Chapter 14
Angular Kinetics of
Human Movement
PET 4340 BIOMECHANICS
Learning Objectives
Identify the angular analogues of mass, force,
momentum, and impulse
Explain why changes in the configuration of a
rotating airborne body can produce changes in
the body’s angular velocity
Identify and provide examples of the angular
analogues of Newton’s laws of motion
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Learning Objectives:
Define centripetal force and explain where and
how it acts
Solve quantitative problems relating to the
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factors that cause or modify angular motion
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Resistance to Angular Acceleration
What is moment of inertia?
•
The inertial property for rotating bodies representing resistance to
angular acceleration; based on both mass and the distance the
mass is distributed from the axis of rotation
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Resistance to Angular Acceleration:
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Moment of inertia is the sum of the products of each
particle’s mass, m, and the radius of rotation, r, for that
particle squared
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Resistance to Angular Acceleration;
Although both bats have the same mass, bat A is harder to
swing than bat B because the weight ring on it is positioned
farther from the axis of rotation
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Resistance to Angular Acceleration’
What is the radius of gyration?
• Distance from the axis of rotation to a point where the body’s mass
could be concentrated without altering its rotational characteristics
• When the moment of inertia for a body of known mass has been
assessed, the value may be characterized using the following
formula:
•
k is a distance known as the radius of gyration
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Resistance to Angular Acceleration.
Knee angle affects the moment of inertia of the swinging leg
with respect to the hip because of changes in the radius of
gyration for the lower leg, k2, and foot, k3
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Resistance to Angular Acceleration,
©Lori Adamski Peek/The Image Bank/Getty Images
During sprinting, extreme flexion at the knee reduces the
moment of inertia of the swinging leg
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I=mk2
https://www.youtube.com/watch?v=PH3cHxXAK0
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Resistance to Angular Acceleration..
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©Photodisc/Getty Images
The ratio of muscular strength, that is the ability to produce
torque at a joint, to segmental moments of inertia, that is the
resistance to rotation at a joint, is important for performance
capability in gymnastic events
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Resistance to Angular Acceleration…
Principal moments of inertia of the human body in different
positions with respect to different principal axes
• Principal axis
• Moment of inertia in kilograms per meter squared
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Stature Contrast
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Angular Momentum
What is angular momentum?
• Quantity of angular motion possessed by a body
• Measured as the product of moment of inertia and angular
velocity:
• As mass or angular velocity increases, angular momentum increases
proportionally
•
•
A factor that influences angular momentum is the distribution of
mass with respect to the axis of rotation
Angular momentum is proportional to the square of the radius of
gyration
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Angular Momentum:
Angular momentum of the swinging leg is the sum of the local
term, Is s, and the remote term, mr2 g
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Angular Momentum, 3
What is the principle of conservation of angular momentum?
• When gravity is the only acting external force, angular momentum
is conserved
• The total angular momentum of a given system remains constant in
the absence of external torques
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Angular Momentum, 4
When angular momentum is conserved, changes in body
configuration produce a trade-off between moment of inertia
and angular velocity, with a tuck position producing greater
angular velocity
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Backflip example
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Angular Momentum in the Long Jump
Htotal = Htrunk+head + Harms + Hlegs = constant
CW
To prevent trunk+head from rotating forward (CW)
rotate arms and legs CW to account for Htotal
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Iarms and Ilegs are smaller than Itotal so
warms and wlegs must be larger to produce
H’s large enough to accommodate Htotal
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Angular Momentum, 5
During the airborne execution of
a spike in volleyball, a
compensatory rotation of the
lower extremity offsets the
forceful swinging arm so that
total body angular momentum is
conserved
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Angular Momentum;
A skillful human performer can
rotate 180 degrees or more in the
air with zero angular momentum
because in a piked position, there
is a large discrepancy between
the radii of gyration for the upper
and lower extremities with
respect to the longitudinal axes of
these two major body segments
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Cat Twist
• Can be initiated with ZERO angular
momentum
• Must be flexed at waist
• Twist by rotating one part of the body that has
reduced rotary inertia against another which
has higher rotary inertia
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Initiation of Rotation in Air
Newton’s Laws specifically
state that you can NOT
initiate rotation (e.g. in the
air) without an external torque
being applied to you
So -- can you initiate rotation
while airborne?
