Chapter 5
Torques and Moments of
Force
Maintaining Equilibrium or
Changing Angular Motion
To this juncture
• Analysis focused on linear motion
(translation)
• kinematics: position, change of position, rate of
change of position, acceleration
• kinetics: Newton’s 3 laws of linear motion
• F = ma
• Ft =  mv
• Fd =  KE +  GPE
What about Rotation?
• All points on a body or object move in
circles (or parts of circles) about the same
fixed central line or axis
• body spins around an axis (real or imaginary)
• Force ==> linear motion
• ????? ==> angular motion
Line of action
relative to axis of rotation
• Centric force
• line of action passes through the axis of rotation
• tends to cause translation
Line of action
relative to axis of rotation
• Centric force
• Eccentric force
• line of action does not pass through the axis of
rotation
Line of action
relative to axis of rotation
• Centric force
• Eccentric force
• Force couple
• two eccentric forces
Torque
• Definition
• the turning effect of a force
• the tendency of a force to cause rotation
What factors affect
the tendency
of the force to
cause rotation???
Torque
• Definition
• the turning effect of a force
• the tendency of a force to cause rotation
Moment Arm
(lever arm)
Perpendicular
distance
from
line of action
of a force to
a specified
axis of rotation
Effect of
changing
the line of
action of
force
To describe a torque
• Specified axis of rotation
• Torque magnitude (F x r)
• units: Newtons x meters (Nm)
•
foot x pound (ft-lb)
• Direction (sense) of the torque
• clockwise (-)
• counterclockwise (+)
Examples
of
Torque
Click on the
picture to go
to a good website
Examples
of
Torque
Show the
moment arm and
identify the sense
for each force
on each figure
Sculling: offsetting torques
to create translation
Are all
three
designs
equal
in net
torque
created
at the
stern??
ADLs must consider torque
for safety and convenience
Medicine caps must
be removable by the
disadvantaged, but
inoperable by kids.
Torque
• Rotary force that produces angular
acceleration.
• An increase in the magnitude of the applied
force, or in the perpendicular distance of the
force's line of action to the axis of rotation,
results in an increase in the acting torque.
Torque
• The greater the amount of torque acting at
the axis of rotation, the greater the tendency
for rotation to occur and the greater the
angular acceleration of a given body.
Muscle Torque
• Muscle applies force by?
Muscle Torque
• Muscle applies force by creating
tension on bones
• Muscle crosses a joint or joints
• brachialis and biceps brachii
• soleus and gastrocnemius
• other examples????
Muscle Torque
• Moment arm - shortest (perpendicular)
distance between a force's line of action and
an axis of rotation.
• The moment arm for a muscle with respect
to a joint center is the perpendicular
distance between the muscle's line of action
and the joint center.
Muscle Torque
• Muscle applies force by creating
tension on bones
• Muscle crosses a joint or joints
• Muscle has a moment arm
Borelli
Muscle Torque
• As a joint moves through a range of motion,
there are changes in the moment arms of the
muscles crossing the joints.
• For any given muscle, the moment arm is
largest when the angle of pull on the bone is
closest to 90 degrees.
Elbow at 90o of flexion
Elbow at 135o of flexion
Elbow at 45o of flexion
Muscle Torque
• Changes in a moment arm directly affect the
joint torque that a muscle generates.
• For a muscle to generate a constant joint
torque during an exercise, it must produce
more force as its moment arm decreases.
Couple
• A pair of equal, oppositely directed forces
that act on opposite sides of an axis of
rotation to produce torque.
Muscle Torque
• Concentric torque - when net torque and
joint movement occur in the same direction.
• Eccentric torque - torque in the direction
opposite joint motion.
Torque
• Movement speed - when other factors
remain constant, increased movement speed
is associated with increased resultant joint
torque during exercise such as the squat.
Torque
• However, increased movement speed during
weight training is generally undesirable
because increased speed increases not only
the muscle tension required, but also the
likelihood of incorrect technique and
subsequent injury.
Torque
• Acceleration of the load early in the
performance of a resistance exercise also
generates momentum, which means that the
involved muscles need not work as hard
throughout the range of motion as would
otherwise be the case.
Torque
• For these reasons it is both safer and more
effective to perform resistive exercises at
slow controlled movement speeds.
Torque
• During eccentric contractions, muscle and
bone function as a second class lever.
