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Chapter 13: The Conditions of Rotary Motion

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Chapter 13: The Conditions of Rotary Motion Rotary Force, Lever, Newton s Laws and Rotational Equivalents, Centripetal and Centrifugal Forces – PowerPoint PPT presentation

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Title: Chapter 13: The Conditions of Rotary Motion


1
Chapter 13 The Conditions of Rotary Motion
  • Rotary Force, Lever, Newtons Laws and Rotational
    Equivalents, Centripetal and Centrifugal Forces

2
Objectives
  • 6. Explain the cause and effect relationship
    between the forces responsible for rotary motion
    and the objects experiencing the motion
  • 7. Define centripetal and centrifugal force, and
    explain the relationships between these forces
    and the factors influencing them
  • 8. Identify the concepts of rotary motion that
    are critical elements in the successful
    performance of a selected motor skill
  • 9. Using the concepts that govern motion, perform
    a mechanical analysis of a selected motor skill

3
Objectives
  • 1. Name, define, and use terms related to rotary
    motion
  • 2. Solve simple lever torque problems involving
    the human body and the implements it uses
  • 3. Demonstrate an understanding of the effective
    selection of levers
  • 4. Explain the analogous kinetic relationships
    that exist between linear and rotary motion
  • 5. State Newtons laws of motion as they apply to
    rotary motion.

4
ROTARY FORCE Eccentric Force
  • When the direction of force is not in line with
    objects center of gravity, a combination of
    rotary and translatory motion is likely to occur
  • An object with a fixed axis, rotates when force
    is applied off center
  • Eccentric force a force whose direction is not
    in line with the center of gravity of a freely
    moving object or the center of rotation of an
    object with a fixed axis of rotation

5
Example of Eccentric Force
6
Torque
  • The turning effect of an eccentric force
  • Equals the product of the force magnitude and the
    length of the moment arm
  • Moment arm is the perpendicular distance form the
    line of force to the axis of rotation
  • May be modified by changing either force or
    moment arm

7
Length of Moment Arm
  • Perpendicular distance from the direction of
    force to the axis of rotation
  • At 450 moment arm is no longer the length of the
    forearm
  • Can be calculated using trigonometry

8
Length of Moment Arm
  • In the body, weight of a segment cannot be
    altered instantaneously
  • Therefore, torque of a segment due to
    gravitational force can be changed only by
    changing the length of the moment arm

9
Torque on Rotating Segments
  • Muscle forces that exert torque are dependent on
    point of insertion of the muscle length,
    tension, and angle of pull changes

10
Muscle Force Vectors
  • Only the rotary component is actually a foctor in
    torque production
  • The stabilizing component acts along the
    mechanical axis of the bone, through the axis of
    rotation
  • Thus, it is not eccentric, or off-center, force
  • The moment arm length is equal to zero

11
Summation of Torques
  • The sum of two or more torques may result in no
    motion, linear motion, or rotary motion
  • Parallel eccentric forces applied in the same
    direction on opposite sides of the center of
    rotation Ex. a balanced seesaw
  • Equal parallel forces are adequate to overcome
    the resistance, linear motion will occur Ex.
    paddlers in a canoe

12
Force Couple
  • The effect of equal parallel forces acting in
    opposite direction

13
Principle of Torques
  • Resultant torques of a force system must be equal
    to the sum of the torques of the individual
    forces of the system about the same point
  • Must consider both magnitude and direction
  • Clockwise are usually labeled as negative
  • Counterclockwise as positive

14
Summation of Moments
  • Negative Moments (-5 x 1.5) (-3 x 10) -37.5
    Nm
  • Positive moment 5 x 3 15 Nm
  • Resultant moment -37.5 15 -22.5 Nm

15
THE LEVER
  • A rigid bar that can rotate about a fixed point
    when a force is applied to overcome a resistance
  • They are used to
  • overcome a resistance larger than the magnitude
    of the effort applied
  • increase the speed and range of motion through
    which a resistance can be moved

16
External Levers
  • Using a small force to overcome a large
    resistance
  • Ex. a crowbar
  • Using a large ROM to overcome a small resistance
  • Ex. Hitting a golf ball
  • Used to balance a force and a load
  • Ex. a seesaw

17
Anatomical Levers
  • Nearly every bone is a lever
  • The joint is the fulcrum
  • Contracting muscles are the force
  • Do not necessarily resemble bars
  • Ex. skull, scapula, vertebrae
  • The resistance point may be difficult to identify
  • May be difficult to determine resistance
  • weight, antagonistic muscles fasciae

18
Lever Arms
  • Portion of lever between fulcrum force points
  • Effort arm (EA)
  • Perpendicular distance between fulcrum line of
    force of effort
  • Resistance arm (RA)
  • Perpendicular distance between fulcrum line of
    resistance force

19
Classification of Levers
  • Three points on the lever have been identified
  • 1. Fulcrum
  • 2. Effort point
  • 3. Resistance point
  • There are three possible arrangements of these
    point
  • That arrangement is the basis for the
    classification of levers