A cat does! (seemingly)
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Angular Momentum’
What produces change in angular momentum?
• Angular impulse: Change in angular momentum equal to the
product of torque and time interval over which the torque acts:
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Angular Momentum.
The product of the springboard reaction force, F, and its moment
arm with respect to the driver’s center of gravity, d , creates a
torque, which generates the angular impulse that produces the
driver’s angular momentum at takeoff
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Angular Momentum,
©Susan Hall
The arm swing during takeoff contributes significantly to the diver’s
angular momentum
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Angular Momentum..
©Susan Hall
The surface reaction force is used by the dancer to generate angular
momentum during the takeoff of the tour jeté.
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Angular Analogues of Linear Kinematic
Quantities
What are the angular equivalents of linear kinematic quantities?
Linear
Mass, m
Force, F
Angular
Moment of inertia, I
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Torque, T
Momentum, M
Angular Momentum, H
Impulse, Ft
Angular Impulse, Tt
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Angular Analogues of Newton’s Laws
What is the angular law of inertia?
• A rotating body will maintain a state of constant rotational motion
unless acted on by an external torque
I = mk2
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Angular Analogues of Newton’s Laws:
What is the angular law of acceleration?
• A net torque produces angular acceleration of a body that is:
•
•
•
Directly proportional to the magnitude of the torque
In the same direction as the torque
Inversely proportional to the body’s moment of inertia
F = ma T = Iα
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Angular Analogues of Newton’s Laws;
What is the angular law of reaction?
• For every angular action, there is an equal and opposite
angular reaction exerted by the second body on the first
Fa = Fb
Ta = Tb
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Centripetal Force
What is centripetal force?
•
Force directed toward the center of rotation for a
body in rotational motion
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Centripetal Force;
Cyclists and runners lean into a curve to offset the torque created
by centripetal force acting on the base of support
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Centripetal Force:
Free body diagram of a cyclist
on a curve
RH is centripetal force
When the cyclist is balanced,
summing torques at the
cyclist’s center of gravity:
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Chapter 15
Human Movement in a
Fluid Medium
PET 4340 BIOMECHANICS
Learning Objectives
Explain the ways in which the composition and
flow characteristics of a fluid affect fluid forces
Define buoyancy and explain the variables that
determine whether a human body will float
Define drag, identify the components of drag,
and identify the factors that affect the magnitude
of each component
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distribution without the prior written consent of McGraw-Hill Education.
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Learning Objectives;
Define lift and explain the ways in which it can
be generated
Discuss the theories
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regarding propulsion of the
human body in swimming
Understand the forces produced by both air and
water and their differences
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What is Fluid Mechanics?
• Fluid Mechanics is the branch of mechanics
dealing with the properties and behavior of
gases and liquids.
– Important role in consideration of human
movement
– Athletes and/or objects encounter fluids (air/water)
– These fluids “Flow” around the athlete or object
• Forces created by this “Flow” can produce:
Drag,Copyright
Lift,© 2019
Buoyancy,
Spin
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Skiing examples
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Fluid Forces
• Air and Water exert similar forces
– Water almost 800 times denser than air
– Virtually incompressible. Pressure increases w/depth
• Forces exerted by both air and water:
– Hydrostatic Pressure – exerted by the wt. of a fluid
• Directly related to buoyancy
– Buoyancy – force opposing gravity, acting on object
partially or fully immersed in liquid or gas
– Drag – force opposing motion through a fluid
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– Lift – force
acting perpendicularly to motion that 15-‹#›
Hydrostatic Pressure in Air
• Hydrostatic Pressure
• Pressure – force per unit area
• Force exerted by a fluid when supporting its
own weight
• Directly related to buoyancy
• Atmospheric pressure – gravity’s pull on the
atmosphere
– Greatest pressure at sea level, less at altitude
– 14.7 psi
(pounds per square inch)
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Hydrostatic Pressure in H20
• Water more dense than air (800 times more)
• Pressure increases with depth
• Pressure increases by 1 atmosphere (14.7 psi)
for every 10m (33 ft.)
