Angular Kinetics And Angular Momentum - Animation 98

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Angular Kinetics similar comparison between linear andangular kinematicsLinearAngular Mass Moment of inertia Force Torque Momentum Angular momentum Newton’s Laws Newton’s Laws (angular analogs)resistance to angularmotion (like linearmotion) dependent onmasshowever, the more closelymass is distributed to theaxis of rotation, the easierit is to rotatetherefore: resistance toangular motion dependent onboth the quantity anddistribution of massDefined as: Moment ofInertia1

Moment of Inertia ANGULAR FORM OF INERTIA (I)– resistance to changes in the state of angularmotion I mr2– for a single particle– proportional to mass and distance squared SI unit kg.m2Different Axes recognize thatrotation can occurabout different axes– each axis has itsown moment ofinertia associatedwith it2

Whole Body I consider human movement to occur about 3 principal axes each principal axis has a principal moment of inertiaassociated with it when mass is distributed closer to axis the moment ofinertia is lowerTorque(a.k.a. moment of force) The turning or rotational effect of aneccentric force. Equal to the product of perpendicularcomponents of force and distance (from theforce’s line of action).– Any eccentric force will cause a torque– “Moment arm” is a special name given to thedistance from force’s line of action and the axisof rotation.3

Centric and Eccentric Forces Centric forces result in linear motion only. Eccentric (off-center) forces always resultin rotational motion (sometimes linearmotion, ll4

ar)d(moment arm)Moment caused by muscle force Fmuscle(perp) x dExampleFmuscled(perp)(moment arm)Moment caused by muscle force Fmuscle x d(perp)5

Eccentric Forces: Couple A couple is a pair of forces which are equalin magnitude but opposite in direction, areequidistant from the axis of rotation, andact to produce pure rotation.Angular AnalogNewton’s Laws1) a rotating body will continue to turn aboutits axis of rotation with constant angularmomentum, unless an external couple oreccentric force is exerted upon it linear momentumM m.v angular momentumAKA - The principleof conservation ofangular momentumH I. ω6

Angular AnalogNewton’s Laws2) the rate of change of angular momentum ofa body is proportional to the torque causingit and the change takes place in thedirection in which the torque actsΣT Iωf – ωitΣT Iα7

Angular AnalogNewton’s Laws3) for every torque that is exerted by one bodyon another there is an equal and oppositetorque exerted by the second body on thefirstTRANSFER OFANGULARMOMENTUMenter pike - Hlegsbecause legs slow downHtrunk arms to maintaina constant Htotalthe opposite occurs atentry - Htrunk armsto give a clean entryHlegsto maintain Htotal8

Angular Momentumin Long JumpHtotal Htrunk head Harms Hlegs constant CWto prevent trunk head from rotating forward (CW)rotate arms and legs CW to account for HtotalIarms and Ilegs are smaller than Itotal soωarms and ωlegs must be larger to produceH’s (respectively) large enough to accommodate Htotal9

Sources of Angular Momentum Whole body H sumof all segmental H’s Each segmental H has 2sourcess NH Hss 1s N(H I sωs / Gs ms r ωGs / Gs 12)– Isωs/Gs (H caused byrotation of segmentabout its own CG)– msr2ωGs/G (H caused byrotation of segment’sCG about the wholebody CG). This is themost important source!10

Angular 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) Linear Angular resistance to angular motion (like linear motion) dependent on mass however, the more closely mass is distributed to the

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