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PPT – Chapter 13: The Conditions of Rotary Motion PowerPoint presentation | free to download - id: 486ad3-NmVhY

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Chapter 13 The Conditions of Rotary Motion

- Rotary Force, Lever, Newtons Laws and Rotational

Equivalents, Centripetal and Centrifugal Forces

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

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.

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

Example of Eccentric Force

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

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

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

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

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

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

Force Couple

- The effect of equal parallel forces acting in

opposite direction

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

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

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

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

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

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

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

First-Class Levers

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

Second-Class Levers

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

Third-Class Levers

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

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

Relation of Speed to Range in Movements of Levers

- In angular movements, speed and range are

interdependent

Selection of Levers

- Skill in motor performance depends on the

effective selection and use of levers , both

internal and external

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

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

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?

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?

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

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

Moment of Inertia

Inertia in the Human Body

- Body position affects mass distribution, and

therefore inertia

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

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

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 ?

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)

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

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

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

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

Summary

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