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NY0#)P/37;\=>zAGeHLWWPC 1' !  12  I  .3  BodySegmentParameters....2  1  .3  D.GordonE.Robertson,Ph.D. SchoolofHumanKineticsUniversityofOttawa  ;1!()456 ;2  I  .3  BodySegmentParameters....2  1  .3  SubdivisionofAnthropometry..2  A  .3  Necessarytoderivekineticsfromkinematics(I.e., $F= ma , $Mcg= I  , a isaccelerationofcentreofgravity)called inversedynamics..2  A  .3  Needtocompute:....2  1  .3  segmentmass....2  1  .3  segmentcentreofgravity....2  1  .3  segmentmomentofinertia  6,,:;< 62  I  .3  SegmentMass....2  1  .3  Definition..2  A  .3  massisabodysresistencetochangesinlinearmotion..2  A  .3  needtomeasuretotalbodymassusing balancescale..2  A  .3  eachsegmentisaproportionofthetotal;1 $123 ;2  I  .3  SegmentMass....2  1  .3  Proportionalmethod..2  A  .3  Pthigh=thighsmassproportion..2  A  .3  Pthigh=mthigh/mtotal..2  A  .3  mtotal=totalbodymass..2  A  .3  Therefore,̀ mthigh=Pthighmtotal ..2  A  .3  Note,Q?@  Z$Symbol RegularQ@@@&O, \AZ"Arial RegularO@@@ԀP i =1.0006, 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+,- ;2  I  .3  CentreofGravity....2  1  .3  Empiricalmethod..2  A  .3  recordplumblines..2  A  .3  intersectionofplumblinesiscentreofgravity  ;1 *+789 ;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 @6 ! ./0 @2  I  .3  SegmentCentreofGravity....2  1  .3  Proportionalmethod..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  @6 ./0>?@ @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 ނ;1 # ;2  I  .3  MomentofInertia ނ....2  1  .3  Definition..2  A  .3   ނ ނbodysresistencetochangeinitsangularmotion..2  A  .3  ނsecondmomentofmass(i.e.,squareddistance) ނ..2  A  .3  ނforapointmass ނ....2  1  .3  ނIa=mr2..2  A  .3  ނforadistributedmass ނ....2  1  .3   ނIa=(r2dm # #;1 "%&'  ;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 ނ;1  &   ;2  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=segmentlength;1  ' ;2  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=segmentmass;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 ChartData ChartCombinationWPCT}C:P\\TIN-3'XXXXKKKK5/ @1 'Q; ? 3uPYcl v  *D_yf(u/5;AG L R X ^!l4zH[ofu    1%MAj^z=.O;`LrVcp̙ܥ$DYނB(#G-)L20P76U<=ZAC_FJdLPiQWmV]r[cw`j|epjwo}tufp{lws}yź3">)L3$U8*`@/lG5wO:V@^EoZn̲9WPCXX81%lȢ 3'XXXXKKKK5139_JWPCT}x/ ?"3'XXXXKKKK5/ @1 f9WPCXX81%~/v3'XXXX____ ? ///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/:EP\fuɒџزf3uPYcl v  *D_yf(u/5;AG L R X ^!l4zH[ofu    1%MAj^z=.O;`LrVcp̙ܥ$DYނB(#G-)L20P76U<=ZAC_FJdLPiQWmV]r[cw`j|epjwo}tufp{lws}yź3">)L3$U8*`@/lG5wO:V@^EoZn̲9_J"WP.0 2.0 C ` ` , \AZ"Arial Regular +O;YC ` ` , \AZ"Arial Regular +O;YC ` ` , \AZ"Arial Regular +O;YC ` ` , \AZ"Arial Regular +O;YC ` ` , \AZ"Arial Regular +O;YC ` ` , \AZ"Arial Regular +O;Y)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$ 22  I  .3  1.  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///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/:EP\fuɒџزf3uPYcl v  *D_yf(u/5;AG L R X ^!l4zH[ofu    1%MAj^z=.O;`LrVcp̙ܥ$DYނB(#G-)L20P76U<=ZAC_FJdLPiQWmV]r[cw`j|epjwo}tufp{lws}yź3">)L3$U8*`@/lG5wO:V@^EoZn̲9_"2+R/#jR/#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>2  I  .3  TitleofSlide  R/#+%`L13Y B /#9O, \AZ"Arial RegularO        @  Q QO, \AZ"Arial RegularO     `L   @Y TitleofSlide+%19׿3aQ `R//R+13"=/j/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 fA2  I  .3  SubtitleofSlide  /+%#13# 5F/9O, \AZ"Arial RegularO        @  Q QO, \AZ"Arial RegularO     #   @#SubtitleofSlide+%13"X 6` C  \AZ"Arial Regular -@YC  \AZ"Arial Regular +#C RR \AZ"Arial Regular +#C RR \AZ"Arial Regular +#C RR \AZ"Arial Regular +#C RR \AZ"Arial Regular +#9/!!!!!!  