Linear KineticsCHAPTER 3Basic Dimensions Need common units of measure for quantitative analysis Qualitative variables have quantitative counterparts LENGTH TIME SPACE OTHERSLENGTH Describes position in space Critical component of sport1) Anthropometrics2) Equipment3) Dimension of sport4) International system used5) METER (m)TIME Important dimension in sport Performance measure Initial or start time Final or end time SECONDS (s)Other Descriptors Mass Inertia Weight Force Length, Time, & Mass are the BASIC dimensions used in mechanics Everything else is derived from these 3 MASS (m)- quantity of matter composing a body WEIGHT (N or lb)- gravitational forceacting on a body; proportional to m …wt = mag INERTIA - resistance to action, change, to move; directly proportional to mass FORCE - push or pull acting on a body; magnitude direction & point of applicationFORCE any interaction (push or pull) between two objects that can cause an object to accelerate either + or - magnitude (vector) direction (angle) pt. of application line of actionNEWTON’S LAWS Sir Isaac Newton Born the year Galileo died Cambridge educated The Black Plague 1686 ~ PrincipiaLaw of Inertia A body will maintain a state of rest or constant velocity unless acted on by an external force that changes the state Principle of Conservation of MomentumMechanical Behavior of Bodies in Contact Linear Momentum: Quantity of Motion M = mv Units - kg • m/sPrinciple of conservation of momentum:In the absence of external forces, the total momentum of a given system remains constantMechanical Behavior of Bodies in Contact Newton:When two bodies undergo a direct collision, the difference in their velocities immediately after impact is proportional to the difference in their velocities immediately before impact-e = relative velocity after impact = v1-v2relative velocity before impact u1-u2Mechanical Behavior of Bodies in Contact Impact:Perfectly elastic impact: -e ≈ 1Perfectly plastic impact: -e ≈ 0Coefficient of restitution:Absolute value of the ratio of the v of separation to the v of approachLaw of Acceleration A force applied to a body causes an acceleration of that body of a magnitude proportional to the force, in the direction of the force, and inversely proportional to the body’s mass F = ma ~or~ a = F / mMechanical Behavior of Bodies in Contact Impulse: Impulse = FtDerived from Newton’s Second law: F = ma F = m ([v2-v1] / t) Ft = (mv2) - (mv1) Ft = ∆MLaw of Reaction For every action, there is an equal and opposite reaction When one body exerts a force on a second, the second body exerts a reaction for that is equal in magnitude and opposite in direction of the first bodyLaw of Gravitation All bodies are attracted to one another with a force proportional to the product of the masses and inversely proportional to the square of the distance between them Fg= G(m1m2/