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
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