Chapter 1: Forces

A force is a push or a pull.
A force is something that has the ability to accelerate an object.

Mass is the measure of inertia, whereas weight is the measure of the force of gravity acting on an object.
Einstein confused

Man running

Forces are described in units of Newtons or pounds
1N = 0.225lb
1lb = 4.45N
How much do you weigh?

Internal forces-Forces that act within the object or system whose motion is being investigated.

External forces-Forces that act on an object as a result of its interaction with the environment surrounding it.

Sum of forces (net or resultant force)

Static and dynamic friction

Shoe friction in running

Ground forces in running


Introduction: What is Biomechanics?

The study of forces and their effects on living systems

Technique improvement

  • Dick Fosbury
    7' 4 1/4"
  • Dwight Phillips

Equipment improvement or unimprovement

  • Javelin
    Mick Hill
  • Pole vault

Improved training and accelerated learning

  • Pole vault
  • Hammer throw

Injury prevention and rehabilitation

  • Javelin
  • Distance running

Units of Measurement

Quantity Symbol SI Unit Abbreviation for SI Unit Other Units
Time t second s millisecond, minute, hour, day, week, year
Length l meter m millimeter, centimeter, inch, foot, yard, kilometer, mile
Mass m kilogram kg gram, slug
Force F Newton N pound

Review Concepts


Chapter 2: Linear Kinematics

Kinematics is the branch of dynamics concerned with the description of motion.

100m analysis

Formulas for average speed and average velocity

What about changing speeds and velocities?

Formula for average acceleration

What does this imply for running around a curve?
Is someone accelerating when running a constant speed around a curve?


Chapter 8: Angular Kinematics

                           ANGULAR DISPLACEMENT
AVE ANGULAR VELOCITY = ---------------------------
                             CHANGE IN TIME
                            CHANGE OF ANGULAR VELOCITY
AVE ANGULAR ACCELERATION = ---------------------------
                                  CHANGE IN TIME
  • Slope of angular position versus time equals angular velocity
    Running Example

  • Connection of Linear and Angular Velocity: Hammer example

    V = w * r

  • Tangential Acceleration: The component of of linear acceleration tangent to the circular path of a point on a rotating object

    aT = a * r

  • Centripetal Acceleration: The linear acceleration directed toward the axis of rotation

    ar = w 2 r

Hammer throw example


Chapter 3: Projectile Motion

A Projectile is any body that has been set on its path by some force and continues in motion by its own inertia. (Gravity has a major effect on motion).

Let's begin simply with purely vertical motion
Projectile Cartoon
Now let's add horizontal motion

Horizontal and vertical components are independent

Equations of motion for projectiles

Characteristics of projectiles

Demonstration on what happens as initial conditions are altered

Things get more complex when takeoff and landing heights are different
Formula for flight time

  • Practice Question:
    A shot is realeased with the following conditions:

    Vh = 9 m/s
    Vv = 8 m/s

    height = 2 m

    Flight Time = ?
    Maximum Height = ?
    Horizontal Displacement = ?
    Shot Put Example

Flight and Center of Mass


Chapter 4: Linear Kinetics

Review Concepts

Isaac Newton (1642-1727)
Isaac Newton

Newton's Laws of Motion

Force affects motion

Measuring Ground Reaction Forces

Ground Reaction Forces in Walking and Running


John Godina
Formulas for Impulse and Change in Momentum

Alter-g Treadmill: How Do Weight and Inertia affect preferred movement?


Chapter 9: Angular Kinetics

Newton's First Law of Motion (relating to angular motion)

Angular Inertia: The property of an object to resist changes in angular motion

I = mk2

Angular inertia depends upon mass distribution

Moment of inertia about eccentric axes
Ib = Icg + mr2

Moment of inertia in a runners leg
What is the benefit to having limbs that are tapered (The proximal ends are larger than the distal ends)?
Bernard Lagat running
Moment of inertia in cycling

Ice-skating examples of manipulating inertia (Calculation)
Angular Momentum: H=Iω

Angular momentum in a non-rigid body can be estimated by:
H = ∑Iω

Angular momentum is conserved when no external torques are created on the body.

