Angular Kinetics 3

definition

• understand ration in humans movment requires an appreciation of angualr interpretation of newtons 3 laws

• linear laws restated to describe their analogs in angular kinetics

1st law: angular

• body will maintain a constant state of angular motion unless acted on by an external force

• at rest and at motion

• body maintains constant stage of angualr motion unless acted on by external route

  • object in motion has momentum and momentum is inter in motion

    • P = mv

• angualr momentum defined as tendency for an object other than remain in angular motion

  • angualr motion is determined by moment of inertia of object and angular velocity

    • L =Iw

angular inertia

• proper of an object ot resist changes in its angular motion

• affected by mass of object nad distribution of mass of an object relative to axis of rotation

  • what defines angualr interia

• moment of interim quantified angualr interim

  • suppose object is composed of many particles of matter with mass

  • each particle resists motion

  • greater the distance particles are located from axis of rotation the harder to rotate

equation of moment of inertia

• moment of inertia dependent on some of product of distributed masses of an object and radial distances of masses away from an axis of rotation

• distribution of mass has greater influence on angualr inter than mass

• I = m * k²

  • moment of interim is dependent on total mass of object (m) and radius of gyration (k)

determining moment of inertia

• determine moment of inter by summing the moment of inter of each mass about axis of rotation

• equivalent to summing masses and taking the distance that represents where summed masses would be located (k) and maintain the same moment of inertia

• radius of gyration (k) is length measurement that represents the concentrated mass of object from axis of rotation

angualr kinetics and anthropometry

• moment of interim of limb segments and even the whole body can be useful when considering resistance of human or whole body to rotate

angualr kinetics of implements

• object in air and free to rotate it will rotate about its centre of gravity

• resistance to rotate will be dependent on its moment of inertia

• moment of inertia is related to mass and distribution of mass

rotation about CoG

• calculating moment of inter about different points shows us smallest moment of inter occurs at centre of gravity

manipulating moments of intertia of human body

• change orientation of limbs and thus distribution of mass

  • moment of inertia will also change

moment of interia about a different axis

• moment of inertia for each axis

• mass of object may be distributed more in one axis and less in another

angualr kinetics during sprint

• sprinter recues moment off nteria about hip by flexing the knee

• sprinter flexes leg at knee when accelerating leg during swing

  • reduced the moment of interita about hip joint

• improve performance by moving body segments closer to axis of rotation

conservation of angualr momentum

• angular momentum initial = angualr momentum final

• because the human body is non-rigid object a person can alter their moment of inter and thus change their angular velocity while maintaining same angular momentum

  • during human movement there is change in the potential for rotation about many axes

    • thus altering amount of inertia

newton’s 2nd law: angular

• torque applied to body causes an angualr acceleration of body of a magnitude proportional to the torque in direction of moment and inversely proportional to moment of inentria

  • T = Fd or M=Ia

    • T or M is torque

    • I is moment of inertia

    • a is angualr acceleration

  • greater the inter of an object the more force required to accelerate

• if net external torque is exerted on an object at a distance from axis of rotation

  • object will accelerate angaurly in reaction of net external torque and angualr acceleration while be proportional to the net external torque and inversely proportional to moment of inertia

    • when applied for certain time we look at impulse

angualr impulse

• measure of a torque applied for certain amount of time

• net torque aacitiber over interval of time will cause change in angular momentum of an object

angular impulse - momentum relationship

• changes in momentum of a system depends on

  1. magnitude of external torques

  2. time over which torques act

• an impulse can cause change in momentum