ࡱ>  ~~tvn6  !"#$%&'()*+,-./012345789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}Root Entry t Gj\{`'a@ PerfectOffice_MAIN& PerfectOffice_OBJECTS,`$%a`$%aSummaryInformation(  "#$%&'(*+,-./0Oh+'Oh+'0 P ` lD. Gordon E. Robertson3d:\Corel\Suite8\Programs\Masters\Color\DEFAULT.MSTAdmin68$D:\COREL\SUITE8\PROGRAMS\PRWIN8.EXE? ///333???OOO___fffooof1?O/_??ߟ߿c3f3&f3?LU`l w#'*-/257:=T bjs({3=GQ[s3&?1L; UFaQl[xfp{#',04̳9׿Q.V5b;lAvGLT ` h o rux|(-8DOZfq|3fH uUb#p/:WPC ~ 5_@`oo@RuXu^u`````]|"XXXX'3XXXX3' >/?7 Y<Z"ksw'0-|2S8<@DLJKMOUeWZ[WPC 1'#$  12  I  .3  BodySegmentParameters....2  1  .3  D.GordonE.Robertson,PhD,FCSB SchoolofHumanKineticsUniversityofOttawa #O, \AZ"Arial RegularO@@@ ;1123 ;2  I  .3  BodySegmentParameters....2  1  .3  SubdivisionofAnthropometry..2  A  .3  Necessarytoderivekineticsfromkinematics(I.e., $F=  ma , $Mcg=  I   , a isaccelerationofcentreofgravity,  isang.acceleration)..2  A  .3  Called inversedynamics..2  A  .3  Needtocompute:....2  1  .3  segmentmass....2  1  .3  segmentcentreofgravity....2  1  .3  segmentmomentofinertia  6,!789 62  I  .3  SegmentMass....2  1  .3  Definition..2  A  .3  massisabodysresistencetochangesinlinearmotion..2  A  .3  needtomeasuretotalbodymassusing balancescale..2  A  .3  eachsegmentisaproportionofthetotal6, 456 62  I  .3  SegmentMass....2  1  .3  Thighsegment..2  A  .3  Pthigh=mthigh/mtotal..2  A  .3  Pthigh=thighsmassproportion..2  A  .3  mtotal=totalbodymass..2  A  .3  Therefore,̀ mthigh=Pthighmtotal ..2  A  .3  Note,Q?@ Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@ԀP i =1.000 6,":;< 62  I  .3  CentreofGravity....2  1  .3  Definition..2  A  .3  pointatwhichabodycanbebalanced..2  A  .3  ( xcg,ycg )=centreofgravity..2  A  .3  alsocalledcentreofmass..2  A  .3  firstmomentofmass..2  A  .3  i.e.,turningeffectononesidebalancesturningeffectofothersideofcentreofmass6,()*  62  I  .3  CentreofGravity....2  1  .3  Empiricalmethod..2  A  .3  balancebodyona knifeedge..2  A  .3  balancealongadifferentaxis..2  A  .3  intersectionisc.ofg.  ;1,./0 ;2  I  .3  CentreofGravity....2  1  .3  Empiricalmethod..2  A  .3  recordplumblines..2  A  .3  intersectionofplumblinesiscentreofgravity @6 #$+=>? @2  I  .3  SegmentCentreofGravity....2  1  .3  Proportionalmethod..2  A  .3   Rp=rp/seg.length ..2  A  .3  rp=distancefromproximalendtoc.ofg...2  A  .3  needtableofproportionsderivedfromapopulationsimilartosubject ..2  A  .3  formanysegmentsR p isapproximately43%ofsegmentlength  '%@ '2  I  .3  TableofProportions;1-+,- ;2  I  .3  SegmentCentreofGravity....2  1  .3  Thighsegment..2  A  .3  R p =distancetoc.ofg.fromproximalendasproportionofseg.length..2  A  .3  xcg=xp+Rp(xd-xp)..2  A  .3  ycg=yp+Rp(yd-yp) ..2  A  .3  (xcg,ycg)=centreofgravity..2  A  .3  (xp,yp)=proximalend..2  A  .3  (xd,yd)=distalend ;1. ;2  I  .3  CentreofGravityofaLimb....2  1  .3  Lowerextremity..2  A  .3  weighted ނaverageofsegmentcentres..2  A  .3  ނxlimb=Q?@ Z$Symbol RegularQ@@@SO, \AZ"Arial RegularO@@@(Pixi)/Q?@ Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@ԀPi..2  A  .3  ނylimb=Q?@ Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@(Piyi)/ ނQ?@ Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@ԀPi ނ..2  A  .3  (xi,yi)=masscentreofsegment i..2  A  .3  Pi=massproportionofsegment i@6 &'(ABC @2  I  .3  TotalBodyCentreofGravity....2  1  .3  Needtocomputecentresofeachsegment..2  A  .3  ނweightedsumofallsegmentscentres ..2  A  .3  xtotal=Q?@ Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@ԀPixi..2  A  .3  ytotal=Q?@ Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@ԀPiyi..2  A  .3  ނ(xtotal,ytotal)=totalbodycentreofgravity ނ6, 62  I  .3  MomentofInertia ނ....2  1  .3  Definition..2  A  .3   ނ ނbodysresistencetochangeinitsangularmotion..2  A  .3  ނsecondmomentofmass(squareddistance) ނ..2  A  .3  ނforapointmass ނ....2  1  .3  ނIa=mr2..2  A  .3  ނforadistributedmass ނ....2  1  .3   ނIa=(r2dm #;1 )*DEF ;2  I  .3  MomentofInertia ނ....2  1  .3  Empiricalmethod..2  A  .3   ނIa=mgrt2/4Q?