Strength training and torque
Biceps Curl
• Muscle as torque generator
• moment arm changes through ROM
• muscle’s ability to create force changes through
ROM (Read Chapter 12 in McGinnis)
• External forces as torque generators
• segment weight
• handheld weight (dumbbell)
Strength training and torque
Calculate Extensor Muscle
Force
Forces:
P (hand held load) = 90 N
W (HAT weight) = 80 N
Moment Arms
Lw = 25 cm
Lp = 60 cm
Lm = 5 cm
Calculate Extensor Muscle
Force
Clockwise torque:
-90 N * 60 cm = ?
-90 N * 0.60 m = -54 Nm
-80 N * 25 cm = ?
-80 N * .25 m = -20 Nm
(-54 Nm) + (-20Nm) = -74 Nm
Calculate Extensor Muscle
Force
T = 0
-74 Nm = F * 5 cm
-74 Nm = F * 0.05 m
F = -74Nm ÷ 0.05 m
F = 1500 N
Additional calculations
Measuring torque to assess the
effects of Lifetime Fitness
Torque Decline with Age
Athletes vs Sedentary
Power Decline
Torque
&
Baseball
Pitching
Forces and Torques
in Equilibrium
• Static Equilibrium
• sum of forces on the body = 0
• F = 0
• sum of torques on the body = 0
• T = 0
Human Machines
• Torques and Moments of Force
Human Machines
• The human body has many structures that
function in a machine-like fashion
Human Machines
• When analyzing human machines, it is
important to recall Newton’s 3 Laws of
motion.
• Law of Inertia
• Law of Acceleration
• Law of Action-reaction
Functions of a Machine
•
•
•
•
•
Provide mechanical force advantage.
Provide speed of motion advantage.
Provide range of motion advantage.
Change the direction of the resistive force.
Balance two or more forces.
Human Machines
• Levers.
• Bones and muscles.
• Wheel and axle.
• Vertebrae and ribs.
• Pulley.
• Femur (quads), patella, and tibia.
Classes of Levers
First Class
M
Sit-up
Looking upward
Rising up on your toes*
R
Classes of Levers
Second Class
R
M
Lowering a weight held in the hand
eccentrically
Classes of Levers
Third Class
M
Lifting a weight held in the hand
concentrically
R
http://www.dynamicscience.com.au/tester/solutions/hydraulicus/humanbody.htm
Class 1 Lever in the Body
Class 3 Lever in the Body
Class 2 Lever in the Body**
**Please note that the "Class 2 lever in the body" detailed above is not correct. It has
been pointed out that the fulcrum will be the ankle during any plantarflexion
movement and not the contact with the ground, making it a third class lever (1st). At the
present time we are unable to identify a class 2 lever in the body. This example of a
level 2 lever is provided in a number of Physical Education books.
Torque
• Most muscle-bone systems of the human body are
also of the third class for concentric contractions,
with the muscle supplying the applied force and
attaching to the bone at a short distance from the
joint center compared to the distance at which the
resistance supplied by the weight of the body
segment or that of a more distal body segment
acts.
Mechanical advantage, ROM, and Speed
of Motion
• The moment arm of an applied force can
also be referred to at the force arm, and the
moment arm of a resistance can be referred
to as the resistance arm.
Torque
• Skilled athletes in many sports intentionally
maximize the length of the effective
moment arm for force application to
maximize the effect of the torque produced
by muscles about a joint.
Torque
• The longer the radius of rotation, the greater
the linear velocity of the racket head or
hand delivering the pitch, and the greater
the resultant velocity of the struck or thrown
ball.
Torque
• The force-generating capability of a muscle
is affected by muscle length, cross-sectional
area, moment arm, angle of attachment,
shortening velocity, and state of training.
Torque
• The angle of maximum mechanical
advantage for any muscle is the angle at
which the most rotary force can be
produced.
• The maximum mechanical advantages for
the brachialis, biceps, and brachioradialis
occur between angles at the elbow of
approximately 75 and 90 degrees.
Torque
• As joint angle and mechanical advantage
change, muscle length also changes.
• Variable resistance training devices are
designed to match the resistance offered to
the torque-generating capability of the
muscle group as it varies throughout a range
of motion.
Torque
• The term isokinetic implies constant angular
velocity at a joint when applied to exercise
machinery.
Equations of static
equilibrium
• Equilibrium is a state characterized by
balanced forces and torques.
•
• In keeping with Newton's first law, a body
in equilibrium is either motionless or
moving with constant velocity.
Equilibrium
• Whenever a body is completely motionless,
it is in static equilibrium.
• Three conditions must be met for a body to
be in a state of static equilibrium:
1) The sum of all vertical forces (or force
components) acting on the body must be 0,
Equilibrium
2) the sum of all horizontal forces (or force
components) acting on the body must be 0, and
3) the sum of all torques must be 0.
