LINEAR KINEMATICS

DESCRIBING OBJECTS IN MOTION

Chapter 2

Define Motion:

Motion is a change in position over a period of time.

Space and Time

Types of Motion

Linear Motion (translation) all points on the body move

the same distance in the same direction at the same time

Rectilinear and Curvilinear

Linear Motion

Rectilinear Translation: straight line figure skater gliding across the ice

Linear Motion

Curvilinear Motion: curved line free-fall in sky-diving

Simultaneous motion in x & y directions• Horizontal and vertical motion superimposed

Types of Motion

Angular Motion (rotation) All points on the body move

through the same angle Whole body rotation

giant swing, pirouette Segment rotation

flexion, abduction, …

Types of Motion

General Motion combines angular & linear motion most common

pedaling a bike walking drawing a straight line

Large Motions

Large Motions

Small Movement

Linear Kinematics

Study of the time and space factors of motion

Linear Kinematic Quantities

Kinematics is the form, pattern, or sequencing of movement with respect to time.

Kinematics spans both qualitative and quantitative form of analysis.

Linear Kinematic Quantities

For example, qualitatively describing the kinematics of a soccer kick entails identifying the major joint actions,

including hip flexion, knee extension, and possibly plantar flexion at the ankle.

Linear Kinematic Quantities

A more detailed qualitative kinematic analysis might also describe the precise sequencing and timing of body segment movements, which translates to the degree of skill evident on the part of the kicker.

Linear Kinematic Quantities

Although most assessments of human movement are carried out qualitatively through visual observation, quantitative analysis is also sometimes appropriate.

Linear Kinematic Quantities

Physical therapists, for example, often measure the range of motion of an injured joint to help determine the extent to which range of motion exercises may be needed.

Linear Kinematic Quantities

When a coach measures an athlete's performance in the shot put or long jump, this too is a quantitative assessment.

Linear KinematicsDescription of Linear MotionHow far? What direction? How fast? Speeding up, slowing down?

Position

Identifying location in space At the start of movement? At the end of movement? At a specific time in the midst of movement?

Use a fixed reference point 1 dimension

starting line, finish line 2 dimension

Bloomington-Normal: north, east, south, west (goal line, sideline), (0,0), Cartesian coordinate system

Cartesian Coordinate System

X direction

Y direction

Z direction

(0,0,0)

Research & Gait Analysis

Linear Kinematic Quantities

Constructing a model performance.Scalar and vector quantities.

Linear Kinematic Quantities

Displacement - change in position.

Distance - distance covered and displacement may be equal for a given movement or distance may be greater than displacement, but the reverse is never true.

Vector & Scalar QuantitiesScalar: Fully defined by magnitude (how much)

Mass

Vector: Definition requires magnitude and direction Force

Distance and Displacement

Measuring change in positioncomponent of motion

Start and finish

Distance = 1/4 mile

Displacement = 0

Distance and Displacement

Another example:

Football player (fig 2.2, p 51): receives kickoff at 5 yard line, 15 yards

from the left sidelineruns it back, dodging defenders over a

twisted 48 yard path, to 35 yard line, 5 yards from the left sideline

Distance and Displacement

Distancelength of path traveled: 48 yards

Displacementstraight line distance in a specified

directiony direction: yfinal - yinitial

x direction: xfinal - xinitial

Distance and Displacement

Resultant Displacementlength of path traveled in a straight line from initial position to final position y direction: yfinal - yinitial

x direction: xfinal - xinitial

Components ofresultant displacement

R2 = (x)2 + (y)2

Distance and Displacement

Resultant Displacementlength of path traveled in a straight line from initial position to final position y direction: yfinal - yinitial

x direction: xfinal - xinitial

Components ofresultant displacement

R2 = (x)2 + (y)2

= arctan (opposite / adjacent)

Bloomington to Chicago

Assign x & y coordinates to each of the markers (digitize)

Speed and Velocity

For human gait, speed is the product of stride length and stride frequency.

Runners traveling at a slow pace tend to increase velocity primarily by increasing SL.

At faster running speeds, recreational runners rely more on increasing SF to increase velocity.

Speed and Velocity

Most runners tend to choose a combination of stride length and SF that minimizes the physiological cost of running.

Speed and Velocity

The best male and female sprinters are distinguished from their less-skilled peers by extremely high SF and short ground contact times, although their SL are usually only average or slightly greater than average.

Speed and Velocity

In contrast, the fastest cross-country skiers have longer-than-average cycle lengths, with cycle rates that are only average.

Speed and Velocity

Pace is the inverse of speed.

Pace is presented as units of time divided by units of distance (6 min/mile)

Pace is the time taken to cover a given distance and is commonly quantified as minutes per km or mins. per mile.

Speed and Velocity

Acceleration - rate of change in velocity. Acceleration is 0 whenever velocity is constant.

Average velocity is calculated as the final displacement divided by the total time period.

Instantaneous velocity - occurring over a small period of time.

Speed and Velocity

Measuring rate of change in positionhow fast the body is moving

Speedscalar quantity

how fastSpeed =

time

distance meters

seconds

Examples

Who is the faster runner: Michael Johnson

100m in10.09s 200m in 19.32s (world record) 300m in 31.56 s 400m in 43.39s (world record)

Donovan Bailey (Maurice Greene) 50m in 5.56 s (world record)

http://www.runnersweb.com/running/fastestm.html

Instantaneous Speed

We have calculated average speeddistance by time to cover that distance

Maximum speed in a race? make the time interval very small 0.01 second or shorter

Speed and Velocity

Measuring rate of change in positionhow fast the body is moving

SpeedVelocity

vector quantity how fast in a specified directionvelocity =

time

displacement m

s

Example

Swimmer100 m race in 50 m pool24s and 25s splits

Calculate velocities & speeds first length, second length total race (lap)

Example

Football player (fig 2.2, p 54): receives kickoff at 5 yard line, 15 yards

from the left sidelineruns it back, dodging defenders over a

twisted 48 yard path, to 35 yard line, 5 yards from the left sideline

time is 6 secondsCalculate velocities & speeds

forward, side to side, resultant

Use speed to calculate time

Running at 4 m/s

How long to cover 2 m?

2 m ÷ 4 m/sec= .5 sec

QuizIf a body is traveling in the + direction and it undergoes a – acceleration, the body will ____________________.

If a body is traveling in the – direction and it undergoes a + acceleration, the body will ___________________.

Speed up or slow down

AccelerationQuantifying change of motion

speeding up or slowing down rate of change of velocity

Acceleration = velocity

time

vf - vi

tf - ti

=

Soft landing from 60 cm

80% 1RM BP, Narrow vs Wide Grip