9׿aQ 4 @ @ @ @ @ @ f" ddddddX2  I  .3  FirstItem2  A  .3  Subitem2  I  .3  SecondItem2  A  .3  Subitem2  I  .3  ThirdItem2  I  .3  FourthItem  X +1 kX 3O, \AZ"Arial RegularORRR        @  a /!!!!!!aO, \AZ"Arial RegularO        @  /O, \AZ"Arial RegularO        @Y0..FirstItemO, \AZ"Arial RegularO        @#..        @O, \AZ"Arial RegularO        @#06..SubitemfO, \AZ"Arial RegularO        @/O, \AZ"Arial RegularO        @Y0..SecondItemO, \AZ"Arial RegularO        @#..        @O, \AZ"Arial RegularO        @#06..SubitemfO, \AZ"Arial RegularO        @/O, \AZ"Arial RegularO        @Y0..ThirdItemfO, \AZ"Arial RegularO        @/O, \AZ"Arial RegularO        @Y0..FourthItem+1"|^/b^/#?Y@4@#?Y@4@#?@?cc 9@ZM M 9@ZM M   22226ffffffֿp= ף(\?TQ ! 19׿3&  ! 13&  ! 1ɒ3&  ! 1 3&   ! 13&  ! 13&  ! 1wO:3&  ! 1p3&  ! 1   ! 1    ! 1    ! 1    ! 1    ! 1   ! 1  ! 1  ! 1  ! 1  ! 1?  ! 1  ! 1  ! 1  ! 1  ! 1  43&>1J; UF`Ql[wfq{#l[C ` ` , \AZ"Arial Regular +3&  1#aQC , \AZ"Arial Regular +3&  1#aQC ee, \AZ"Arial Regular +DD  1C ee, \AZ"Arial Regular +DD  1C ee, \AZ"Arial Regular +DD  1C ee, \AZ"Arial Regular +$$  1C , \AZ"Arial Regular +  1Z# UFC , \AZ"Arial Regular +  1C , \AZ"Arial Regular +  1C ee, \AZ"Arial Regular +   1  C , \AZ"Arial Regular +   1  C , \AZ"Arial Regular +    1 Z9׿l[ C , \AZ"Arial Regular +    1  C , \AZ"Arial Regular - @   3 @   // ?Title of ChartSubtitleLegendd 1@1st Qtr2nd Qtr3rd Qtr4th QtrNorth# Z2AU@South# 2(-F@East# (@West# - q |^/.%'/ Z@1 M 3M l"G " n  m"G "//G  n "G /G b- +13 o "h/h p "/ q +"/ r M"/) s\# %G  t& ?)G  u * ,G ) vK/ !  w! !M x. K!  yK! K! z.h h  { h  & " .+%1k`3 |$ $ $$e19׿33& }" $ $e"e1,3' ~$e$>#"e1k`3 ' A( A(r'"19׿33& D& ' '"D&"1,3' '"A(r&rD&"1k`3 G+ + + G+19׿33& ) G+ G+)1,3' G++ ) )1k`3 . . .,.19׿33& , . .,1,3' ..,D-,, $ I"0 M.1@m3 #0 G$ G$#133& I"0 #0 #I"1 `3' #G$"I"1@m3 L'0 ' 'L'r133& %0 L'0 L'r%r1 `3' L'r'%%r1@m3 *0 * *J*133& (0 *0 *(1 `3' **JJ)J(1@m3 -0 M. M.-133& O,0 -0 -O,1 `3' -M.,O, $ ! -"1dIv3 R# # # R#9 1ɒ33& ! R# R#9 !9 1n3' R#9 # ! !9 1dIv3 & & && 1ɒ33& $ & & $ 1n3' & &O%$ 1dIv3 * R* R*"*1ɒ33& U( * *U(1n3' *R*"("U(1dIv3 X- - - X- 1ɒ33& + X- X- + 1n3' X- - + +  $ ! - 1]@3 " #@ #P " 1 33& ! " " ! 1 `3' " #P U!P ! 1]@3 & X&@ X&a & 1 33& [$ & & [$ 1 `3' & X&a $a [$ 1]@3 ^) )@ )r ^)" 1 33& ' ^) ^)" '" 1 `3' ^)" )r (r '" 1]@3 , -@ - ,1 33&  + , , +1 `3' ,- [+  ++%13 ! !, .13 # >#O, \AZ"Arial RegularO        @  1stQtr.13 % %, .13 S#&O, \AZ"Arial RegularO        @  2ndQtr.13 _( _(, .13 &)O, \AZ"Arial RegularO        @  3rdQtr.13 + +, .13 !*L-O, \AZ"Arial RegularO        @  4thQtr.13  i .13 }# 4 O, \AZ"Arial RegularO        @  0.13  i .13 D U O, \AZ"Arial RegularO        @  20.13  i .13 e vO, \AZ"Arial RegularO        @  40.13  +i+.13 O, \AZ"Arial RegularO        @  60.13  MiM.13 O, \AZ"Arial RegularO        @  80.13  nin.13 Ð^O, \AZ"Arial RegularO        @  100 0 ̐ ,n.