Ex. At 10m depth => (14.7psi x 2) = 29.4 psi
20m depth => (14.7psi x 3) = 44.1 psi
30m depth => (14.7 psi x 4) = 58.8 psi
Sinuses, lungs and inner ear affected most
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Pressure
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Hydrostatic Pressure in H20;
• As divers descend in the ocean, the air
regulators balance the air pressure in
their lungs with that of the oceans
depth.
• At 10m air is reduced to ½ that at
surface
• At 20m air is reduced to 1/3 that of
surface
• At 30m air is reduced to ¼ that of
surface volume
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Oh The Pressure!
• “Don’t hold your breath”
– @ 20m one lungful of air becomes 3 at surface
– Result of ascent holding breath ..pulmonary embolism
• Nitrogen narcosis – high concentrations in blood due to
extreme depths
– Affects CNS, memory loss, inebriation affects
• “The Bends” – diver crippled and bent over
– Nitrogen goes from liquid to bubbles at depth, must be
expired slowly or become lodged in joints, muscles and
other tissues.
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Buoyancy: Air and Water
• Buoyant Force – vertical force exerted on an object
immersed in a fluid
• Always acts upwards
• Air - Object filled with air less dense than
surrounding fluid
– Ex. Blimp or hot air balloon (Helium filled)
• Water – extension of hydrostatic pressure
– Greater pressure with depth => more powerful upward
force pushing on object from below
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Archimedes’ Principle
• Greek mathematician
• AP states that “the buoyant force acting on an object is equal to
the weight of the fluid that the object displaces”
• Whether or not something floats is determined by:
– the volume of the object immersed
– the weight of the object compared to the weight of the
same volume of water
• Density (mass : volume)
• Where, Fb = buoyant force
Vd = displaced fluid volume
= fluid specific weight
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Buoyancy, 2
What is Archimedes’ principle?
•
A physical law stating that the buoyant force acting
on a body is equal to the weight of the fluid
displaced by the body
• Where, Fb = buoyant force
Vd = displaced fluid volume
= fluid specific weight
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Different sized ships
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Buoyant Forces
Other Factors:
Temperature of water
Warmer water => less density=> less
floatation
Colder water => more dense=>more
floatation
Type of water
Salt water => more dense => more floatation
Fresh water => less dense > less floatation
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Sensory Deprivation
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Buoyancy of the Human Body
• Specific Gravity is the ratio of the weight of an
object divided by the weight of the same
volume of water
– An object with specific gravity less than 1.0 will
float
• Muscle and bone is very dense (>1.0) while fat is less
dense (<1.0)
– This is the basis of underwater assessment of body
composition
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• Gases in the lungs and other body cavities affect
Buoyancy of the Human Body;
• The line of action of buoyant force is through
the center of volume (where the center of the
buoyant force concentrates its upward thrust)
– Center of gravity of the displaced water
• The line of action of gravity is through the
center of mass
– This is the why the legs tend to drop when you
try to float on your back
– To keep the legs in line with the torso, you have
to exert internal muscular forces
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• Counterbalance by dropping head into water when
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swimming
Buoyancy of the Human Body
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Dynamic Fluid Forces - Drag and
Lift
• The dynamic fluid force that results from motion
within a fluid is commonly resolved into two
components
– Drag Force – same direction of travel but opposes motion
– Pushes, Pulls, Tugs on an athlete
– Lift Force – acts perpendicular to the relative motion of the
object with respect to the fluid
• Resultant Force = product of Lift and Drag Force
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Lift and Drag
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Dynamic Fluid Force:
Force Due to Relative Motion
• When an object moves through a fluid, dynamic fluid
forces are exerted on the object
• The dynamic fluid force (F) is proportional to
– The density of the fluid (p)
– The surface area of the object immersed in the fluid (A)
– The square of the relative velocity of the object to the fluid
(v)
F α pAv2
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Dynamic Fluid Force:
Drag Force
• Drag Force (or drag) acts in opposition to the
relative motion of the object with respect to the
fluid.
