5. Linear and Angular Kinetics_Student.pptx
Transcript
Linear and Angular Kinetics Kinetics Forces that cause the movements Newton’s Laws: Linear Form the bases for understanding human movement Laws 1. Inertia 2. Acceleration 3. Action-reaction Newton’s 1 Law of Motion st 1.Inertia If no external forces act on a body then the...
Linear and Angular Kinetics Kinetics Forces that cause the movements Newton’s Laws: Linear Form the bases for understanding human movement Laws 1. Inertia 2. Acceleration 3. Action-reaction Newton’s 1 Law of Motion st 1.Inertia If no external forces act on a body then the velocity of the body remains constant If a body is stationary and no force acts upon it, it does not move If a body is moving at a given velocity it will continue to move at that velocity unless a force acts upon it Force is required to start, stop, or alter motion Newton’s 1st Law of Motion 1.Inertia Newton’s 2 nd Law of Motion 2.Acceleration The acceleration of an object is directly proportional to, and in the same direction as, the force acting on it and inversely proportional to its mass F=ma Where, F= force m=mass a=acceleration Newton’s 2 nd Law of Motion 2.Acceleration Newton’s 2 nd Law of Motion 2.Acceleration Units Mass … kg Acceleration... m/s2 Force... kg*m/s2 or Newton (N) 1 N = the force required to change the acceleration of a 1kg mass by 1 m/s2 Mass vs. Weight An application of Newton’s 2nd law Mass: how much matter there is in the body Indicates how difficult it is to accelerate the object Masses attract one another Larger mass = larger attraction Think: gravity Gravity: accelerates bodies toward center of earth at 9.81 m/s2 Mass vs. Weight An application of Newton’s 2nd law Weight: measure of your attraction to the earth It is a force!!! Weight = mass * acceleration due to gravity Weight = mg Mass vs. Weight An application of Newton’s 2nd law If we have a 100kg block, calculate its weight on earth and on the moon. g on the moon is 1/6th that of earth W=mg Mass vs. Weight Earth Moon Weight = mg Weight = mg Weight = 100 * 9.81 Weight = 100 (9.81/6) Weight = 981N Weight = 163.5N Newton’s 3 Law of Motion rd 3.Action-reaction For every action, there is an equal and opposite reaction Each force exerted by one object on another is counteracted by a comparable force exerted by the second object on the first Newton’s 3rd Law of Motion 3.Action-reaction Newton’s 3rd Law of Motion 3.Action-reaction reaction actio n Ground Reaction Force Ground Reaction Force Reaction force provided by the surface on which movement is performed Derived from Newton’s 3rd law Measured using force platform Components Vertical Forward-backward Side to side Ground Reaction Force Ground Reaction Force Extent to which a segment contributes to GRF depends on Mass Acceleration of COM Estimates Trunk and head = 50% Legs = 17% each Arms = 5% each Ground Reaction Force During running Initial Mid-stance – contact- toe off mid- vGRF stance smaller Upward hGRF vGRF and forward as backward runner hGRF to propels decelerate self forward GRF counteracts downward motion of runner Ground Reaction Force During running Initial Mid-stance – contact- toe off mid- vGRF stance smaller Upward hGRF vGRF and forward as backward runner hGRF to propels decelerate self forward Ground Reaction Force During running GRF counteracts downward motion of runner Ground Reaction Force During running Ground Reaction Force During running high speed running and grf deceleration with grf overlay Newton’s laws: Angular Newton’s Laws: Angular Moment of Inertia Resistance of a body to rotation about a given axis Where, I= moment of inertia N= number of particles making up the rigid body mi= mass of a particle ri= distance from axis Newton’s Laws: Angular Moment of Inertia Units If we consider our equation in terms of units… Mass... kg Distance … m Therefore Inertia … kg*m2 Newton’s Laws: Angular Moment of Inertia Is a function of mass and the distribution of that mass https://ophysics.com/r3.html Newton’s Laws: Angular Moment of Inertia Mass distribution is more influential than mass Consider 4 objects of different masses and distributions: Newton’s Laws: Angular Moment of Inertia Newton’s Laws: Angular Moment of Inertia Bat A and B have same mass B easier to swing b/c mass is closer to axis of rotation Newton’s Laws: Angular Angular Momentum Product of angular velocity and moment of inertia Angular momentum = moment of inertia x angular velocity Where, H= angular momentum I= moment of inertia w= angular velocity Newton’s Laws: Angular 1. Law I If no external moments act on a body the angular momentum remains constant A moment is required to start/stop/alter angular motion Newton’s Laws: Angular 1. Law I This is especially relevant in flight as no external moments act Decrease I ïƒ increase w Increase I ïƒ decrease w Example Ice skater, twisting gymnast Newton’s Laws: Angular 2. Law II The angular acceleration of a body is proportional to the moment causing it Moment is calculated in two ways Where, Where, T=moment T=moment I=moment of inertia F=force causing moment a=angular acceleration d=moment arm of the force Newton’s Laws: Angular 2. Law II More common application Units: Nm Newton’s Laws: Angular 3. Law III Bodies exert equal and opposite moments on Tfemur=Tti each other Example: adjacent bia segments in the human body exert equal and opposite moments on one another Newton’s Laws: Angular Important in understanding the biomechanics of somersaulting, gymnastics, diving, etc. Newton’s Laws: Angular Whole Body Center of Mass Mass: measure of the amount of matter comprising an object (units: kg) Center of mass (COM): location about which the mass of a body is evenly distributed **does not have to lie within the body** In flight, the path of a rigid body can be traced by tracking path of COM In flight, rotation occurs about axes passing thru COM Newton’s Laws: Angular Somersaulting Law II T=Fd Moment arm is distance from axis of rotation to line of action of the force If force acts thru the axis of rotation, d=0 and T=0 If d has magnitude, F will cause turning moment Newton’s Laws: Angular Somersaulting Created by applying a force that does not act through the body’s COM Newton’s Laws: Angular Somersaulting *causes turning moment (T) in direction of COM d=0.0m d=0.2m d=0.2m Newton’s Laws: Angular Somersaulting *causes turning moment (T) in direction of COM d=0.0m d=0.2m d=0.2m Newton’s Laws: Angular Forward roll mg Key Topics Addressed Kinetics Newton’s Linear Laws 1. Inertia 2. Acceleration 3. Motion Ground Reaction Force Newton’s Angular Laws Whole Body Center of Mass