20
First-Class Levers
  • E Effort
  • A Axis or fulcrum
  • R Resistance or weight

21
Second-Class Levers
  • E Effort
  • A Axis or fulcrum
  • R Resistance or weight

22
Third-Class Levers
  • E Effort
  • A Axis or fulcrum
  • R Resistance or weight

23
The Principle of Levers
  • Any lever will balance when the product of the
    effort and the effort arm equals the product of
    the resistance and the resistance arm
  • E x EA R x RA

24
Relation of Speed to Range in Movements of Levers
  • In angular movements, speed and range are
    interdependent

25
Selection of Levers
  • Skill in motor performance depends on the
    effective selection and use of levers , both
    internal and external

26
Selection of Levers
  • It is not always desirable to choose the longest
    lever arm
  • Short levers enhance angular velocity, while
    sacrificing linear speed and range of motion
  • Strength needed to maintain angular velocity
    increases as the lever lengthens

27
Mechanical Advantage of Levers
  • Ability to magnify force
  • The output relative to its input
  • Ratio of resistance overcome to effort applied
  • MA R / E
  • Since the balanced lever equation is,
  • R / E EA / RA
  • Then MA EA / RA

28
Identification and Analysis of Levers
  • For every lever that use observe, these questions
    should be answered
  • 1. Where are fulcrum, effort point resistance
    point?
  • 2. At what angle is the effort applied to the
    lever?
  • 3. At what angle is the resist applied to the
    lever?
  • 4. What is the effort arm of the lever?

29
Identification and Analysis of Levers
  • 5. What is the resistance arm of the lever?
  • 6. What are the relative lengths of the effort
    resistance arms?
  • 7. What kind of movement does this lever favor?
  • 8. What is the mechanical advantage?
  • 9. What class of lever is this?

30
NEWTONS LAWS AND ROTATIONAL EQUIVALENTS
  • 1. A body continues is a state of rest or uniform
    rotation about its axis unless acted upon by an
    external force
  • 2. The acceleration of a rotating body is
    directly proportional to the torque causing it,
    is in the same direction as the torque, and is
    inversely proportional to moment of inertia of
    the body
  • 3. When a torque is applied by one body to
    another, the second body will exert an equal and
    opposite torque on the first

31
Moment of Inertia
  • Depends on
  • quantity of the rotating mass
  • its distribution around the axis of rotation
  • I ?mr2
  • M mass
  • r perpendicular distance between the mass
    particle and the axis of rotation

32
Moment of Inertia
33
Inertia in the Human Body
  • Body position affects mass distribution, and
    therefore inertia

34
Acceleration of Rotating Bodies
  • The rotational equivalent of F ma
  • T I?
  • T torque, I moment of inertia, ? angular
    acceleration
  • Change in rotary velocity (?) is directly
    proportional to the torque (T) and inversely
    proportional to the moment of inertia (I)
  • ? T / I

35
Angular Momentum
  • A measure of the force need to start or stop
    motion
  • The product of moment of inertia (I) and angular
    velocity (?)
  • Angular momentum I?
  • Can be increased or decreased by increasing
    either the angular velocity or the moment of
    inertia

36
Conservation of Angular Momentum
  • The total angular momentum of a rotating body
    will remain constant unless acted upon by
    external torques
  • A decrease in I produces an increase in ?

37
Action and Reaction
  • Any changes is the moments of inertia or
    velocities of two bodies will produce equal and
    opposite momentum changes
  • I (?v1 - ?u1) I (?v2 - ?u2)

38
Transfer of Momentum
  • Angular momentum may be transferred for one body
    to body part to another at the total angular
    momentum remains unaltered
  • Angular momentum can be transferred into linear
    momentum, and vice versa

39
CENTRIPETAL AND CENTRIFUGAL FORCES
  • Centripetal force a constant center-seeking
    force that acts to move an object tangent to the
    direction in which it is moving at any instant,
    thus causing it to move in a circular path
  • Centrifugal force an outward-pulling force equal
    in magnitude to centripetal force
  • Equation for both (equal opposite forces)
  • Fc mv2 / r

40
THE ANALYSIS OF ROTARY MOTION
  • As most motion of the human body involve rotation
    of a segment about a joint, any mechanical
    analysis of movement requires an analysis of the
    nature of the rotary forces, or torques,
    involved.
  • Internal torques by applied muscle forces
  • External torques must be identified as they are
    produced identified in the analysis of linear
    motion

41
General Principles of Rotary Motion
  • The following principle need to be considered
    when analyzing rotary motion
  • Torque
  • Summation of Torques
  • Conservation of Angular Momentum
  • Principle of Levers
  • Transfer of Angular Momentum

42
Summary
  • Rotary Force,
  • Lever
  • Newtons Laws and Rotational Equivalents
  • Centripetal and Centrifugal Forces
  • Analysis of Rotary Motion
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