FD = ½ CD p A v2
• FD = drag force
• CD = coefficient of drag
• p = fluid density
• A = area of the object
• v = relative velocity of the object relative to the fluid
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Dynamic Fluid Force:
Relative Velocity
• The relative velocity is the difference between
the object’s absolute velocity and the fluid’s
absolute velocity
– Remember that velocity is direction specific
• Ex. Sprinter and wind resistance
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Relative Velocity
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Dynamic Fluid Force:
Drag Force;
• Three types of Drag Force:
– Surface Drag
– Form Drag
– Wave Drag
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Dynamic Fluid Force:
Types of Drag
• Surface Drag –also called skin friction or
viscous drag
• Amount determined by:
–
–
–
–
Relative velocity of object and fluid
Area of surface exposed to flow
Roughness of objects surface
Fluid’s viscosity
• Surface Drag is the sum of the friction forces
acting between the fluid molecules and the
surface of the object
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Reducing Surface Drag
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Dynamic Fluid Force:
Types of Drag;
• Form Drag – also called shape or pressure drag
• Amount determined by:
– Relative motion of object and fluid
– Pressure differential between leading and trailing
edges of object
– Amount of surface acting at right angles to flow
• Increases according to square of the velocity
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Streamlined vs Non-Streamlined
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Form Drag
• Form Drag is the sum of the impact forces resulting
from the collisions between the fluid molecules and
the surface of the object
• The forces exerted by the fluid molecules have
components directed towards the rear of the object,
which contribute to form drag.
– Laminar flow – if fluid molecules stay close to the object
by deflection of other molecules, then trailing forces have
components directed to the front of the object
– Turbulent flow – if the change in surface curvature is too
great and molecules are not deflected close to the object,
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may
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backwards-directed force
The Nature of Fluids
What is laminar flow?
Jump to The Nature of Fluids, 5, Appendix
• Laminar flow – smooth , parallel pattern of
movement
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The Nature of Fluids;
What is turbulent flow?
Jump to The Nature of Fluids, 6, Appendix
•
Turbulent flow – more chaotic flow pattern, characterized
by more turbulent and multidirectional fluid movement
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Flow Patterns
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distribution without the prior written consent of McGraw-Hill Education.
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Form Drag
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Dynamic Fluid Force:
Form Drag
• Form drag is increased by roughness of the
object especially at low velocities
• Sometimes roughness will decrease form drag
– Rough surface at high velocity may create
turbulence all around the object which may carry it
along (ex: golf ball)
Laminar and turbulent flow
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Boundary Layer
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Boundary Layer and Velocity
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Dynamic Fluid Force:
Wave Drag
• Wave Drag – occurs at interface between water
and air
• Amount determined by:
– Relative velocity at which object and wave meet
– Surface area of object acting at right angles to
wave
– Fluid’s viscosity
• Increases according to cube of the velocity
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Drag
What should competitive swimmers do to
minimize wave drag?
• Competitive swimmers
typically propel
themselves underwater
• In most swimming pools,
the lane lines in are
designed to minimize
wave action
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https://www.youtube.com/watch?v=RHgb9SCakjI
10-‹#›
Strategies to Reduce Drag Force
• Reduce fluid density:
– Compete with lower density of fluid (high altitude)
• Reduce drag coefficient
–
–
–
–
Smooth clothing, shaving
Streamline the body or object
Reduce total surface area exposed to the flow
Swim in warmer water which is less viscous
– Thrown implements are oriented to reduce frontal area
(football, discus, javelin)
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Strategies to Reduce Drag Force;
• Form Drag accounts for most of the drag forces at
high velocities, whereas surface drag accounts for
most of the drag force at slower velocities.