@ Z$Symbol RegularQ@@@pO, \AZ"Arial RegularO@@@2 ނ..2  A  .3  m=mass..2  A  .3  r=radiusofpendulum..2  A  .3  g=9.81m/s ނ2 ނ..2  A  .3  t=periodofoscillation(time20oscillationsthen20)..2  A  .3  oscil ނ ނlationsmustbelessthan5degrees;1/%&'  ;2  I  .3  SegmentalRadiusofGyration ނ....2  1  .3  Thighsegment..2  A  .3  Ithigh=mthighkthigh2..2  A  .3  Thus,kthigh=(Ithigh/mthigh)..2  A  .3  kthigh=radiusofgyration..2  A  .3  DefineKthigh=radiusofgyrationasproportionofsegmentlength..2  A  .3  Lthigh=[(xd-xp)2+(yd-yp)2]..2  A  .3  ނKthigh=kthigh/Lthigh ނ6,  62  I  .3  SegmentalMomentofInertia ނ....2  1  .3  Thighsmomentofinertiaaboutthighcentreofgravity..2  A  .3  ނIthigh=mthigh(KthighLthigh)2 ނ..2  A  .3  Ithigh=momentofinertiaaboutcentreofmass..2  A  .3  mthigh=segmentmass..2  A  .3  Kthigh=radiusofgyrationasproportionofsegmentlength..2  A  .3  Lthigh=segmentlength6,  62  I  .3  ParallelAxisTheorem ނ....2  1  .3  Thighsmomentofinertiaabouthip..2  A  .3  rhip=distancefromcentreofgravitytohip..2  A  .3  rhip=[rx2+ry2]..2  A  .3  ނIhip=Ithigh+mthighrhip2 ނ..2  A  .3  Ithigh=momentofinertiaaboutcentreofmass..2  A  .3  mthigh=segmentmass6, 62  I  .3  Limb/TotalBodyMomentofInertia ނ....2  1  .3  RepeatedlyapplyParallelAxisTheorem..2  A  .3  ނItotal=Q?@ Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@ԀIi+Q?@ Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@Ԁmiri2 ނ..2  A  .3  Ii=segmentmomentsofinertiaabouteachsegmentscentreofgravity..2  A  .3  mi=segmentmasses..2  A  .3  ri=distanceofeachsegmentfromlimbortotalbodycentreofgravity;1      ;2  I  .3  ImpactatCentreofGravity....2  1  .3  TranslationOnly..2  A  .3  animpacttothecentreofgravitycausestheobjecttomoveinpuretranslation@6   @2  I  .3  EccentricImpact....2  1  .3  TranslationandRotation..2  A  .3  aneccentricimpactcausestheobjecttorotateandtranslate ނ;1    ;2  I  .3  CentreofPercussion....2  1  .3  TranslationandRotationaboutSuspensionPoint..2  A  .3  ނpoint ނ ނ( ނq ނ)atwhichanimpactwillcausenoshock(translation)atthegriporpointofsuspension;1   ;2  I  .3  CentreofPercussion( ނq `LY)....2  1  .3  TranslationandRotationaboutSuspensionPoint..2  A  .3  `LYq `LY= `LYk `LY2/ `LYr `LY=I/m `LYr `LY..2  A  .3  `LYarrow `LYrepresentsamountoftranslation..2  A  .3  `LYk `LYisradiusofgyrationaboutsuspensionpoint..2  A  .3   `LYr `LYisdistancetomasscentre..2  A  .3  Iismomentofinertiaaboutsuspensionpoint `LY;1  ;2  I  .3  RelationshipsamongCentresandRadiusofGyration..2  A  .3  ނcentreofgravity ނisnearestcentreofrotation((2  I  .3  SweetSpotsonRacquets,Bats,HockeySticks&Clubs....2  1  .3  Thereareatleastthree!..2  A  .3  ނcentreofpercussion ނgivestheleastshock(accelerationorforce)atpointofsuspension..2  A  .3  pointwhere ނcoefficientofrestitution ނislargest(i.e.,givesgreatestreboundspeed)..2  A  .3  ނnodeoffirstharmonic ނ,whichproducesleastvibrationfromanimpact;1  !"  ;2  I  .3  CoefficientofRestitution....2  1  .3  Collisionbetweentwoobjectsoranobjectandasurface..2  A  .3  Collisionoftwoobjects..2  A  .3  c.ofr.=!(Q?@ Z$Symbol RegularQ@@@DO, \AZ"Arial RegularO@@@vafter/Q?@ Z$Symbol RegularQ@@@DO, \AZ"Arial RegularO@@@vbefore)..2  A  .3  ނVelocitiesshouldtakenafteranydeformation. ނ VO;&>pXrC5XBackground BlankBackground 3 TitleBulleted ListTextOrg 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Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   7o1.'13 6o1O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނbodysresistencetochangeinitsangularmotionfO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނsecondmomentofmass(squareddistance)        @ނfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނforapointmass        @ނO, \AZ"Arial RegularOxxx        @#M..M        @    O, \AZ"Arial RegularOxxx        @#0..        @ނIa=mr2fO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނforadistributedmass        @ނO, \AZ"Arial RegularOxxx        @#M..M        @    O, \AZ"Arial RegularOxxx        @#0..        @ނIa=(r2dm        @#WPCXX81%XX81%=3'XXXXKKKK90"<=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   </.+%#13# ;5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularODefinitionWPCXX81%XX81%`3'XXXX,,,,9"]2(R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  ]R/#.