1. CHAPTER 12:PART 1 THE CONDITIONS OF LINEAR MOTION
KINESIOLOGY
Scientific Basis of Human Motion, 12th edition
Hamilton, Weimar & Luttgens
Presentation Created by
TK Koesterer, Ph.D., ATC
Humboldt State University
Revised by Hamilton & Weimar
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

2. Objectives
1. Name, define, and use the terms of linear motion. 2. Define magnitude, direction, and point of application of force and use terms properly. 3. Explain the effect of changes in magnitude, direction, and point of application of force have on the motion state of a body. 4. Define and give examples of linear forces, concurrent forces, and parallel forces. 5. Determine magnitude, direction, and point of application of muscle forces. 6. State Newton’s laws as they apply to linear motion.

3. Objectives
7. Explain cause and effect relationship between forces causing linear motion and the objects in motion. 8. Name & define basic external forces that modify motion. 9. Draw and analyze a 2D free-body diagram. 10. Explain the work-energy relationship applied to a body experiencing linear motion. 11. Define and use properly the terms work, power, kinetic energy, and potential energy. 12. Perform a mechanical analysis of a motor skill.

4. The Nature of Force
Force is that which pushes or pulls through direct mechanical contact or through the force of gravity to alter the motion of an object.
Internal forces are muscle forces that act on various structures of the body.
External forces are those outside the body:
Weight, gravity, air or water resistance, friction, or forces of other objects acting on the body.
In this beginning level text we really only deal with muscle forces as internal forces.

5. Aspects of Force Force is a vector quantity: Magnitude and direction
Also has a point of application
All three characteristics must be identified.
For a weight lifter to lift a 250 N barbell:
Lifter must apply a force greater than 250 N, in an upward direction, through the center of gravity of the barbell.

6. w = mg Magnitude Amount of force being applied.
Force exerted by the barbell had a magnitude of 250 N.
This force was the result of gravity acting on the mass of the barbell.
In this case, the force is referred to as weight.
Weight is mass times acceleration due to gravity:
w = mg

7. Magnitude of Muscular Force
In direct proportion to the number & size of fibers contracting in a muscle.
Muscles normally act in groups whose force or strength is measured collectively.
Maximum muscular strength is measured by a dynamometer.
Measures force applied by a group of muscle through an anatomical lever.
I get what you were doing with your change. I thought this was simpler. Feel free to change it back.

8. Point of Application Point at which force is applied to an object.
Where gravity is concerned this point is always through the center of gravity.
For muscular force, this point is assumed to be the muscle’s attachment to a bony lever.
The point of intersection of the line of force and the mechanical axis of the bone.
Took out some words here to makle the slide less wordy.

9. Mechanical Axis
Fig. 12.3
The mechanical axis of a bone is a straight line that connects the midpoint of the joints at either end of the bone.
Not necessarily the long axis of the bone.
Again, I cut down on the amount of text.

10. Direction Direction of a force is along its action line.
Gravity is a downward-directed vector through the center of gravity of the object.
Direction of a muscular force vector is the direction of line of pull of the muscle.

11. Direction of Muscular Force Vector
Muscle angle of pull: the angle between the line of pull and the mechanical axis of the bone.
Fig 12.1

12. Resolution of Forces Magnitude Point of Application is at point B.
Fig 12.2
Magnitude
Point of Application is at point B.
Direction is represented by the arrowhead and the angle 

13. Angle of Pull
Force may be resolved into x (horizontal) and y (vertical) components.
The x-axis is always the mechanical axis of the bone.
The y-axis is always perpendicular to the mechanical axis of the bone.
Size of each depends on angle of pull.
Since a muscle’s angle of pull changes with every degree of joint motion, so do the x & y components .
The larger the angle (0º - 90º), the greater the y and less the x component.
How is this for a compromise? I am not really fond of the term “local frame of reference” when we are simply talking about bones and muscles. I would rather use straight forward and simple language.

14. Angle of Pull
Fig 12.1a
Rotary
component
Nonrotary
The y component is perpendicular to the lever, called rotary component.
The x component is parallel to the lever and is the non-rotary component.
Most resting muscles have an angle of pull < 90º.