– High velocities (> 10m/s or 20 mi/hr) => streamline
– Lower velocities => reduce total surface area in contact
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Lift Force
• Lift Force is the dynamic fluid force component that
acts perpendicular to the relative motion of the object
in relation to the fluid
– The effect of lift force is to change the direction of the
object’s motion (not oppose it)
– Caused by the lateral deflection of fluid molecules as they
pass an object
– Newton’s third law
– Proportional to the lateral acceleration of the fluid
molecules and to the mass of the molecules.
• Ex: airplane’s wings, boat’s rudder, racecar spoilers, hands during
sculling,
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FOIL
What is a foil?
A shape capable of generating lift in the presence of a
fluid flow
Lift force generated by
a foil shape is directed
from the region of
relative high pressure
on the flat side of the
foil toward the region
of relative low pressure
Jump to Lift, 4, Appendix
on the curved side of
the foil
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McGraw-Hill Education.
10-‹#›
The Spoiler
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distribution without the prior written consent of McGraw-Hill Education.
15-‹#›
Lateral Acceleration of Molecules
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distribution without the prior written consent of McGraw-Hill Education.
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Lift Force;
• Bernoulli’s Principle (Daniel Bernoulli, 1738)
– Faster moving fluids exert less pressure laterally
than do slower-moving fluids
– Ex: Airfoil shape results in top flow faster than
bottom flow (greater distance in same time)
producing uplift
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distribution without the prior written consent of McGraw-Hill Education.
15-‹#›
Lift Force:
• A lift force caused by a spin is called a Magnus Force
(Gustav Magnus, 1852)
– Lift forces are created by spinning balls
– The side of the ball that is spinning toward the ball’s
overall motion slows the air molecules while the side of
ball spinning away from the overall motion don’t slow the
air molecules as much
– The velocity of the spinning away side is greater than the
spinning away from motion side
– The ball moves in the direction of lowest resistance, lift
force curves the ball
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distribution without the prior written consent of McGraw-Hill Education.
15-‹#›
Magnus Effect
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15-‹#›
Lift Force.
• Backspin will keep a ball aloft longer
• Topspin will cause a ball to drop earlier
• Sidespin will cause a ball to swerve to the right or left
• Golf clubs are designed to increase backspin to keep
the ball in the air longer and to carry further
• Soccer players use sidespin so corner kicks or penalty
kicks to swerve around opponents
• Table tennis players use spin to cause wide swerves
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distribution without the prior written consent of McGraw-Hill Education.
15-‹#›
Lift Force..
•
The trajectory of a ball thrown with sidespin follows
a regular curve due to the Magnus effect
•
Pitched “curveballs” follow curved paths in the
direction of the spin they were pitched at
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distribution without the prior written consent of McGraw-Hill Education.
15-‹#›
Lift Force…
•
The loft on a golf club is designed to produce
backspin on the ball
•
A properly hit ball rises because of the Magnus effect
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distribution without the prior written consent of McGraw-Hill Education.
15-‹#›
Exam 6 Review
Chapter 14 – Angular Kinetics
Angular analogues of mass, force, momentum, impulse etc.
Moment of Inertia – How it works to change position of body while airborne
• Moment of Inertia
o
o
The inertial property for rotating bodies representing resistance to angular
acceleration; based on both mass and the distance the mass is distributed from
the axis of rotation
Principal moments of inertia of the human body in different positions with
respect to different principal axes
▪ Principal axis
▪ Moment of inertia in kilograms per meter squared
Angular versions of Newton’s three Laws
• Angular Law of Inertia
o
A rotating body will maintain a state of constant rotational motion unless acted
on by an external torque
• Angular Law of Acceleration
o A net torque produces angular acceleration of a body that is:
▪ Directly proportional to the magnitude of the torque
▪ In the same direction as the torque
▪ Inversely proportional to the body’s moment of inertia
• Angular Law of Reaction
o For every angular action, there is an equal and opposite angular reaction
exerted by the second body on the first
Centripetal Force - know equations for Fc
• Centripetal Force
o Force directed toward the center of rotation for a body in rotational motion
Conservation of Momentum
• What is the principle of conservation of angular momentum?
