Linear Impulse – Momentum Relationship  F  t = m  v = m(v2-v1) Impulse (Ns) Product of a force applied over a period of time (  F  t) Momentum (kg m/s) Quantity of motion. Product of mass * velocity (m  v) Positive (negative) changes in Linear Momentum are created by Net positive (negative) Linear Impulse. Course Reader: Kinetics, p ; Linear Impulse 53-61

LINEAR IMPULSE Why? Mechanism for controlling linear velocity of the total body center of mass Necessary for successful completion of general locomotion tasks, and athletic movements Vv1 Vh1 Vv2 Vh2  F  t = m  v = m(v2-v1) = mv2 - mv1 tt

Net Linear Impulse (  F*  t) Generation Linear impulse magnitude = area under the force-time curve, is dependent upon … 1) Ground reaction force magnitude (  F) 2) ground contact duration (  t) Free Body Diagram FvFvFvFv FhFhFhFh BW Net Vertical Force = Fv (+) + BW (-) touchdown take-off

Net Linear Impulse, the sum of negative and positive linear impulse generated during the entire ground contact phase (touchdown – take-off) time=0 touchdown force=0 take-off time (s) Ground reaction force (N)  F  t = m  v = m(v2-v1) = mv2 - mv1 V1 V2 Free Body Diagram FvFvFvFv FhFhFhFh BW

How do you generate large Horizontal Impulse (force*time)? –  force,  time, or a combination of  force & time The mechanical goal of the task influences how Impulse is generated e.g. sprinters need to generate horizontal impulse quickly Time (s) after ground contact Horizontal GRF (N)

time (s) after contact Horizontal GRF (N)  Vh = 1.30 m/s  Vh = 1.29 m/s Similar net changes in linear momentum can be achieved with different force-time linear impulse characteristics

H GRF V GRF Time (s) after contact Touchdown Impulse-Momentum Relationship  F  t = HI = m(V 2 -V 1 ) mV h 1 FhtFhtFhtFht Take-Off mV h 2

H GRF V GRF Time (s) after contact Touchdown Impulse-Momentum Relationship  F  t = HI = m(V 2 -V 1 ) mV v 1 Take-Off mV v 2 FvtFvtFvtFvt

H GRF V GRF Time (s) after contact Touchdown Calculating Net Linear Impulse Using Geometry mV v 1 Take-Off mV v 2 mV h 1 Take-Off mV h 2

Push Tip Load Plate Departure Back Somersault: Take-off Phase VvVv VhVh Backwards Rotation Needs: Vertical Impulse (net positive), Horizontal Impulse (net negative), Horizontal Impulse (net negative), Backward-directed Angular Impulse Backward-directed Angular ImpulseHow?

BACK Somersault FVFVFVFV FHFHFHFH FRFRFRFR FVFVFVFV FHFHFHFH time prior to take-offtake-off Generation of Linear Impulse During a Back Dive Near Zero Initial TBCM Momentum (mv) Net Positive Vert. mv Net Negative Horiz. mv Initiation Take-Off

VRF BACK Somersault time prior to take-offtake-off FVFVFVFV FHFHFHFH FRFRFRFR FVFVFVFV Generation of Linear Impulse During a Back Dive time prior to take-offtake-off FHFHFHFH

Mechanical objective of the shot put: Vertical Impulse (net positive) Horizontal impulse (net negative - translate backward)

 F=ma linear acceleration of the athlete’s center of mass is determined by the sum of forces acting on the center of mass Free Body Diagram Mass-Acceleration Diagram FvFvFvFv FhFhFhFh F BW Vertical  F v = F BW (-) + F v (+)  F v = ma v  F v = m (  v/  t)  F v  t = m (  v) ahah avavavav Linear Impulse – Momentum Relationship  F  t = m  v = m(v2-v1)

 F=ma linear acceleration of the athlete’s center of mass is determined by the sum of forces acting on the center of mass Free Body Diagram Mass-Acceleration Diagram FvFvFvFv FhFhFhFh F BW Horizontal  F h = F h (+)  F h = ma h  F v = m (  v/  t)  F v  t = m (  v) ahah avavavav Linear Impulse – Momentum Relationship  F  t = m  v = m(v2-v1)

Vertical force Horizontal force BW HGRF VGRF BW BW V GRF = BW V GRF > BW Linear Impulse – Momentum Relationship  F  t = m  v = m(v2-v1) V GRF = 0

Vertical force Horizontal force Body weight Time (s) prior to departure Ground Reaction Forces (Newtons) BW BW BW HGRF VGRF

Body weight Time (s) prior to departure Ground Reaction Forces (Newtons) Net Impulse = Change in Momentum (  Force) *(  time) = (mass)*(  velocity) Increase in the positive vertical velocity Increase in the negative horizontal velocity (+) vertical impulse (-) horizontal impulse

Mechanics of each phase influence the mechanics during the next phase. Impulse generation during the unseating phase will influence initial conditions of the blocking phase. Impulse Projectile motion MomentumTransfer

Mechanical Objective of the Shot Put Maximize the horizontal distance traveled by the shot Projectile Motion

How does the shot become a projectile? Total body momentum is generated and passed on to the shot

Take-Home Message Each foot (ground) contact is an opportunity to: a) increase, b) decrease, or c) maintain your total body momentum.