Concepts of Impulse-Momentum Relationship

• Inertia:

  • Inertia is the observed natural tendency of an object in motion to keep moving in the same direction & at the same speed, or if at rest, to stay at rest
• Inertia:

  • Inertia = resistance to change (in motion state)
  • One of the biggest inertia values is our mass
  • greater mass, greater inertia to change
  • Not really that helpful or descriptive for human motion or motion on earth
• Momentum:

  • To fully describe the property of inertia with units we can measure, we must quantify an object’s speed of motion, & resistance to change of motion
  • Momentum (L) = Mass x Velocity
  • How do we change trajectory?
  • Once has certain amount of momentum
• Momentum:

  • A heavy object travelling fast will have a greater momentum than a light object travelling at the same speed
  • Avg inside centre (#12) = 100 kg, 185 cm
  • Avg scrum half (#9) = 82 kg, 176 cm
• Momentum:

  • Momentum - grown in its resistance
  • Have to work harder to change it
  • Larger momentum got to work harder
• But, how do we change our state of motion?

  • Recall from Kinematics that a change in velocity causes an object to accelerate or decelerate
  • F = ma
  • So, to change the state of motion we need to apply a force, but how does this inform us about the change in motion?
• But, how do we change our state of motion?

  • The magnitude of acceleration or deceleration is proportional to the net force acting on the object & inversely proportional to the mass
  • Change of velocity = proportional to force
  • Object mass is still greatest resistance in changing trajectory
  • If mass changes need more force
  • If wanna change trajectory need to apply force
  • F = ma
• Concepts - Important interpretations of the ∑F = ma relationship:

  • ∑ = sum of
  • Cause (∑F) & effect (a) relationship
  • a directly proportional to & in the same direction as ∑F (net force)
  • ∑F - talking about net force = sum of all forces applying (some acting direction against us & for us)
  • Magnitude & direction is important (the vector)
  • To produce a given a, it takes a larger ∑F for a more massive object
  • Force will have to change dependent on the mass
• Concepts:

  • Recall Newton’s 2nd Law
  • F= ma
  • F = applied force (N)
  • m = mass of the body (kg)
  • a = acceleration of the body (m/s^2)
• Consider that for impulse-momentum equation:

  • Time becomes important factor as force
  • Effort not same throughout ROM of lift/movement → as joint angle changes, as muscle changes length amount can apply changes depending on length
  • Over a period of time force we apply changes, force is not constant so time is important as can’t apply constant force
• How do we change the state of motion of system:

  • ∫∑ F dt = L final - L initial
  • Left: Impulse of net external forces exerted on the system
  • As apply force going to change overtime
  • ∫ = area under the curve
  • Take small bits of area under curve
  • ∑ = sum of
  • Right: Change in momentum of the system
  • Conventional form:
  • L inital +∫∑ F dt = L final
  • Final momentum = where we want to be
  • How much force over time = how much change in trajectory
• Impulse changes the quantity of motion of the system:

  • Since Impulse = the area under the force curve
  • Which jump generated greater change in momentum (vertical velocity)?
• Impulse changes the quantity of motion of the system:

  • Momentum that changes the trajectory/impulse
  • What effective, look at impulse to see how change trajectory
  • Greatest impulse over force over time is going to jump the highest
  • Large reaction in small amount of time
  • At keeping momentum transferring in direction
• Consider:

  • The anterior-posterior forces during walking
  • L inital +∫∑ F d * t = L final
  • Questions to consider:

  1. What is the net impulsive if forward momentum doesn’t change?
  2. Which force peak would likely increase if we attempt to increase our walking speed?
  3. Which force peak to likely increase if we wanted to arrest our forward motion?
• Consider:

  • Braking & propulsion impulse
  • Cadence of gait affected by these 2 forces depending which one is greater
  • With no change in velocity has to be equal
  • Then initial is same as final so no change in impulse - doesn’t mean no force applied
  • Is about change (final - initial = difference)
  • Equal = 0 impulse
• Consider:

  • If want to walk faster
  • Increase anterior impulse in the direction wanting to go in
  • Increase acceleration
  • If want to slow down
  • Increasing braking/posterior impulse
  • Increase in deceleration
  • Direction & magnitude
• Generating Motion - maximising impulse with GRF:

  • Improve performance by maximising final velocity
• Generating Motion - maximising impulse with GRF:

  • Impulse-momentum relationship shown
  • Final velocity = to impulse & initial velocity
  • Impulse = mass (m) & net force (Fnet), change in time
• Generating Motion - maximising impulse with GRF:

  • Can’t change gravity so change net force by maximising GRF = force athlete is applying
  • Time is tricky (force over time - would think more force with more time doesn't work for human movement), want more force in shorter time (time not thought about here)
  • Mass also important - velocity, short time, flight, want less mass to be able to move further with less force
• Controlling motion - absorbing force with time:

  • Reduce injury by decreasing forces acting on the body
• Consider that for impulse-momentum equation:

  • acceleration = change in velocity / time
  • a = Δ v/t
  • Force = m (change in velocity) / time
  • F = m (Δ v) / t
  • Force x time = m (change in velocity)
  • F x t = m (Δ v)
  • F t = m (V final - V initial)
  • F t = m V final - m V initial

  
  

  • Force x time (Ft) = impulse
  • m Vinital = momentum