o
o
When gravity is the only acting external force, angular momentum is
conserved
The total angular momentum of a given system remains constant in the
absence of external torques
Cat Twist
• Can be initiated with ZERO angular momentum
• Must be flexed at waist
• Twist by rotating one part of the body that has reduced rotary inertia against another
which has higher rotary inertia
Angular Momentum
• What is angular momentum?
o Quantity of angular motion possessed by a body
o Measured as the product of moment of inertia and
angular velocity:
o
o
As mass or angular velocity increases, angular momentum increases
proportionally
A factor that influences angular momentum is the distribution of mass with
respect to the axis of rotation
▪ Angular momentum is proportional to the square of the radius of gyration
Chapter 15 – Fluid Dynamics
Fluid Mechanics “Flow”
• Fluid Mechanics
o
Is the branch of mechanics dealing with the properties and behavior of gases
and liquids.
▪ Important role in consideration of human movement
▪ Athletes and/or objects encounter fluids (air/water)
▪ These fluids “Flow” around the athlete or object
o
Forces created by this “Flow” can produce:
▪ Drag
▪ Lift
▪ Buoyancy
▪ Spin
o Amount of “Flow” directly related to speed of object moving through fluid
Buoyancy with air and water (other factors)
• Buoyant Force
o
Vertical force exerted on an object immersed in a fluid
▪ Always acts upwards
• Air
o
Object filled with air less dense than surrounding fluid
▪ Ex. Blimp or hot air balloon (Helium filled)
• Water
o
Extension of hydrostatic pressure
▪ Greater pressure with depth => more powerful upward force pushing on
object from below
Drag - components / types
Surface/Form/Wave
• Surface Drag
o also called skin friction or viscous drag
o Amount determined by:
▪ Relative velocity of object and fluid
▪ Area of surface exposed to flow
▪ Roughness of objects surface
▪ Fluid’s viscosity
o Surface Drag is the sum of the friction forces acting between the fluid
molecules and the surface of the object
o
Surface drag increases according to square of velocity
• Form Drag
o Also called shape or pressure drag
o Amount determined by:
▪ Relative motion of object and fluid
▪ Pressure differential between leading and trailing edges of object
▪ Amount of surface acting at right angles to flow
o Increases according to square of the velocity
o Form Drag is the sum of the impact forces resulting from the collisions
between the fluid molecules and the surface of the object
o
The forces exerted by the fluid molecules have components directed towards
the rear of the object, which contribute to form drag.
▪ Laminar flow – if fluid molecules stay close to the object by deflection of
other molecules, then trailing forces have components directed to the
front of the object (Smooth, parallel pattern of movement)
▪ Turbulent flow – if the change in surface curvature is too great and
molecules are not deflected close to the object, then a vacuum may be
created behind the object with a backwards-directed force (More chaotic
flow pattern)
• Wave Drag
o Occurs at interface between water and air
o Amount determined by:
▪ Relative velocity at which object and wave meet
▪ Surface area of object acting at right angles to wave
▪ Fluid’s viscosity
o Increases according to cube of the velocity
Lift – definition, contributing factors
• Lift
o
Force acting perpendicularly to motion that deflects an object from its original
pathway
Hydrostatic Pressure
• Hydrostatic Pressure
o
Exerted by the wt. of a fluid
o
Pressure – force per unit area
– Directly related to buoyancy
o
o
Force exerted by a fluid when supporting its own weight
Directly related to buoyancy
Atmospheric Pressure
• Atmospheric Pressure
o
Gravity’s pull on the atmosphere
▪ Greatest pressure at sea level, less at altitude
▪ 14.7 psi (pounds per square inch)
• Atmospheric air at sea level consists of:
o Oxygen 21%
o Nitrogen 78%
o Other gases 1%
o At altitude, same % but less air due to less pressure
o Acclimatization crucial to performance of duration
Archimedes Principle …..buoyancy in humans
• Greek mathematician
• AP states that “the buoyant force acting on an object is equal to the weight of the fluid
that the object displaces”
•
• Whether or not something floats is determined by:
o the volume of the object immersed
o the weight of the object compared to the weight of the same volume of water
• Density (mass : volume)
• What is the Archimedes’ Principle
o A physical law stating that the buoyant force acting on a body is equal to the
weight of the fluid displaced by the body
