• Introduce the concepts of force, which causes linear motion, and torque, also called moment of force, which causes angular motion
• Discuss the effect of applied forces and moments of force through the consideration of laws and equations set forth by Newton and Euler
• Explain how to create and use free-body diagrams
• Identify various forces encountered in biomechanical investigations
• Define the mechanical concepts of impulse and momentum, which dictate the effect of changing levels of force and moment applied over a duration
• Describe how to measure force and moment for human biomechanics research

All sections of this chapter will be covered.

FORCE

A force is a push or a pull.

Newton's Laws of Motion

• Newton's First Law of Motion
  Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare (Newton 1686/1934, p. 644).
  
  Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.
  
  
• Newton's Second Law of Motion
  Mutationem motis proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur (Newton 1686/1934, p. 644).
  
  The change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed. (F=ma)
  
  
• Newton's Third Law of Motion
  Actioni contrariam semper et aequalem esse reactionem: sive corporum duorum actiones in se mutuo semper esse aequales et in partes contrarias dirigi (Newton 1686/1934, p. 644).
  
  To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal and directed to contrary parts.
  

Free-Body Diagrams

Page 75 in your book describes each step in detail. We will draw a couple of examples in class.

Types of forces

• Weight: Univerisal law of gravitation
• Ground Reaction Force (GRF)
• Friction
  • Static
  • Dynamic
• Centrifugal and Centripetal Forces
• Coriolis Force

Linear Impulse & Momentum

F = ma

F = m(Δv/Δt)

FΔt = mΔv

∫FΔt = mv_f - mv_i

In the lab:

1. Perform a vertical jump with and without a counter-movement
2. Perform a standing sprint start and a block start
3. Perform various calculations on the raw data (jump height, resultant velocity, impulses, direction of force, ...)
4. Discuss the forces as a group to determine what the forces mean in terms of whole-body movement (this spreadsheet may be of interest)

Moment of Force (Torque)

Torques occur when a force is applied at some distance from an axis of rotation

T=F⊥d

Angular Impulse and Momentum

L = I ω

I = mk²

M = Iα

M = I (Δω/Δt)

M Δt = I Δω

∫M dt = (I Δω)_f - (I Δω)_i

Where does angular impulse apply?

Total body angular impulse

Comparing Force Data Across Subjects

Normalization by

• time
• force magnitude

In the lab:

1. Have everyone in class walk across the force plate
2. Find a way to normalize for time
3. Find a way to normalize for force magnitude

Mini-Project #4