Chapter 2 Linear Kinematics

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13 Νοε 2013 (πριν από 3 χρόνια και 8 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



= 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 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