%`L13Y [8 /#LO, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO Limb/TotalBodyMomentofInertia        @ނ.+%19׿3aQ `\R// R WPCXX81%XX81%`3'XXXX,,,,9"_=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   _/.+%#13# ^5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularORepeatedlyapplyParallelAxisTheoremWPCXX81%XX81%`3'XXXX,,,,9 Zm=_0Bm=_0C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   Zm=_0.'13 Y#=/ O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނItotal=Q?@  Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@ԀIi+Q?@  Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@Ԁmiri2        @ނfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Ii=segmentmomentsofinertiaabouteachsegmentscentreofgravityfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..mi=segmentmassesfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..ri=distanceofeachsegmentfromlimbortotalbodycentreofgravityWPC5 XX81%XX81%g3'XXXX,,,,9 a0HB0HC @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   a0H.'13 `K/O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..animpacttothecentreofgravitycausestheobjecttomoveinpuretranslationWPC'XX81%XX81%g      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}3'XXXX,,,,9"d2)R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  dR/#.%`L13Y b6 /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO ImpactatCentreofGravity.+%19׿3aQ `cR// R WPCXX81%XX81%g3'XXXX,,,,9"f=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   f/.+%#13# e5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOTranslationOnlyWPC XX81%XX81%63'XXXX,,,,9"32R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  3R/#.%`L13Y 18 /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO CentreofPercussion.+%19׿3aQ `2R// R WPCXX81%XX81%63'XXXX,,,,9"5=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   5/.+%#13# 45F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOTranslationandRotationaboutSuspensionPointWPCR XX81%XX81%63'XXXX,,,,9 0 0HB 0HC @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   0 0H.)%'13 /N K/!O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..point        @ނ        @ނ(        @ނq        @ނ)atwhichanimpactwillcausenoshock(translation)atthegriporpointofsuspensionWPC|XX81%XX81%R3'XXXX,,,,9"O2'R/# R/# OR/#.%`L13Y M8 /#FO, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO SegmentalMomentofInertia        @ނ.+%19׿3aQ `NR// R WPC XX81%XX81%R3'XXXX,,,,9"Q=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   Q/.+%#13# P5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOThighsmomentofinertiaaboutthighcentreofgravityWPC_XX81%XX81%R3'XXXX,,,,9 L3o0B3o0C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   L3o0.'13 K3/<O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނIthigh=mthigh(KthighLthigh)2        @ނfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Ithigh=momentofinertiaaboutcentreofmassfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..mthigh=segmentmassfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Kthigh=radiusofgyrationasproportionofsegmentlengthfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Lthigh=segmentlengthWPCXX81%XX81%Y3'XXXX,,,,9"V2$R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  VR/#.%`L13Y T8 /#@O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO ParallelAxisTheorem        @ނ.+%19׿3aQ `UR// R WPCXX81%XX81%Y3'XXXX,,,,9"X=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   X/.+%#13# W5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOThighsmomentofinertiaabouthipWPCjXX81%XX81%Y3'XXXX,,,,9 Smo0Bmo0C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   Smo0.'13 Rm/GO, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..rhip=distancefromcentreofgravitytohipfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..rhip=[rx2+ry2]fO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނIhip=Ithigh+mthighrhip2        @ނfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Ithigh=momentofinertiaaboutcentreofmassfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..mthigh=segmentmassWPC&XX81%XX81%n3'XXXX,,,,9"k2R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  kR/#.