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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

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Chapter 5

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chapter 5
Chapter 5

Torques and Moments of Force

Maintaining Equilibrium or Changing Angular Motion

to this juncture
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
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
Line of actionrelative 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 rotation5
Line of actionrelative 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 rotation6
Line of actionrelative to axis of rotation
  • Centric force
  • Eccentric force
  • Force couple
    • two eccentric forces
  • 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???

  • Definition
    • the turning effect of a force
    • the tendency of a force to cause rotation
moment arm lever arm
Moment Arm(lever arm)




line of action

of a force to

a specified

axis of rotation

to describe a torque
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
Examples of Torque

Click on the

picture to go

to a good website

examples of torque13
Examples of Torque

Show the

moment arm and

identify the sense

for each force

on each figure

sculling offsetting torques to create translation
Sculling: offsetting torques to create translation

Are all




in net



at the


adls must consider torque for safety and convenience
ADLs must consider torque for safety and convenience

Medicine caps must

be removable by the

disadvantaged, but

inoperable by kids.

  • 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.
  • 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 Torque
  • Muscle applies force by?
muscle torque19
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 torque20
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 torque21
Muscle Torque
  • Muscle applies force by creating tension on bones
  • Muscle crosses a joint or joints
  • Muscle has a moment arm
muscle torque23
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.
muscle torque27
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.
  • A pair of equal, oppositely directed forces that act on opposite sides of an axis of rotation to produce torque.
muscle torque29
Muscle Torque
  • Concentric torque - when net torque and joint movement occur in the same direction.
  • Eccentric torque - torque in the direction opposite joint motion.
  • Movement speed - when other factors remain constant, increased movement speed is associated with increased resultant joint torque during exercise such as the squat.
  • 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.
  • 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.
  • For these reasons it is both safer and more effective to perform resistive exercises at slow controlled movement speeds.
  • During eccentric contractions, muscle and bone function as a second class lever.
strength training and torque biceps curl
Strength training and torqueBiceps 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)
calculate extensor muscle force
Calculate Extensor Muscle Force


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 force38
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 force39
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


Measuring torque to assess the

effects of Lifetime Fitness






forces and torques in equilibrium
Forces and Torquesin Equilibrium
  • Static Equilibrium
    • sum of forces on the body = 0
      •  F = 0
    • sum of torques on the body = 0
      •  T = 0
human machines
Human Machines
  • Torques and Moments of Force
human machines48
Human Machines
  • The human body has many structures that function in a machine-like fashion
human machines49
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
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 machines51
Human Machines
  • Levers.
    • Bones and muscles.
  • Wheel and axle.
    • Vertebrae and ribs.
  • Pulley.
    • Femur (quads), patella, and tibia.
classes of levers
Classes of Levers

First Class




Looking upward

Rising up on your toes*

classes of levers53
Classes of Levers

Second Class



Lowering a weight held in the hand eccentrically

classes of levers54
Classes of Levers

Third Class



Lifting a weight held in the hand concentrically



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.

  • 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
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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • The term isokinetic implies constant angular velocity at a joint when applied to exercise machinery.
equations of static equilibrium
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.
  • 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,


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
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
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 gravity70
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 gravity72
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 gravity73
Center of gravity
  • It is also possible for an object's CG to be located physically outside of the object.
center of gravity74
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 gravity75
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 gravity77
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 gravity78
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 gravity79
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.
methods of locating the cg
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 gravity83
Center of gravity
  • Balance method - uses reaction board.
center of gravity84
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 gravity85
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 and Balance
  • Stability - resistance to disturbance of equilibrium.
  • Balance - ability to control


stability and balance87
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 balance88
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 balance89
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 balance90
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
Base of Support
  • Area bound by the outermost regions of contact between a body and support surface or surfaces.
base of support92
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 support93
Base of Support
  • The larger the base of support is, the less the likelihood that this will occur.
base of support94
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 support95
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 support96
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
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 stability99
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 stability100
Principles of Mechanical Stability
  • Vertically positioning the center of gravity as low as possible.