15. Rotary vs. Non-rotary Components
Fig 12.1a
Rotary
component
Non-rotary
Angle of pull < 90º
Non-rotary force is directed toward fulcrum.
Helps maintain integrity of the joint (stabilizes).

16. Rotary vs. Non-rotary Components
Fig 12.1c
Angle of pull > 90º
Dislocating force is directed away fulcrum.
Does not occur often.
Muscle is at limit of shortening range and not exerting much force.

17. Rotary vs. Non-rotary Components
Fig 12.1b
Angle of pull = 90º
Force is all rotary.
Angle of pull = 45º
Rotary & non-rotary components are equal.
Muscular force functions:
Movement
Stabilization

18. Anatomical Pulley
Changes the angle of pull of the muscle providing the force.
This increase in angle of pull increases the rotary component.
e.g. Patella for the quadriceps.
Fig 12.4
Rotary force in red

19. Resolution of External Forces
Accomplished in the same manner as muscular forces applied at an oblique angle.
Only horizontal force will move the table.
Vertical force serves to increase friction.
Fig 12.7

20. Composite Effects of Two or More Forces
Two or more forces can be applied to objects.
A punted ball’s path is the result of force of the kick, force of gravity, and force of wind.
Muscles work in groups, e.g. the 3 hamstrings.
Composite forces on the body may be classified according to their direction and application as linear, concurrent, or parallel.

21. Linear Forces
For forces applied in the same direction, the resultant is the sum of the forces:
a + b = c
For forces applied in the opposite directions, the resultant is the sum of the forces:
a + (-b) = c = + a b c

22. Concurrent Forces
Act at the same point of application at different angles.
Resultant of two or more concurrent forces depends on both the magnitude of each force and the angle of application.
Fig 12.8

23. Parallel Forces
Fig 12.9
Forces not in the same action line, but parallel to each other.
Three parallel forces:
two upward
one downward

24. Parallel Forces 10 N weight at 90º. Gravity acts at points B & C.
Fig 12.9
10 N weight at 90º.
Gravity acts at points B & C.
A is the force of biceps.
Effect of parallel forces on an object depends on magnitude, direction & application point of each force.

25. Newtons’ Laws of Motion
1. Law of Inertia
A body continues in its state of rest or of uniform motion unless an unbalanced force acts on it.
An object at rest remains at rest.
An object in motion remains in same motion
Unless acted upon by an outside force.
Friction & air resistance effect objects in motion.
F ≠ 0

26. Law of Inertia
Gravity Vy Vx
A body continues in its state of rest or of uniform motion unless an outside, unbalanced force acts on it.
Fig 12.11

27. F = ma 2. Law of Acceleration
The acceleration of an object is directly proportional to the force causing it and inversely proportional to the mass of the object.
What is the force needed to produce a given linear acceleration?
Since m = w/g, F = (w/g) x a
Force to accelerate a 300 N object 2 m/sec2
F = (300 N / 9.8m/s2) x 2 m/s2 = 61 N
F = ma

28. Impulse
Ft = m(vf – vi)
The product of force and the time it is applied.
F = ma
Substitute (vf – vi) / t for a:
F= m (vf – vi) / t
Multiply both sides by time:
Ft = m (vf – vi)
Fig 12.12

29. Momentum Ft = mvf - mvi The product of mass and velocity
20 N force applied for 5 sec has equal momentum to a 100 N force falling for 1 sec. Why?
Any change in momentum is equal to the impulse that produces it.
Force applied in direction of motion will increase momentum.
Force applied opposite to direction of motion will decrease momentum.

30. 3. Law of Reaction
For every action there is an equal and opposite reaction.
F = -F
Fig & 12.14

31. Conservation of Momentum
Fig 12.15
In any system where forces act on each other the momentum is constant.
An equal and opposite momentum change must occur to object producing reaction force.
Therefore:
m1vf1 – m1vi1 = m2vf2 – m2vi2

32. Summation of Forces
Force generated by muscle may be summated from one segment to another.
Typical throwing pattern:
Force from legs is transferred to the trunk.
Further muscular force increases momentum and is transferred to upper arm.
Mainly as an increase velocity because mass is smaller.
Sequential transfer of momentum continues with mass decreasing and velocity increasing.
Finally, momentum is transferred to thrown ball.