# Chapter 2 Linear Kinematics

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13 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

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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 Kinematics

Description of Linear Motion

How 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 Quantities

Scalar
: Fully defined by
magnitude
(how much)

Mass

Vector
: Definition requires
magnitude

and
direction

Force

Distance and Displacement

Measuring
change in position

component 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 sideline

runs it back, dodging defenders over a twisted 48
yard path, to 35 yard line, 5 yards from the left
sideline

Distance and Displacement

Distance

length of path traveled: 48 yards

Displacement

straight line distance in a specified direction

y direction: y
final

-

y
initial

x direction: x
final

-

x
initial

Distance and Displacement

Resultant
Displacement

length of path traveled in a straight line
from initial position to final position

y direction: y
final

-

y
initial

x direction: x
final

-

x
initial

Components of

resultant displacement

R
2
= (

x)
2

+ (

y)
2

Distance and Displacement

Resultant

Displacement

length of path traveled in a straight line
from initial position to final position

y direction: y
final

-

y
initial

x direction: x
final

-

x
initial

Components of

resultant displacement

R
2
= (

x)
2

+ (

y)
2

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 position

how fast the body is moving

Speed

scalar quantity

how fast

Speed =

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 speed

distance 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 position

how fast the body is moving

Speed

Velocity

vector quantity

how fast
in a specified direction

velocity =

time

displacement

m

s

Example

Swimmer

100 m race in 50 m pool

24s 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 sideline

runs it back, dodging defenders over a twisted 48
yard path, to 35 yard line, 5 yards from the left
sideline

time is 6 seconds

Calculate 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

Quiz

If 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

Acceleration

Quantifying
change of motion

speeding up or slowing down

rate of change of velocity

Acceleration =

velocity

time

v
f

-

v
i

t
f

-

t
i

=

Soft landing from 60 cm

80% 1RM BP, Narrow vs Wide Grip