• Specific Gravity is the ratio of the weight of an object divided by the weight of the same
volume of water
o An object with specific gravity less than 1.0 will float
• Muscle and bone is very dense (>1.0) while fat is less dense (<1.0)
o This is the basis of underwater assessment of body composition
• Gases in the lungs and other body cavities affect buoyancy
o Gases are much less dense than water
o Inhalation increases chest volume, therefore decreases total body density
Bernoulli Principle
• Bernoulli’s Principle (Daniel Bernoulli, 1738)
o
Faster moving fluids exert less pressure laterally than do slower-moving
fluids
o Ex: Airfoil shape results in top flow faster than bottom flow (greater
distance in same time) producing uplift
Line of Buoyancy vs Line of Gravity
• The line of action of buoyant force is through the center of volume (where the center
of the buoyant force concentrates its upward thrust)
o Center of gravity of the displaced water
• The line of action of gravity is through the center of mass
o This is the why the legs tend to drop when you try to float on your back
o
To keep the legs in line with the torso, you have to exert internal muscular
forces
▪ Counterbalance by dropping head into water when swimming
Dynamic Fluid Forces
• Dynamic Fluid Forces
• The dynamic fluid force that results from motion within a fluid is commonly resolved
into two components
o
Drag Force – same direction of travel but opposes motion
o
Lift Force – acts perpendicular to the relative motion of the object with respect
▪ Pushes, Pulls, Tugs on
an athlete
o
to the fluid
Resultant Force = product of Lift and Drag Force
• Forces Due to Relative Motion
o When an object moves through a fluid, dynamic fluid forces are exerted on the
o
object
The dynamic fluid force (F) is proportional to
▪ The density of the fluid (p)
▪ The surface area of the object immersed in the fluid (A)
▪ The square of the relative velocity of the object to the fluid (v)
• Drag Force
o (or drag) acts in opposition to the relative motion of the object with respect to
the fluid.
Relative Velocity
• The relative velocity is the difference between the object’s absolute velocity and the
fluid’s absolute velocity
• Remember that velocity is direction specific
o
Ex. Sprinter and wind resistance
Biomechanics Exam 6
Chapter 14:
Moment of inertia: inertial property for rotating bodies representing resistance to angular
acceleration; based on both mass and the distance the mass is distributed from the axis of
rotation; I=(sigma)mr^2
Radius of gyration: distance from the axis of rotation to a point where the bodies mass could be
concentrated without altering its rotational characteristics; I=mk^2 (k is radius of gyration)
Muscular strength: ability to produce torque at a joint
Segmental moments of inertia: resistance to rotation at a joint
Angular momentum: quantity of angular motion possessed by a body; H=Iw; H=mk^2w; as
mass or angular velocity increases, angular momentum increases proportionally; a factor that
influences angular momentum is the distribution of mass with respect to rhe axis of rotation;
angular momentum is proportional to the square of the radius of gyration
Principle of conservation of angular momentum: when gravity is the only acting external
force, angular momentum is conserved; the total angular momentum of a given system remains
constant in the absence of external torques
Cat twist: can be initiated with zero angular momentum; must be flexed at waist; twist by
rotating one part of the body that has reduced rotary inertia against another which has higher
rotary inertia
Angular impulse: change in angular momentum equal to the product of torque and the time
interval over which the torque acts; Tt=(delta)H=(Iw)2-(Iw)1
Angular law of inertia: a rotating body will maintain a state of constant rotational motion
unless acted upon by an external torque; I=mk^2
Angular law of acceleration: a net torque produces angular acceleration of a body that is
directly proportional to the magnitude of torque, in the same direction of the torque, inversely
proportional to the bodys moment of inertia; F=ma; T=Ia
Angular law of reaction: for every angular action, there is an equal and opposite angular
reaction exerted by the second body on the first; Fa=Fb; Ta=Tb
Centripetal force: force directed toward the center of rotation for a body in rotational motion;
Fc=mv^2/r
;
Fc=mrw^2
Chapter 15:
Fluid mechanics: branch of mechanics dealing with the properties and behaviors of gases and
liquids; these fluids flow around the athlete or object; forces created by this flow can produce
drag, lift, buoyancy, and spin.
