Spiros Prassas California State University Κινητικές αρχές και η εφαρμογή...

Spiros PrassasCalifornia State University

Κινητικές αρχές και η εφαρμογή τους στην Γυμναστική


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Important performance variables from a biomechanical perspective

…ability to gain height…ability to rotate…ability to swing…ability to land


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


…force

The relationship between force an motion is addressed by Newton’s laws of motion:


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


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 =


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?


Friction




…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


…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


…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,


Static friction

Arises between surfaces at rest in relation to each other…

Nf ss μ≤

•…is variable in magnitude…


Kinetic friction

Arises between surfaces in relative motion…

Nf kk μ=


Torque


…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


τ sinFd=

d

F τ = F d (1)

τ =F d (2)


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.)


…torque

The rotational equivalent to F=ma (Newton’s 2nd Law) is:

ατ I=


WorkEnergyPowerMomentum


Work

Mechanical work is defined as :

cos

...

dFW

dFW

=

∗=

d

F


Work

…for rotary motion, mechanical work is defined as :

τ ∗=W


…Mechanical Energy…

…is represented by the ability of objects to do Work because of…

Their motion (kinetic…) Position (gravitational potential…) Configuration (elastic…)


)2

1()()

2

1

2

1( 222 kxmghImvME

EEPEKEME

+++=

++=

ω


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


Work-Energy relationship

KEW

KEKEW

WKEKE

if

if

Δ=

−=

+=

…practical applications


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…


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


FB HB


Linear Momentum


…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 =


…in the absence of external forces, the linear momentum of a system is constant…(equation)


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…


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…


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


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


…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 =


Conservation of angular momentum

…Angular momentum is constant, i.e. it is “conserved” in the absence of external torques…


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


…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


…”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


From Kreighbaum, E…(modified)


…and so… what?

Spiros Prassas California State University Κινητικές αρχές και η εφαρμογή...

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