KIN 3309 1nd Edition Lecture 14 Outline of Last Lecture I. Angular KinematicsII. Rotational MotionIII. General MotionIV. Instantaneous Center of RotationV. Components of an AngleVI. Measuring AnglesVII. What is a Radian?VIII. Angular VariablesIX. ConversionsX. Types of AnglesXI. Lower Extremity Joint AnglesXII. Segment Angle vs. Joint AngleXIII. Rear Foot AngleXIV. Angular Position, Distance, DisplacementXV. Angular VelocityXVI. Angular Motion VectorsXVII. Angular AccelerationXVIII. Finite DifferentiationXIX. QuizOutline of Current Lecture I. Angular KinematicsII. Types of AnglesIII. Calculating Absolute AnglesIV. Calculating Relative AnglesV. Angular Position, Distance, DisplacementVI. Angular Motion VectorsVII. Angular and Linear MotionVIII. Angular and Linear VelocityIX. Tangential VelocityX. Maximize Linear Velocity?XI. Tangential AccelerationXII. Centripetal (radial) AccelerationXIII. Angle-Angle DiagramsThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.XIV. QuizCurrent LectureI. Angular Kinematicsa. Angular kinematics deals with angular motionII. Types of Anglesa. Absolute Angles vs. Relative AnglesIII. Calculating Absolute Anglesa. Absolute angles can be calculated from the endpoint coordinates by using the arctangent (inverse tangent) functionIV. Calculating Relative Anglesa. 1) Law of Cosinesi. Useful if the segment lengths are knownb. 2) Calculated from two absolute anglesi. Useful if the absolute angles are knownV. Angular Position, Distance, Displacementa. Angular positioni. An objects position relative to a defined spatial reference systemb. Angular distancei. The length of the angular path taken along a path c. Angular displacementi. The change in angular positionii. A vectord. Analogous to linear distance and displacementVI. Angular Motion Vectorsa. The right hand rule is used to determine the direction of angular motionVII. Angular and Linear Motiona. Consider an arm rotating about the shoulderb. Point b on the arm moves through a greater distance than point a, but the time of movement is the samei. Therefore, the linear velocity of point b is greater than point ac. The magnitude of this linear velocity is related to the distance from the axis of rotationd. All points on the forearm travel through the same angle (angular displacement)e. Each point travels through a different linear displacementf. One radian is the angle at the center of a circle described by an arc equal to the length of the radiusg. The linear displacement can be determined when the length of the segment (radius) and the angular displacement are knowni. r = distance from axis of rotation(Radius)ii. theta = angular displacement VIII. Angular and Linear Velocitya. The linear velocity can be determined when the length of the segment (radius) and the angular velocity are knowni. r = distance from axis of rotation (radius)ii. omega = angular velocityIX. Tangential Velocitya. The direction of the linear velocity is tangent to the curved pati. v is actually the “tangential velocity”ii. Hence, the subscript t is added to the v termX. Maximize Linear Velocity?a. Larger angular velocities (omega) and/or larger radii (r) will maximize tangential velocityi. Golf clubs vary in length to allow the same angular velocity to produce different club head linear velocitiesii. Club head speed is crucial for this sticking activityXI. Tangential Accelerationa. Similarly, tangential acceleration:i. r = distance from axis of rotation (radius)ii. alpha = angular accelerationXII. Centripetal (radial) Accelerationa. Even at constant angular velocities, the direction of the linear velocity changes when going around a curveb. Since velocity is changing, there must be accelerationc. This acceleration is towards the center of rotationi. Called centripetal accelerationd. Note that the units for linear acceleration m/s2 can only result if radian based units are usedXIII. Angle-Angle Diagramsa. Most graphical representation of human movement plot some parameter againsttimeb. However, activities like running are cyclic, and it can be useful to plot the relationship between two angles during the movementXIV. Quiza.b. What is true of a cyclist’s pedals?i. The angular velocity is zero if his angular acceleration is zero (angular velocity can be positive or negative)ii. The angular displacement is always equal to the angular distance traveled(angular displacement is changes in angular position)iii. The angular distance is always greater than or equal to the angular displacementiv. Cetripetal acceleration always points away from the axis of rotationc. A hockey stick 1.1 m long completes a swing in 0.15 seconds through a range of 85 degrees. Assume a uniform angular velocity.i. What is the average angular velocity of the stick?1. 567 degrees per second2.ii. What is the linear distance moved by the end of the stick?1. 1.6 m2.iii. What is the tangential velocity of the end of the stick?1. 10.9 meters per second2.iv. What is the tangential acceleration of the end of the stick?1. r times alpha (angular acceleration)2. how do we get angular acceleration? Angular velocity is constantlyincreasing. Average 3. 145.12