Hydrostatic pressure: exerted by the weight of a fluid; directly related to buoyancy
Buoyancy: force opposing gravity, acting on object partially or fully immersed in liquid or gas
Drag: force opposing motion through a fluid
Lift: force acting perpendicully to motion that deflects an object from original pathway
atmospheric pressure: gravitys pull on the atmosphere; greatest pressure at sea level, less at
altitude
Atmospheric air: 21% oxygen, 78% nitrogen, 1% other gases
hydrostatic pressure in H2O: water more dense than air; pressure increases with depth,
pressure increases by 1 atmosphere for every 10m
Pulmonary embolism: result of ascent holding breath
Nitrogen narcosis: high concentrations in blood due to extreme depths; affects CNS, memory
loss, and inebritation effects
Buoyant force: vertical force exerted on an object immersed in a fluid; always acts upwards
Air: object filled with air less dense than surrounding fluid
Water: extension of hydrostatic pressure; greater pressure with depth, more powerful upward
force pushing on object from below
Archimedes principle: greek mathematician; states that the buoyant force acting on an object is
equal to the weight of the fluid that the object displaces; whether or not something floats is
determined by the volume of the object immersed, the weight of the object compared to the
weight of same volume of water
Warm water>less density>less floatation
Colder water>more dense>more floatation
Salt water>more dense>more floatation
Fresh water>less dense>less floatation
Specific gravity: ratio of the weight of an object divided by the weight of the same volume of
water
-Muscle bone is dense while fat is less dense
-Gases are less dense than water
-The line of action of buoyant force is through the center of volume
-The line of action of gravity is through the center of mass
drag force: same direction of travel but opposes motion
Lift force: acts perpendicular to the relative motion of the object with respect to the fluid
Resultant force: product of lift and drag force
-The dynamic fluid force (F) is proportional to the density of fluid (p) , the surface area of the
object immersed in fluid (A), the square of the relative velocity of the object to the fluid (v)
Relative velocity: difference between the objects absolute velocity and the fluids absolute
velocity
3 types of drag force: surface drag, form drag, and wave drag
Surface drag: also called skin friction or viscous drag; sum of friction forces acting between the
fluid molecules and the surface of the object; increases according to square of velocity
Form drag: also called shape or pressure drag; increases according to the square of the velocity
Form drag: sum of the impact forces resulting from the collisions beyween the fluid molecules
and the surface of the object
Laminar flow: if fluid molecules stay close to the object by deflection of other molecules then
trailing forces have components dorected to the front of the object; smooth, parallel pattern of
movement
Turbulent flow: if the change in surface curvature is too great and molecules are not deflected
close to the object, then a vacuum may be created behind the object with a backwards directed
force; more chaotic flow pattern, characterized by more turbulent and multidirectional fluid
movement
Wave drag: occurs at interface between water and air; increases according to cube of the
velocity
Strategies to reduce drag force: reduce fluid density, reduce drag coefficient; form drag
accounts for most of the drag forces at high velocities whereas surface drag accounts for most of
the drag force at slower velocities
Lift force: dynamic fluid force component that acts perpendicular to the relative motion of the
object in relation to the fluid; the effect is to change the direction of the objects motion; newtons
third law; caused by lateral deflection of fluid molecules as they pass an object; proportional to
the acceleration of the fluid molecules and to the mass of molecules
Foil: a shape capable of generating lift in the presence of a fluid flow
Bernoullis principle: faster moving lfuids exert less pressure laterally than do slower moving
fluids
Magnus force: lift force caused by a spin