• The application of any unopposed (net)
force to a body results in acceleration of the
body.
Equations of dynamic
equilibrium
• Bodies in motion are considered to be in a
state of dynamic equilibrium, with all forces
acting resulting in equal and oppositely
directed inertial forces.
• A balance exists between applied forces and
inertial forces for a body in motion.
Center of gravity
• A unique point around which the body's
mass and weight are equally distributed in
all directions.
• The CG of a perfectly symmetrical object of
homogeneous density and therefore
homogeneous mass and weight distribution,
is at the exact center of the object.
Center of Gravity
• Theoretical point about which the force of
gravity is considered to be evenly
distributed.
• It can also be considered the body’s balance
point.
Center of gravity
• If the object is a homogeneous ring, the CG
is located in the hollow center of the ring.
• However, when mass distribution within an
object is not constant, the CG shifts in the
direction of greater mass.
Center of gravity
• It is also
possible for an
object's CG to
be located
physically
outside of the
object.
Center of gravity
• Location of the CG of the human body is
complicated by the fact that its constituents
(such as bone, muscle, and fat) have
different densities and are unequally
distributed throughout the body.
Center of gravity
• The location of a body's CG is of interest
because, mechanically, a body behaves as
though all of its mass were concentrated at
the CG.
Center of gravity
• For example, when the human body acts as
a projectile, the body's CG follows a
parabolic trajectory, regardless of any
changes in the configurations of the body
while in air.
Center of gravity
• The strategy of lowering the CG prior to
takeoff enables the athlete to lengthen the
vertical path over which the body is
accelerated during takeoff, thus facilitating
a high vertical velocity at takeoff.
Center of gravity
• The speed and angle of takeoff primarily
determine the trajectory of the performer's
CG during the jump.
• The only other influencing factor is air
resistance, which exerts an extremely small
effect on performance in the jumping
events.
Application
Methods of locating the
CG
• Every time the body changes configuration, its
weight distribution and CG location are changed.
• The location of the CG of a multi-segmented
object is more influenced by the positions of the
heavier segments than by those of the lighter
segments.
Center of gravity
• Balance method - uses reaction board.
Center of gravity
• Segmental method - procedure for
determining total body center of mass
location based on the masses and center of
mass locations of the individual body
segments.
Center of gravity
• The segmental method is most commonly
implemented through a computer program
that reads x,y coordinates of joint centers
from a file created by a digitizer.
Stability and Balance
• Stability - resistance to disturbance of
equilibrium.
• Balance - ability to control
equilibrium.
Stability and Balance
• Different mechanical factors affect a body's
stability.
• According to Newton's second law of
motion, the more massive an object is, the
greater the force required to produce a given
acceleration.
Stability and Balance
• Football lineman who
are expected to
maintain their
positions despite the
forces exerted on
them by opposing
lineman are therefore
more mechanically
stable if they are
more massive.
Stability and Balance
• In contrast, gymnasts
are at a disadvantage
with greater body
mass because
execution of most
gymnastic skills
involves disruption of
stability.
Stability and Balance
• The greater the amount of friction between
an object and the surface, or surfaces it
contacts, the greater the force requirement
for initiating or maintaining motion.
Base of Support
• Area bound by the outermost regions of
contact between a body and support surface
or surfaces.
Base of Support
• When the line of action of a body’s weight
moves outside the base of support, a torque
is created that tends to cause angular motion
of the body, thereby disrupting stability
with the CG falling toward the ground.
Base of Support
• The larger the base of support is, the less
the likelihood that this will occur.
Base of Support
• The horizontal location of the CG relative to the
base of support can also influence stability.
• The closer the horizontal location of the CG to the
boundary of the base of support, the smaller the
force required to push it outside the base of
support, thereby disrupting equilibrium.
Base of Support
• Alternatively, if a horizontal force must be
sustained, stability is enhanced if the CG is
positioned closer to the oncoming force,
since the CG can be displaced farther before
being moved outside the base of support.
Base of Support
• The height of the CG relative to the base of
support can also affect stability.
• The higher the positioning of the CG, the
greater the potentially disruptive torque
created if the body undergoes an angular
displacement.
Principles of Mechanical
Stability
When other factors are held constant, a body’s
ability to maintain equilibrium is increased
by the following:
• Increasing body mass
• Increasing friction between the body and the
surface or surfaces contacted
Principles of Mechanical
Stability
• Increasing the size of the base of support in
the direction of the line of action of an
external force.
• Horizontally positioning the CG near the
edge of the base of support on the oncoming
external force.
Principles of Mechanical
Stability
• Vertically positioning the center of gravity
as low as possible.