Vector Summation and Composition Kinetic vector quantities –force weight, pressure, specific weight & torque Kinematic vector quantities –Displacement, velocity & acceleration Scalar quantities –Mass, volume, length & speed

Vector Composition (Addition) Resultant vector “Tip-to-tail” vector composition Vector #1 Vector #2 Resultant vector

Vector Addition Problems found in human motion analysis Combining forces –Net effect of two forces applied to any object –What is maximum safe speed for a curve? Centrifugal force, frictional force, & gravity –What makes a curveball curve? Wind force and weight Combining velocities –In crossing a river, what direction is best? Velocity of water and swimmer –In aviation, correcting for wind air speed and ground speed

Vector Resolution Vertical Horizontal Example: A ball is thrown into the air Resultant

Vector resolution problems found in human motion analysis (pp 76-81) Projectile motion situations –Find horizontal velocity –Find vertical velocity Friction problems –Find horizontal force component (Friction) –Find vertical component (Normal) First step in adding, or combining vectors –When more than one force is acting on an object –When adding velocity vectors

Trigonometric Solution of Vector Problems A more accurate procedure for quantitatively dealing with vector problems

Vector resolution: Turning comp = FdsinΘ Radial comp = FdcosΘ (  d = dsinθ) Vert comp = FsinΘ Horiz comp = FcosΘ Θ Vert comp = FsinΘ Horiz comp = FcosΘ Θ Θ Θ Θ d

Sum of two forces: Sum of two velocities: Vector composition, or addition

Final step – what is the effect of the sum of these vectors? If the vectors are forces, then the net effect is to accelerate the object: a = F/m

6. Effect of net force: a = F/m = 86.9 N/ 2 kg = ms -2

Homework assignment on Vector Summation Handout homework problem to turn in Monday, February 9 Self-test problems: –Additional problems, p 81 # 4 and 5

COM Concepts and calculation procedures Obbjectives –To review concept of COM –To review reasons for studying COM –To review calculation method for calculating COM of human body

Why study Center of Mass of Human Body? It simplifies the movement of the complex system so that we can understand its overall motion It allows us to easily consider the effect of net external forces (F = ma; a = F/m) Example of important issues related to COM –Is COM different for children and adults in a way that affects movement? –Can an athlete really “hang in the air” –Is COM different for males and females in a way that affects movement?

COM/COG Calculation Method (pp : Kreighbaum pp , ) Concept of balancing segmental torques Segmental Calculation of COM –General calculation method –Information needed Proportionate mass of each segment (p 520) location of COM of each segment (p 521) –Homework problem (handout in class)

Segmental concept of center of mass

Segmental Calculations & Homework Problem

Segmental concept of center of mass –Information needed Proportionate mass of each segment (p 520) location of COM of each segment (p 521)

Summary Chapter 3 introduced basic concepts related to kinetics: –Several types of mechanical loads act on the human body. –The distribution of force within a body structure is termed mechanical stress. –Vectors quantities have magnitude & direction –Vector problems may be solved by a graphic or a trigonometric approach. –Calculation methods for vector summation and resolution of vectors were presented –Center of mass (COM) concepts were reviewed –Calculation methods for total body COM were presented

Next Class – Wednesday, Feb 11 Read text, pp Take web-based quiz for Chapter 10 Objectives –Review characteristics of projectile motion –Review factors influencing projectile motion –Present and explain calculation methods for analyzing projectile motion Homework – due Monday, Feb 16 –Problems 7,9,10 on page 347