1Angular Kinetics• similar comparison between linear and angular kinematics•Mass •Moment of inertia•Force •Torque•Momentum •Angular momentum• Newton’s Laws •Newton’s Laws (angular analogs)LinearLinearAngularAngularresistance to angular motion (like linear motion) dependent on masshowever, the more closely mass is distributed to the axis of rotation, the easier it is to rotatetherefore: resistance to angular motion dependent on both the quantity and distribution of massDefined as: Moment of Inertia2Moment of Inertia• ANGULAR FORM OF INERTIA (I)– resistance to changes in the state of angular motion•I = mr2– for a single particle– proportional to mass and distance squared• SI unit = kg.m2Different Axes• recognize that rotation can occur about different axes– each axis has its own moment of inertia associated with it3Whole Body I• consider human movement to occur about 3 principal axes• each principal axis has a principal moment of inertia associated with it• when mass is distributed closer to axis the moment of inertia is lowerTorque (a.k.a. moment of force)• The turning or rotational effect of an eccentric force. • Equal to the product of perpendicularcomponents of force and distance (from the force’s line of action).– Any eccentric force will cause a torque– “Moment arm” is a special name given to the distance from force’s line of action and the axis of rotation.4Centric and Eccentric Forces • Centric forces result in linear motion only.• Eccentric (off-center) forces always result in rotational motion (sometimes linear motion, too).ExampleWforearmWballFmuscledmuscledforearmdball5ExampleFmuscleFmuscle(perpendicular)Fmuscle(parallel)d(moment arm)Moment caused by muscle force = Fmuscle(perp)x dExampleFmuscleMoment caused by muscle force = Fmusclex d(perp)d(perp)(moment arm)6Eccentric Forces: Couple• A couple is a pair of forces which are equalin magnitude but opposite in direction, are equidistant from the axis of rotation, and act to produce pure rotation. Angular AnalogNewton’s Laws1) a rotating body will continue to turn about its axis of rotation with constant angular momentum, unless an external couple or eccentric force is exerted upon it•linear momentumM = m.v•angular momentumH = I.ωAKA - The principleof conservation ofangular momentum7Angular AnalogNewton’s Laws2) the rate of change of angular momentum of a body is proportional to the torque causing it and the change takes place in the direction in which the torque actsωf– ωiΣT = ItΣT = Iα8Angular AnalogNewton’s Laws3) for every torque that is exerted by one body on another there is an equal and opposite torque exerted by the second body on the firstTRANSFER OFANGULAR MOMENTUMenter pike - Hlegsbecause legs slow downHtrunk+armsto maintaina constant Htotalthe opposite occurs at entry - Htrunk + armsto give a clean entryHlegsto maintain Htotal9Angular Momentum in Long Jump Htotal= Htrunk+head+ Harms+ Hlegs= constant CWto prevent trunk+head from rotating forward (CW)rotate arms and legs CW to account for HtotalIarmsand Ilegsare smaller than Itotalsoωarmsand ωlegsmust be larger to produceH’s (respectively) large enough to accommodate Htotal10Sources of Angular Momentum()HHHI mrsssNssG s GGssNss==+====∑∑121ωω//• Whole body H = sum of all segmental H’s• Each segmental H has 2 sources– Isωs/Gs(H caused by rotation of segmentabout its own CG)– msr2ωGs/G(H caused by rotation of segment’s CG about the whole body CG). This is the most important