%`L13Y i8 /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO CentreofPercussion(        @ނq     `L   @Y).+%19׿3aQ `jR// R WPCXX81%XX81%n3'XXXX,,,,9"m=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   m/.+%#13# l5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOTranslationandRotationaboutSuspensionPointWPCXX81%XX81%n3'XXXX,,,,9"h]0B0C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   h0.'13 gNO/bO, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..     `L   @Yq        @ނ=     `L   @Yk     `L   @Y2/     `L   @Yr     `L   @Y=I/m     `L   @Yr     `L   @YfO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..     `L   @Yarrow        @ނrepresentsamountoftranslationfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..     `L   @Yk     `L   @YisradiusofgyrationaboutsuspensionpointfO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..     `L   @Yr        @ނisdistancetomasscentrefO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Iismomentofinertiaaboutsuspensionpoint     `L   @YWPC>XX81%XX81%-3'XXXX,,,,9",%UR/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  ,R/#.%`L13Y *x/#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO RelationshipsamongCentresandRadiusofGyration.+%19׿3aQ `+R//EREWPC XX81%XX81%-3'XXXX,,,,9 )/B/C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   )/.'13 (9+/UO, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނcentreofgravity        @ނisnearestcentreofrotationWPC&XX81%XX81%3'XXXX,,,,9tl"2R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   R/#.%`L13Y 8 /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO EccentricImpact.+%19׿3aQ `R// R WPCXX81%XX81%3'XXXX,,,,9tl"=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   /.+%#13# 5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOTranslationandRotationWPCL XX81%XX81%3'XXXX,,,,9tl 30HB30HC @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   30H-.)*+%'13 w3K/O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..aneccentricimpactcausestheobjecttorotateandtranslateWPC XX81%XX81%(3'XXXX,,,,9""u/"Bu/"C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   "u/".'13 !+:/ O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނcentreofpercussion        @ނgivestheleastshock(accelerationorforce)atpointofsuspensionfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..pointwhere        @ނcoefficientofrestitution        @ނislargest(i.e.,givesgreatestreboundspeed)fO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނnodeoffirstharmonic        @ނ,whichproducesleastvibrationfromanimpactWPCHXX81%XX81%(3'XXXX,,,,9"%(R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  %R/#.%`L13Y #x/#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO SweetSpotsonRacquets,Bats,HockeySticks&Clubs.+%19׿3aQ `$R//EREWPCXX81%XX81%(3'XXXX,,,,9"'/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   '/.+%#13# &5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOThereareatleastthree!WPC&XX81%XX81%(3'XXXXKKKK9"%2+R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  %R/#.%`L13Y #A /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO CoefficientofRestitution.+%19׿3aQ `$R// R WPC XX81%XX81%(3'XXXXKKKK9"'=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   '/.+%#13# &5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOCollisionbetweentwoobjectsoranobjectandasurfaceWPCKXX81%XX81%(3'XXXXKKKK9""t0Bt0C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   "t0.'13 !*/N O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..CollisionoftwoobjectsfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..c.ofr.=!(Q?@  Z$Symbol RegularQ@@@DO, \AZ"Arial RegularO@@@vafter/Q?@  Z$Symbol RegularQ@@@DO, \AZ"Arial RegularO@@@vbefore)fO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނVelocitiesshouldtakenafteranydeformation.        @ނWPC&XX81%XX81%&3'XXXX____9"#2)R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  #R/#%`L'13Y !> /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO BodySegmentParameters.+%19׿3aQ `"R// R WPC XX81%XX81%d3'XXXXKKKK9̀| "=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   /.)