Chapter 13: The Conditions of Rotary Motion

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Chapter 13The Conditions of Rotary Motion

• Rotary Force, Lever, Newtons Laws and Rotational
  Equivalents, Centripetal and Centrifugal Forces

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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

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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.

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ROTARY FORCEEccentric 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

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Example of Eccentric Force
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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

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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

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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

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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

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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

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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

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Force Couple

• The effect of equal parallel forces acting in
  opposite direction

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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

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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

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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

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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

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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

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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

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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

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First-Class Levers

• E Effort
• A Axis or fulcrum
• R Resistance or weight

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Second-Class Levers

• E Effort
• A Axis or fulcrum
• R Resistance or weight

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Third-Class Levers

• E Effort
• A Axis or fulcrum
• R Resistance or weight

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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

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Relation of Speed to Range in Movements of Levers

• In angular movements, speed and range are
  interdependent

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Selection of Levers

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

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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

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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

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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?

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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?

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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

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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

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Moment of Inertia
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Inertia in the Human Body

• Body position affects mass distribution, and
  therefore inertia

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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

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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

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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 ?

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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)

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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

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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

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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

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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

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Summary

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