Angular Kinematics

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Angular Kinematics

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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

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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?

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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

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Measuring angles

Angle = 2 sides that intersect at a vertex

Measure of angle and change in angle position = quantitative kinematic analysis

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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

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Angles

Anatomical position ALL joint angles = 0°

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Angles

Absolute angle uses: Trunk inclination in a runner

Technique ? Effect on required

extensor torque

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Angular Kinematics

Angular relationships

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Angular Relationships

Similar relationships as linear Units of measure differ

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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°

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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?

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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?

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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

+

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Degrees, rads & revolutions

90 degrees 180 degrees 270 degrees

/2 radians radians 3/2 radians

¼ revolution ½ revolution ¾ revolution

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Angular speed & velocity

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

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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

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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

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Angular acceleration

Rate of change of angular velocity

= /t

Units: °/s2, rad/s2, rev/s2

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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

1

2 2

1s1

s2

r1

r2

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Relationships between linear & angular displacement

Formulas = 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

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Relationships between linear & angular velocity

Similar relationshipv = r

v = tangential velocityr = radius of rotation = angular velocity

**rads are not balanced on both sides of the equation

20 cm

30 cm

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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

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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

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Relationships between linear & angular acceleration

Tangential:at = v2 – v1/tat = r

Radial:ar = v2/r