KIN 3309 1nd Edition Lecture 14 Outline of Last Lecture I II III IV V VI VII VIII IX X XI XII XIII XIV XV XVI XVII XVIII XIX Angular Kinematics Rotational Motion General Motion Instantaneous Center of Rotation Components of an Angle Measuring Angles What is a Radian Angular Variables Conversions Types of Angles Lower Extremity Joint Angles Segment Angle vs Joint Angle Rear Foot Angle Angular Position Distance Displacement Angular Velocity Angular Motion Vectors Angular Acceleration Finite Differentiation Quiz Outline of Current Lecture I Angular Kinematics II Types of Angles III Calculating Absolute Angles IV Calculating Relative Angles V Angular Position Distance Displacement VI Angular Motion Vectors VII Angular and Linear Motion VIII Angular and Linear Velocity IX Tangential Velocity X Maximize Linear Velocity XI Tangential Acceleration XII Centripetal radial Acceleration XIII Angle Angle Diagrams These 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 Quiz Current Lecture I Angular Kinematics a Angular kinematics deals with angular motion II Types of Angles a Absolute Angles vs Relative Angles III Calculating Absolute Angles a Absolute angles can be calculated from the endpoint coordinates by using the arctangent inverse tangent function IV Calculating Relative Angles a 1 Law of Cosines i Useful if the segment lengths are known b 2 Calculated from two absolute angles i Useful if the absolute angles are known V Angular Position Distance Displacement a Angular position i An objects position relative to a defined spatial reference system b Angular distance i The length of the angular path taken along a path c Angular displacement i The change in angular position ii A vector d Analogous to linear distance and displacement VI Angular Motion Vectors a The right hand rule is used to determine the direction of angular motion VII Angular and Linear Motion a Consider an arm rotating about the shoulder b Point b on the arm moves through a greater distance than point a but the time of movement is the same i Therefore the linear velocity of point b is greater than point a c The magnitude of this linear velocity is related to the distance from the axis of rotation d All points on the forearm travel through the same angle angular displacement e Each point travels through a different linear displacement f One radian is the angle at the center of a circle described by an arc equal to the length of the radius g The linear displacement can be determined when the length of the segment radius and the angular displacement are known i r distance from axis of rotation Radius ii theta angular displacement VIII Angular and Linear Velocity a The linear velocity can be determined when the length of the segment radius and the angular velocity are known i r distance from axis of rotation radius ii omega angular velocity IX Tangential Velocity a The direction of the linear velocity is tangent to the curved pat i v is actually the tangential velocity ii Hence the subscript t is added to the v term X Maximize Linear Velocity a Larger angular velocities omega and or larger radii r will maximize tangential velocity i Golf clubs vary in length to allow the same angular velocity to produce different club head linear velocities ii Club head speed is crucial for this sticking activity XI Tangential Acceleration a Similarly tangential acceleration i r distance from axis of rotation radius ii alpha angular acceleration XII Centripetal radial Acceleration a Even at constant angular velocities the direction of the linear velocity changes when going around a curve b Since velocity is changing there must be acceleration c This acceleration is towards the center of rotation i Called centripetal acceleration d Note that the units for linear acceleration m s2 can only result if radian based units are used XIII Angle Angle Diagrams a Most graphical representation of human movement plot some parameter against time b However activities like running are cyclic and it can be useful to plot the relationship between two angles during the movement XIV Quiz a 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 displacement iv Cetripetal acceleration always points away from the axis of rotation c 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 second 2 ii What is the linear distance moved by the end of the stick 1 1 6 m 2 iii What is the tangential velocity of the end of the stick 1 10 9 meters per second 2 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 constantly increasing Average 3 145 12 m s2 4 5