Angular momentum conservation requires H to be constant.
However, I and ω can change.

Newton's Second Law of Motion (relating to angular motion)

Linear Angular
F=ma T=Iα

F=ma led to FΔt = mΔv
In angular motion, T=Iα leads to:
TΔt = IΔω

A change in angular momentum may result in:
  • A change in angular velocity (hammer throw)
  • A change in direction of the axis of rotation (bicycle wheel gyroscope)
  • A change in moment of inertia
Newton's Third Law of Motion (relating to angular motion)

For every torque exerted by one object on another, the other object exerts an equal torque back on the first body but in the opposite direction

Carl Lewis long jumping (video)


Chapter 5: Work, Energy, & Power

A pole vaulter uses the relationship between mechanical work and energy.

Work is the product of force and displacement.

  • U = Fd
    • U = Work done to the object
    • F = Average force exerted on the object
    • d = displacement of the object along the line of action of the average force

Energy is the capacity to do work

  • Potential Energy
    • Gravitational Energy=-mgh
    • Strain Energy=0.5kΔx2
  • Kinetic Energy=0.5mv2

Energy transfer in trampolining

Why does a high jumper use a run-up?

Why did a shot putters starting postion change?

Shot putters starting postion years ago Shot putters starting postion nowadays (Jillian Camarena)


Work & energy in the javelin

Power is the rate of doing work (measured in Watts)
P = U/t or P = F(v)


Chapter 6: Center of Mass

Stability: The capacity of an object to return to equilibrium or to its original position after being displaced

Factors affecting stability:

  • Height of the center of mass
  • Size of base of support
  • Weight of object

Chapter 10: Fluid Mechanics

What affects motion through a fluid?
Surface - Shape - Size - Velocity - Medium

Fluid Force

Drag Force: The component of dynamic fluid force that acts in opposition to the relative motion of the object with respect to the fluid.
Surface Drag: Drag force acting on an object within a fluid and caused by friction between the fluid and the surface of the object.
Form Drag: Drag force acting on an object within a fluid and caused by the impact forces of the fluid molecules with the object.

Drag Force: FD = CDρAv2/2

Bob Beamon's Long Jump Record (Relative and absolute motion)
How was each factor from the drag force equation modified in Bob Beamon's jump?

Drag Forces in Running

Should grown men shave their legs?

Terminal velocity: The ultimate speed that can be attained when falling under the influence of gravity

Lift Force
Bernoulli's Principle: Faster-moving fluids exert less pressure laterally that do slower-moving fluids.

FL = CL A ρ v2/2

Wing Lift
Airplane example

Magnus Force

Magnus Force

Javelin trajectories

Discus flight


Chapter 11: The Musculoskeletal System

Muscle Physiology

  • Parallel and Pennate Fiber Arrangements
    • Force
    • Range of motion
  • Mono and Bi-Articular Muscles
  • Lever Systems and Angle of Pull

Quadriceps Force and Quadriceps Moment Arm

Connective Tissue

  • Ligaments
  • Tendons
  • Fascia

Types of Contractions

  • Isometric
  • Concentric
  • Eccentric

Chapter 12: Kinesiological Concerns for Performance

Factors related to injury development

  • Intrinsic factors
    • Bone mineral density
    • Force magnitude
    • Force direction
  • Intrinsic factors
    • Running surface
    • Shoe
    • Level of performance
  • Tissue Characeristics
    Cortical 90-170 MPa 100-280 MPa 50-100 MPa
    0.7-5% 1-2.4%
    Cancellous 1.5-2 MPa
    Ligament 1-2 MPa
    Tendon 40-100 MPa

    Joint Structure

    Firing Orders

    Transmission of Forces

    Elastic Energy


Chapter 13: Kinesiological Concerns for Training

Repetition and Compounding of Errors

Backtracking as a Troubleshooting Tool

Anticipation as a Cause of Errors


USATF Coaching Education