+%#'153# c5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOD.GordonE.Robertson,PhD,FCSB        @#SchoolofHumanKineticsUniversityofOttawa     #   @#O, \AZ"Arial RegularO@@@        @#WPCXX81%XX81%K3'XXXXKKKK90"H2"R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  HR/#.%`L13Y F: /#GO, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO SegmentalRadiusofGyration        @ނ.+%19׿3aQ `GR// R WPCXX81%XX81%K3'XXXXKKKK90"J=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   J/.+%#13# I5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOThighsegmentWPCXX81%XX81%K3'XXXXKKKK90 E|W2B|W2C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   E|W2.'13 D|1O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Ithigh=mthighkthigh2fO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Thus,kthigh=(Ithigh/mthigh)fO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..kthigh=radiusofgyrationfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..DefineKthigh=radiusofgyrationasproportionofsegmentlengthfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Lthigh=[(xd-xp)2+(yd-yp)2]fO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނKthigh=kthigh/Lthigh        @ނWPCXX81%XX81%I3'XXXX____9"F2$R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  FR/#.%`L13Y D> /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO CentreofGravity.+%19׿3aQ `ER// R WPCXX81%XX81%I3'XXXX____9"H=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   H/.+%#13# G5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOEmpiricalmethodWPC XX81%XX81%I3'XXXX____9"C, 1B, 1C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   C, 1.'13 B, [0|O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..balancebodyona knifeedgefO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..balancealongadifferentaxisfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..intersectionisc.ofg.        @ނWPCXX81%XX81%/3'XXXXKKKK90",2$R/# R/# ,R/#.%`L13Y *: /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO SegmentCentreofGravity.+%19׿3aQ `+R// R WPCXX81%XX81%/3'XXXXKKKK90".=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   ./.+%#13# -5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOThighsegmentWPC9XX81%XX81%/3'XXXXKKKK90")31B31C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   )31.'13 (3[0| O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Rp=distancetoc.ofg.fromproximalendasproportionofseg.lengthfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނxcg=xp+Rp(xd-xp)fO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނycg=yp+Rp(yd-yp)        @ނfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..(xcg,ycg)=centreofgravityfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..(xp,yp)=proximalendfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..(xd,yd)=distalend        @ނWPCXX81%XX81%(3'XXXXKKKK90"%2 R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  %R/#.%`L13Y #: /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO CentreofGravity.+%19׿3aQ `$R// R WPCXX81%XX81%(3'XXXXKKKK90"'=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   '/.+%#13# &5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOEmpiricalmethodWPC XX81%XX81%(3'XXXXKKKK90 " 0B 0C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   " 0.'13 ! 90&O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..recordplumblinesfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..intersectionofplumblinesiscentreofgravity        @ނWPC#XX81%XX81%(3'XXXXKKKK9"%2R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  %R/#.%`L13Y #A /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO BodySegmentParameters.+%19׿3aQ `$R// R WPCXX81%XX81%(3'XXXXKKKK9"'=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   '/.+%#13# &5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOSubdivisionofAnthropometryWPCm XX81%XX81%(3'XXXXKKKK9"" o/RBo/RC @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   "o/R.'13 !%?