ITS PROPERTIES EXERCISE 118 Page 77 1. Calculate the length of the circumference of a circle of radius 7. cm. Circumference, c = r = (7.) = 45.4 cm. If the diameter of a circle
Spinning Stuff Review 1. A wheel (radius = 0.20 m) is mounted on a frictionless, horizontal axis. A light cord wrapped around the wheel supports a 0.50-kg object, as shown in the figure below. When released
End-of-Chapter Exercises Exercises 1 12 are conceptual questions that are designed to see if you have understood the main concepts of the chapter. 1. Figure 11.20 shows four different cases involving a
Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled
3-D Dynamics of Rigid Bodies Introduction of third dimension :: Third component of vectors representing force, linear velocity, linear acceleration, and linear momentum :: Two additional components for
Circular Motion Physics 1425 Lecture 18 Michael Fowler, UVa How Far is it Around a Circle? A regular hexagon (6 sides) can be made by putting together 6 equilateral triangles (all sides equal). The radius
Bat Speed Part 1 Adam Swayze January 14 th, 2008 Background Objective of hitting is to hit the ball hard this increases the chance of getting on base Velocity of batted ball is determined by Speed of pitch
Chapter 8: Rotational Motion Radians 1) 1 radian = angle subtended by an arc (l) whose length is equal to the radius (r) 2) q = l r r l Convert the following: a) 20 o to radians (0.35 rad) b) 20 o to revolutions
Circular motion & relative velocity Announcements: Prelectures from smartphysics are now being counted. Tutorials tomorrow pages 13-17 in red book. CAPA due Friday at 10pm Web page: http://www.colorado.edu/physics/phys1110/phys1110_sp12/
RIGID BODY MOTION: TRANSLATION & ROTATION (Sections 16.1-16.3) Today s Objectives : Students will be able to analyze the kinematics of a rigid body undergoing planar translation or rotation about a fixed
Phys 111 Fall 2012 Course structure Five sections lecture time 150 minutes per week Textbook Physics by James S. Walker fourth edition (Pearson) Clickers recommended Coursework Complete assignments from
Phys 201 Fall 2009 Thursday, September 17, 2009 & Tuesday, September 19, 2009 Chapter 3: Mo?on in Two and Three Dimensions Displacement, Velocity and Acceleration Displacement describes the location of
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Physics 8.01T Fall Term 2004 Practice Exam Three Solutions Problem 1a) (5 points) Collisions and Center of Mass Reference Frame In the lab frame,
Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular
Angular Velocity Announcements: Midterm on Thursday at 7:30pm! Old exams available on website. Chapters 6 9 are covered. Go to same room as last time. You are allowed one calculator and one doublesided
Chapter 10: Linear Kinematics of Human Movement Basic Biomechanics, 4 th edition Susan J. Hall Presentation Created by TK Koesterer, Ph.D., ATC Humboldt State University Objectives Discuss the interrelationship
Unit 1 - Radian and Degree Measure Classwork Definitions to know: Trigonometry triangle measurement Initial side, terminal side - starting and ending Position of the ray Standard position origin if the
Unit 60: Dynamics of Machines Unit code: H/601/1411 QCF Level:4 Credit value:15 OUTCOME 2 KINEMATICS AND DYNAMICS TUTORIAL 2 PLANE MECHANISMS 2 Be able to determine the kinetic and dynamic parameters of
Rotational Motion 1. 2 600 rev/min is equivalent to which of the following? a. 2600 rad/s c. 273 rad/s b. 43.3 rad/s d. 60 rad/s 2. A grindstone spinning at the rate of 8.3 rev/s has what approximate angular
I. Throwing Warm-up a. Grip softball on seams b. One knee wrist snaps i. Right knee should be down ii. Make sure elbow is level with or above shoulder iii. Glove hand can support under elbow iv. Fingers
Linear and Rotational Kinematics Starting from rest, a disk takes 10 revolutions to reach an angular velocity. If the angular acceleration is constant throughout, how many additional revolutions are required
Conversion Factors Most scientific measurements and calculations make use of the SI (metric) system of units. The English system of units is more commonly used by baseball and softball fans. Some useful
INSTANTANEOUS CENTER (IC) OF ZERO VELOCITY (Section 16.6) Today s Objectives: Students will be able to: a) Locate the instantaneous center (IC) of zero velocity. b) Use the IC to determine the velocity
PHYS 101-4M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in
Physics 160 Biomechanics Projectiles What is a Projectile? A body in free fall that is subject only to the forces of gravity and air resistance. Air resistance can often be ignored in shot-put, long jump
NEWTON S LAWS OF MOTION Background: Aristotle believed that the natural state of motion for objects on the earth was one of rest. In other words, objects needed a force to be kept in motion. Galileo studied
Unit - Radian and Degree Measure Classwork Definitions to know: Trigonometry triangle measurement Initial side, terminal side - starting and ending Position of the ray Standard position origin if the vertex,
The Big Idea The third conservation law is conservation of angular momentum. This can be roughly understood as spin, more accurately it is rotational velocity multiplied by rotational inertia. In any closed
CS W4733 NOTES - Differential Drive Robots Note: these notes were compiled from Dudek and Jenkin, Computational Principles of Mobile Robotics. 1 Differential Drive Kinematics Many mobile robots use a drive
Osteokinematics (how the bones move) & Arthrokinematics (how the joints move) Planes & Axes Planes of Action = Three fixed lines of reference along which the body is divided. Each plane is at right angles
1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate
Physics 2A Chapter 3: Kinematics in Two Dimensions The only thing in life that is achieved without effort is failure. Source unknown "We are what we repeatedly do. Excellence, therefore, is not an act,
Experiment 2 24 Kuwait University Physics 105 Physics Department Determination of Acceleration due to Gravity Introduction In this experiment the acceleration due to gravity (g) is determined using two
Your consent to our cookies if you continue to use this website.