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
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
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.
12A-2
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.
12A-3
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.
12A-4
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.
12A-5
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
12A-6
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.
12A-7
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.
12A-8
Mechanical Axis
• 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.
Fig. 12.3
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.
12A-10
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
12A-11
Resolution of Forces
 Magnitude
 Point of Application is
at point B.
 Direction is
represented by the
arrowhead and the
angle 
Fig 12.2
12A-12
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.
12A-13
Angle of Pull
 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.
Rotary
component
Nonrotary
component
Fig 12.1a
12A-14
Rotary vs. Non-rotary Components
Angle of pull < 90º
 Non-rotary force is directed
toward fulcrum.
 Helps maintain integrity of
the joint (stabilizes).
Rotary
component
Non-rotary
component
Fig 12.1a
12A-15
Rotary vs. Non-rotary Components
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.
Fig 12.1c
12A-16
Rotary vs. Non-rotary Components
Angle of pull = 90º
 Force is all rotary.
Angle of pull = 45º
 Rotary & non-rotary
components are equal.
Muscular force functions:
 Movement
 Stabilization
Fig 12.1b
12A-17
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.
Rotary force in
red
Fig 12.4
12A-18
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
12A-19
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.
12A-20
Linear Forces
 For forces applied in the same direction,
the resultant is the sum of the forces:
a+b=c
a
b
c
+
=
 For forces applied in the opposite
directions, the resultant is the sum of the
forces:
a + (-b) = c
a
b
+
c
=
12A-21
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
12A-22
Parallel Forces
 Forces not in the same
action line, but parallel
to each other.
 Three parallel forces:
 two upward
 one downward
Fig 12.9
12A-23
Parallel Forces
 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.
Fig 12.9
12A-24
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
12A-25
Law of Inertia
 A body continues in its
state of rest or of uniform
motion unless an outside,
unbalanced force acts on
it.
Vx
Vy
Gravity
Fig 12.11
12A-26
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
12A-27
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
12A-28
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.
12A-29
3. Law of Reaction
For every action there is an equal and opposite
reaction.
F = -F
Fig 12.13 & 12.14
12A-30
Conservation of Momentum
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:
Fig 12.15
m1vf1 – m1vi1 = m2vf2 – m2vi2
12A-31
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.
12A-32