Spiros Prassas California State University Κινητικές αρχές και η εφαρμογή...
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Spiros PrassasCalifornia State University
Κινητικές αρχές και η εφαρμογή τους στην Γυμναστική
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Spiros PrassasCalifornia State University
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Spiros PrassasCalifornia State University
Important performance variables from a biomechanical perspective
…ability to gain height…ability to rotate…ability to swing…ability to land
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Spiros PrassasCalifornia State University
Force
…is the quantity that produces or tend to produce a change in the state of motion of an object or body, i.e.…produces acceleration
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Spiros PrassasCalifornia State University
…force
The relationship between force an motion is addressed by Newton’s laws of motion:
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Spiros PrassasCalifornia State University
First Law—Law of Inertia
Every body persists in its state of rest or uniform motion in a straight line, unless it is compelled to change its state by external forces, i.e
An (external) force is required to stop, start, or alter motion, i.e, an (external) force is required to change the velocity of of an object, but not to maintain it
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Spiros PrassasCalifornia State University
Second Law—Law of acceleration
The acceleration of a body is proportional to the force causing it, it is in the direction of that force, and it is inversely proportional to its mass:
m
Fa extcm =
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Spiros PrassasCalifornia State University
Third Law—Law of action/reaction
To every action there is always an equal and opposite reaction.
This law implies that:Forces occur in pairs, andAction/reaction pairs never act on the same object…
Although the magnitude of the action/reaction forces is the same, their effect on the respective objects are not…why?
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Friction
QuickTime™ and aYUV420 codec decompressor
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Spiros PrassasCalifornia State University
…friction
Frictional forces arise between objects in contact. They are parallel to the contact surface and always oppose, or tend to oppose the relative motion of the objects involved
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Spiros PrassasCalifornia State University
…friction
Frictional forces are equal to:
Nf μ=Where:
μ is the coefficient of friction, and
N is the perpendicular (Normal) force between the two objects
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Spiros PrassasCalifornia State University
…friction
…therefore, frictional forces can be altered by altering either μ: how?
Different floorsDifferent shoesDifferent tiresDifferent lubricants
Or N: how?
Alter weight (mass)Alter position,
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Spiros PrassasCalifornia State University
Static friction
Arises between surfaces at rest in relation to each other…
Nf ss μ≤
•…is variable in magnitude…
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Kinetic friction
Arises between surfaces in relative motion…
Nf kk μ=
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Torque
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Spiros PrassasCalifornia State University
…torque
Torque represents the rotational effect of force
When muscles contract, the force produced is applied to bones, which rotate about a joint
The magnitude of the torque produced by a force depends on magnitude of the force, the direction of the force,and the distance from the point of (force) application to the axis of rotation
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Spiros PrassasCalifornia State University
τ sinFd=
d
F τ = F d (1)
τ =F d (2)
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Spiros PrassasCalifornia State University
Torques that produce or tend to produce counterclockwise (CCW) rotations are positive
Torques that produce or tend to produce clockwise (CW) rotations are negative
Positive (CCW) or negative (CW) torques should not be associated with a particular joint movement (flexion, extension, etc.)
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Spiros PrassasCalifornia State University
…torque
The rotational equivalent to F=ma (Newton’s 2nd Law) is:
ατ I=
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WorkEnergyPowerMomentum
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Spiros PrassasCalifornia State University
Work
Mechanical work is defined as :
cos
...
dFW
dFW
=
∗=
d
F
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Spiros PrassasCalifornia State University
Work
…for rotary motion, mechanical work is defined as :
τ ∗=W
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…Mechanical Energy…
…is represented by the ability of objects to do Work because of…
Their motion (kinetic…) Position (gravitational potential…) Configuration (elastic…)
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)2
1()()
2
1
2
1( 222 kxmghImvME
EEPEKEME
+++=
++=
ω
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Work-Energy relationship
Under special circumstances, the sum of the kinetic and (gravitational) potential energy of a system is constant, i.e. it is “conserved”.
…if PE is negligible, the Work-Energy relationship is expressed as follows:
WKEKE if +=• Practical Implications
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Work-Energy relationship
KEW
KEKEW
WKEKE
if
if
Δ=
−=
+=
…practical applications
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W= F d
F
d
The amount of work that the H2O does on the diver is set… By diving deep into the pool, the force doing the work is small…
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d
F
Again, the amount of work that the H2O is doing on the diver is set—the same as in the previous dive. If, however, the diver belly flaps (or back flaps—as he/she did) into the pool, he/she pays the price…
W= F d
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FB HB
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Linear Momentum
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…linear momentum…
…is the “quantity of (linear) motion” possessed by an object/body
…is proportional to the product of the mass and the velocity possessed by an object/body…
mvM =
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…in the absence of external forces, the linear momentum of a system is constant…(equation)
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Impulse/impulse-momentum relationship
The product of Force and time—left side of the equation above—is known as Impulse (J) and equation (1) describes the Impulse-momentum relationship
if mvmvtF −=(1)
Since…
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J= F t
F
t
The Impulse that the H2O is doing on the diver is set… By diving deep into the pool, the force of the Impulse will be small…
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t
F
Again, the Impulse that the H2O is doing on the diver is set—the same as in the previous dive. If, however, the diver belly flaps (or back flaps!) into the pool, he/she pays the price…
J= F t
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Force
Negative Impulse
Positive Impulse
T i m e
Slowing down*
Speeding up*
Speed changes if there is a difference between the positive and negative impulses—in the illustrated case, the subject will “speed-up”* (why?)
*in this example, forward is the positive direction
Locomotion
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QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
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…angular momentum…
…is the “quantity of (angular) motion” possessed by an object/body
…is proportional to the product of the moment of inertia and the angular velocity possessed by an object/body…
ωIL =
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Conservation of angular momentum
…Angular momentum is constant, i.e. it is “conserved” in the absence of external torques…
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Angular impulse/angular momentum relationship
…therefore it changes only when external torques act for a time period
Practical applications
LIIt
tII
if
if
Δ=−=⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛ −==
ωωτ
ωωατ
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…angular momentum…
…The total angular momentum of a multi-segment system is made up of the sum of the angular momenta of its parts, i.e.
...21 ++Σ= llL• Practical implications
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…”transfer” of angular momentum…
The conservation of L principle, plus the fact that total L is made up of the sum of the angular momenta of its parts, is utilized in order to “transfer” momentum… Among the parts, and Among different axes of rotation
• Practical implications
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From Kreighbaum, E…(modified)
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Spiros PrassasCalifornia State University
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
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…and so… what?
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Spiros PrassasCalifornia State University