Angular Kinematics. Today…. Distinguish angular motion from linear Discuss the relationship among angular kinematic variables Examine the relationships between angular and linear displacement, velocity and acceleration. Introduction. Why is a driver longer than a 9 iron?
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Today…. • Distinguish angular motion from linear • Discuss the relationship among angular kinematic variables • Examine the relationships between angular and linear displacement, velocity and acceleration
Introduction • Why is a driver longer than a 9 iron? • Why do batters slide their hands up the handle of the bat to execute a bunt but not a power hit?
Angular motion • Most human movement involves rotation of body segment(s) • Gait = translation (linear) • Gait occurs because of rotational motions at the hip, knee & ankle
Measuring angles • Angle = 2 sides that intersect at a vertex • Measure of angle and change in angle position = quantitative kinematic analysis
Angles • Relative angle: angle at joint formed between long axes of adjacent body segments • Absolute angle: angular orientation of a segment with respect to a fixed line of reference • Angle of inclination of the trunk
Angles • Anatomical position • ALL joint angles = 0°
Angles • Absolute angle uses: • Trunk inclination in a runner • Technique • ? Effect on required extensor torque
Angular Kinematics Angular relationships
Angular Relationships • Similar relationships as linear • Units of measure differ
Angular distance & displacement • Pendulum swings through arc of 60° • Distance = ? • If swings back through 60° • Distance = ? • Angular distance is the sum of all angular changes of a rotating body 60°
Angular distance & displacement • Biceps curls: • 0° to 140° : distance = 140° • Return to 0° total distance = 280° • Repeat 10X total distance = 2800° What is the displacement?
Angular displacement • The change in angular position of a line/segment • The difference in the initial & final positions of the moving body • Biceps curl example: 0° – 140° & return • Displacement?
Angular displacement • Defined by magnitude and direction • Clockwise (-) & counterclockwise (+) • Flexion & extension terms as well • • Units • Degrees • Radian: 1 radian = 57.3° • Size of angle at the center of a circle by an arc equal in length to the radius • Often expressed in multiples of • Revolution: used in diving & gymnastics +
Angular speed Angular distance/time = / tf - ti Angular velocity Angular displacement / change in time = / tf – ti include positive or negative direction Units: °/s, rad/s, rpm Angular speed & velocity
Applications of angular velocity • Baseball pitchers: 6000+°/s during acceleration (IR) 4500+°/s elbow extension • Tennis racket: during serve: 2000°/s to 2200°/s • Skaters: # of revolutions determined by jump height or rotational velocity
Applications of angular velocity • Gymnasts: • Handsprings: 6.80 rad/s • Handspring w/somersault & ½ twist: 7.77 rad/s • Back layout: 10.2 rad/s
Angular acceleration • Rate of change of angular velocity = /t • Units: °/s2, rad/s2, rev/s2
Relationships between linear & angular displacement • The greater the radius between a given point on a rotating body and the axis or rotation…… …the greater the linear distance the point moves during angular motion s2 2 2 s1 1 1 r2 r1
Relationships between linear & angular displacement • Formula s = r r = radius of rotation = angular distance (in rads) **linear distance & radius of rotation must be in the same units of length **angular distance must be in rads
Relationships between linear & angular velocity • Similar relationship v = r v = tangential velocity r = radius of rotation = angular velocity **rads are not balanced on both sides of the equation 30 cm 20 cm
Relationships between linear & angular velocity …the greater the radius of rotation… ……the greater the linear velocity ? Length of implements vs weight of implements (control) Linear velocity of ball velocity of implement
Relationships between linear & angular acceleration • Two perpendicular linear acceleration components 1. Along path of angular motion (tangential acceleration) 2. Perpendicular to path of angular motion (radial acceleration) at ar
Relationships between linear & angular acceleration • Tangential: at = v2 – v1/t at = r • Radial: ar = v2/r