# Chapter 13: The Conditions of Rotary Motion - PowerPoint PPT Presentation

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

The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
Title:

## Chapter 13: The Conditions of Rotary Motion

Description:

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

Number of Views:92
Avg rating:3.0/5.0
Slides: 43
Provided by: judy70
Category:
Tags:
Transcript and Presenter's Notes

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.

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
• 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
• 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