**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? • 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 +

**Degrees, rads & revolutions**

**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