/>O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Necessarytoderivekineticsfromkinematics(I.e.,        @ނ$F=        @ނ        @ނma        @ނ,        @ނ$Mcg=        @ނ        @ނI        @ނ        @ނ        @ނ,        @ނa        @ނisaccelerationofcentreofgravity,        @ނ        @ނisang.acceleration)fO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Called inversedynamicsfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Needtocompute:O, \AZ"Arial RegularOxxx        @#M..M        @    O, \AZ"Arial RegularOxxx        @#0..        @#segmentmassO, \AZ"Arial RegularOxxx        @#M..M        @    O, \AZ"Arial RegularOxxx        @#0..        @#segmentcentreofgravityO, \AZ"Arial RegularOxxx        @#M..M        @    O, \AZ"Arial RegularOxxx        @#0..        @#segmentmomentofinertiaM..M        @#M..M        @#WPCXX81%XX81%;3'XXXX____9"82)R/# R/# 8R/#.%`L13Y 6> /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO SegmentMass.+%19׿3aQ `7R// R WPCXX81%XX81%;3'XXXX____9":=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   :/.+%#13# 95F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOThighsegmentWPCXX81%XX81%;3'XXXX____9 5/HB/HC @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   5/H.'13 4I/O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Pthigh=mthigh/mtotalfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Pthigh=thighsmassproportionfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..mtotal=totalbodymassfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Therefore,̀        @ނmthigh=Pthighmtotal        @ނfO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..Note,Q?@  Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@ԀP        @ނi        @ނ=1.000        @ނWPCXX81%XX81%43'XXXX____9"12'R/# R/# 1R/#.%`L13Y /> /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO SegmentMass.+%19׿3aQ `0R// R WPCXX81%XX81%43'XXXX____9"3=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   3/.+%#13# 25F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularODefinitionWPC XX81%XX81%43'XXXX____9".[/HB[/HC @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   .[/H.'13 -[I/O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..massisabodysresistencetochangesinlinearmotionfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..needtomeasuretotalbodymassusing balancescalefO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..eachsegmentisaproportionofthetotalWPCXX81%XX81%B3'XXXX____9"?2R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  ?R/#.%`L13Y => /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO CentreofGravity.+%19׿3aQ `>R// R WPCXX81%XX81%B3'XXXX____9"A=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   A/.+%#13# @5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularODefinitionWPC-XX81%XX81%B3'XXXX____9"<1B1C @@, \AZ"Aria      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrsuvwxyz{|}~l Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$   <1.'13 ;[0|O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..pointatwhichabodycanbebalancedfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..(        @ނxcg,ycg        @ނ)=centreofgravityfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނalsocalledcentreofmassfO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..firstmomentofmassfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..i.e.,turningeffectononesidebalancesturningeffectofothersideofcentreofmassWPCXX81%XX81%3'XXXXKKKK9̀| "2/R/# R/#  R/#.%`L13Y A /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO SegmentCentreofGravity.+%19׿3aQ `R// R WPCXX81%XX81%3'XXXXKKKK9̀| "=/ /  /.+%#13# 5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOProportionalmethodWPCXX81%XX81%3'XXXXKKKK9̀| "h>/HB>/HC @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  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Z9׿aQ 4 @ @ @ @ @ @ f" dddddd$ {2  I  .3  radiusofgyrationispastcentreofgravity  @ :-U-.+%13 @ ,O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނradiusofgyration        @ނispastcentreofgravity-.+UT%13!4*څy+A 5 {0- $*څy+] z] yv _ |_ I-.+13_ u_ R _ u-.+UT13"),0B,0C @@, \AZ"Arial Regular +ނC xx, \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#C , \AZ"Arial Regular +#9/!!!!!!  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