# 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

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)

Friction
Static and dynamic friction
F=μN

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
• Dwight Phillips

• Javelin
• Pole vault

• 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

SPEED vs VELOCITY

What about changing speeds and velocities?

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

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

• 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)

Newton's Laws of Motion

Force affects motion

Measuring Ground Reaction Forces

Ground Reaction Forces in Walking and Running

F=ma

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)?

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?

U = ΔGPE + ΔKE + ΔSE

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 7: Spatial & Directional Terminology

Spatial and Directional Terminology
Anterior/Posterior
Superior/Inferior
Medial/Lateral
Proximal/Distal

Frontal Plane
Sagittal Plane
Transverse Plane

Longitudinal Axis
Anteroposterior Axis
Transverse Axis

# Chapter 10: Fluid Mechanics

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

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

Airplane example

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

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  Tension Compression Shear Cortical 90-170 MPa 100-280 MPa 50-100 MPa 0.7-5% 1-2.4% Cancellous 1.5-2 MPa 0.6% Ligament 1-2 MPa 30-125% Tendon 40-100 MPa 10-17%

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