Title: Chapter 10: Linear Kinematics of Human Movement
1Chapter 10Linear Kinematics of Human Movement
- Basic Biomechanics, 4th edition
- Susan J. Hall
- Presentation Created by
- TK Koesterer, Ph.D., ATC
- Humboldt State University
2Objectives
- Discuss the interrelationship among kinematic
variables - Correctly associate linear kinematic quantities
with their units of measure - Identify describe effects of factors governing
projectile trajectory - Explain why the horizontal and vertical
components of projectile motion are analyzed
separately - Distinguish between average instantaneous
quantities identify circumstance which each is
a quantity of interest
3Linear Kinematic Quantities
- Kinematics describes appearance of motion
- Kinetics study of forces associated with motion
- Linear kinematics involves the study of the
shape, form, pattern and sequencing of linear
movement through time - Qualitative major joint actions sequencing
- Quantitative Range of motion, forces, distance
etc.
4Distance Displacement
- Measured in units of length
- Metric meter, kilometer, centimeter, etc.
- English inch, foot, yard mile
- Distance
- Scalar quantity
- Linear displacement
- Vector quantity length direction (compass
directions, left, right, up, down, or positive
negative
5Speed Velocity
- Speed length (or distance)
- change in time
- Velocity (v) change in position ? position
- change in time
? time - v displacement d
- change in time ? t
6Speed Velocity
- Velocity position2 - position1
- time2 - time1
- Velocity is a vector quantity
- direction and magnitude of motion
- Laws of vector algebra
710-2
8Acceleration
- Acceleration (a) change in velocity ?v
- change in time
?t - a v2 - v1
- ?t
- When acceleration is zero, velocity is constant
9Positive/Negative Acceleration
10Average Instantaneous Quantities
- Instantaneous
- Instantaneous values
- Average
- Average velocity final displacement
- total
time
11Velocity Curve for Sprinting
12Velocity Curves for Two Sprinters
13Kinematics of Projectile Motion
- Bodies projected into the air are projectiles
- Horizontal Vertical Components
- Vertical is influenced by gravity
- No force (neglecting air resistance) affects the
horizontal - Horizontal relates to distance
- Vertical relates to maximum height achieved
14Kinematics of Projectile Motion Influence of
Gravity
- Major influence of vertical component
- Not the horizontal component
- Force of Gravity
- Constant, unchanging
- Negative acceleration (-9.81 m/s2)
- Apex
- The highest point in the trajectory
1510-6
16Kinematics of Projectile Motion Influence of Air
Resistance
- In a vacuum, horizontal speed of a projectile
remain constant - Air resistance affects the horizontal speed of a
projectile - This chapter, velocity will be regarded as
constant
17Factors Influencing Projectile Trajectory
- Trajectory
- Angle of projection
- Projection speed
- Relative height of projection
1810-9
19Factors Influencing Projectile Trajectory
- Angle of Projection
- General shapes
- Perfectly vertical
- Parabolic
- Perfectly horizontal
- Implications in sports
- Air resistance may cause irregularities
2010-10
21Factors Influencing Projectile Trajectory
- Projection speed
- Range
- Relative Projection Height
2210-14
23Optimum Projection Conditions
- Maximize the speed of projection
- Maximize release height
- Optimum angle of projection
- Release height 0, then angle 450
- ? Release height, then ? angle
- ? Release height, then ? angle
24Range at Various Angles
25Analyzing Projectile Motion
- Initial velocity
- Horizontal component is constant
- Horizontal acceleration 0
- Vertical component is constantly changing
- Vertical acceleration -9.81 m/s2
2610-17
27Equations of Constant Acceleration
- Galileos Laws of constant acceleration
- v2 v1 at
- D v1t ½at2
- V22 v21 2 ad
- d displacement v velocity
- a acceleration t time
- Subscript 1 2 represent first or initial and
second or final point in time
28Equations of Constant Acceleration
- Horizontal component a 0
- v2 v1
- D v1t
- V22 v21
-
29Equations of Constant Acceleration
- Vertical component a -9.81 m/s2
- v2 at
- D ½ at2
- V22 2ad
- Vertical component at apex v 0
- 0 v21 2ad
- 0 v1 at
30Goals for Projectiles
- Maximize range (shot put, long jump)
- Maximize total distance (golf)
- Optimize range and flight time (punt)
- Maximize height (vertical jump)
- Optimize height and range (high jump)
- Minimize flight time (baseball throw)
- Accuracy (basketball shot)
31Goals for Projectiles
- Maximize range (shot put, long jump)
- Shot put optimum angle is approximately 42
- Long jump theoretical optimum is approximately
43 however, due to human limits, the actual
angle for elite jumpers is approximately 20 - 22
32Goals for Projectiles
- Maximize total distance (golf)
- Because the total distance (flight plus roll) is
most important, trajectory angles are lower than
45 - Distance is controlled by the pitch of the club
- Driver 10
33Goals for Projectiles
- Optimize range and flight time (punt)
- Maximum range occurs with 45 trajectory
- Higher trajectory increases hang time with
minimal sacrifice in distance - Lower trajectory usually results in longer punt
returns - Less time for kicking team to get downfield to
cover the punt returner
34Goals for Projectiles
- Maximize height (vertical jump)
- Maximize height of COM at takeoff
- Maximize vertical velocity by exerting maximum
vertical force against ground.
35Goals for Projectiles
- Optimize height and range (high jump)
- Basic goal is to clear maximum height
- Horizontal velocity is necessary to carry jumper
over bar into pit - Typical takeoff velocity for elite high jumpers
is approximately 45
36Goals for Projectiles
- Minimize flight time (baseball throw)
- Baseball players use low trajectories (close to
horizontal) - Outfielders often throw the ball on one bounce
with minimal loss of velocity
37Goals for Projectiles
- Accuracy (basketball shot)
38Projecting for Accuracy
39Minimum Speed Trajectory
40Angle of Entry
41Margin for Error
42Free Throw Optimum Angle
43Summary
- Linear kinematics is the study of the form or
sequencing of linear motion with respect to time. - Linear kinematic quantities include the scalar
quantities of distance and speed, and the vector
quantities of displacement, velocity, and
acceleration. - Vector quantities or scalar equivalent may be
either an instantaneous or an average quantity
44Summary
- A projectile is a body in free fall that is
affected only by gravity and air resistance. - Projectile motion is analyzed in terms of its
horizontal and vertical components. - Vertical is affected by gravity
- Factors that determine the height distance of a
projectile are projection angle, projection
speed, and relative projection height - The equation for constant acceleration can be
used to quantitatively analyze projectile motion.
45The End