+%19׿33& Đ 6 n!n!6.+%13 Ő*#-%>O, \AZ"Arial RegularO        @North.+%133& Ɛt'6t'n(n(6.+%13 ǐ)-,>O, \AZ"Arial RegularO        @South.+%1ɒ33& Ȑ  !!.+%13 ɐ*#%O, \AZ"Arial RegularO        @East.+%1 33& ʐt't'((.+%13 ː),O, \AZ"Arial RegularO        @West1C;3nSL]oCs6HYl}#,>Pbt? 0B668Å6Ѕ6օ6م8Å:݅6{s0lws0l6ѵH6څ6؅666ts0l8Å6Ѕ6668ѵH%_'''jѵHѵHѵHѵHѵHѵHѵH666dddѵH<ѵH'A =%+fGCN7 zW)^e"lsT ~~| {l (24@ (A4N "J)0(7 >ICO(kV_fm= ~A z #!$&q>oAUH]_f tA|B<WPCXX81%XX81%93'XXXX____9"62R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  6R/#.%`L13Y 4C /#<O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO MomentofInertia        @ނ.+%19׿3aQ `5R// R WPCXX81%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 88 /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO CentreofGravity.+%19׿3aQ `9R// R WPC;XX81%XX81%=3'XXXX,,,,9"71B1C @@, \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$   71.)%'13 6[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'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 RegularODefinitionWPCXX81%XX81%93'XXXX____9"3GH1B1C @@, \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 21QO, \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(i.e.,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        @#M..M        @#WPCXX81%XX81%93'XXXX____9"8=/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$   8/.+%#13# 75F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularODefinitionWPC5 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%g3'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%g3'XXXX,,,,9"d2%R/# R/# dR/#.%`L13Y b8 /#FO, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO SegmentalMomentofInertia        @ނ.+%19׿3aQ `cR// R WPC XX81%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 RegularOThighsmomentofinertiaaboutthighcentreofgravityWPCyXX81%XX81%g3'XXXX,,,,9 a3o0B3o0C @@, \AZ"Arial Regular +ނC xx, \      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~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$   a3o0.)%'13 `3/HO, \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%63'XXXX____9"32 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$  3R/#.%`L13Y 1C /#@O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO ParallelAxisTheorem        @ނ.+%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 RegularOThighsmomentofinertiaabouthipWPCjXX81%XX81%63'XXXX____9 0o0Bo0C @@, \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$   0o0.'13 //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'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 /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO CoefficientofRestitution.+%19׿3aQ `$R// R WPC XX81%XX81%(3'XXXX,,,,9"'=/2/C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##C , \AZ"Arial Regular +##)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$   '/.+%#13# &5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOCollisionbetweentwoobjectsoranobjectandasurfaceWPCGXX81%XX81%(3'XXXX,,,,9""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 !C /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO BodySegmentParameters.+%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# $5F/pO, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOD.GordonE.Robertson,Ph.D.        @#SchoolofHumanKineticsUniversityofOttawa     #   @#        @#WPCXX81%XX81%`3'XXXX,,,,9"]2!R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  ]R/#.%`L13Y [8 /#GO, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO SegmentalRadiusofGyration        @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 RegularOThighsegmentWPCXX81%XX81%`3'XXXX,,,,9 ZRW2BRW2C @@, \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$   ZRW2.)%'13 YR1O, \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%/3'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 *C /#<O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO MomentofInertia        @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 RegularOEmpiricalmethodWPC|XX81%XX81%/3'XXXX____9 )qW2BqW2C @@, \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$   )qW2.'13 (q1YO, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނIa=mgrt2/4Q?@  Z$Symbol RegularQ@@@pO, \AZ"Arial RegularO@@@2        @ނfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..m=massfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..r=radiusofpendulumfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..g=9.81m/s2fO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..t=periodofoscillation(time20oscillationsthen20)fO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..oscil        @ނ        @ނlationsmustbelessthan5degreesWPCXX81%XX81%/3'XXXX,,,,9",2%R/#2R/#C , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LYC , \AZ"Arial Regular +`LY)?  9׿aQ 4 @ @ @ @ @ @ f" dddddd$  ,R/#.%`L13Y *8 /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO CentreofGravity.+%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 RegularOEmpiricalmethodWPC XX81%XX81%/3'XXXX,,,,9")q 1Bq 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$   )q 1.)%'13 (q [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'XXXX____9"82R/#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$  8R/#.%`L13Y 6C /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO CentreofGravity.+%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 RegularOEmpiricalmethodWPC? XX81%XX81%;3'XXXX____9 5 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$   5 0.'13 4 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        @ނ        @ނWPCXX81%XX81%D3'XXXX,,,,9"A2!R/# R/# AR/#.%`L13Y ?8 /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO SegmentCentreofGravity.+%19׿3aQ `@R// R WPCXX81%XX81%D3'XXXX,,,,9"C=/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$   C/.+%#13# B5F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularOProportionalmethodWPCXX81%XX81%D3'XXXX,,,,9">D/1KB/1KC @@, \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$   <?1.'13 ;?Y09~O, \AZ"Arial RegularO        @a /!!!!!!aO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނRp=rp/seg.length        @ނfO, \AZ"Arial RegularO@@@        @ނ        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..rp=distancefromproximalendtoc.ofg.fO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..        @ނneedtableofproportionsderivedfromapopulationsimilartosubject        @ނfO, \AZ"Arial RegularO@@@        @  /  O, \AZ"Arial RegularO@@@        @ނ0M..formanysegmentsR        @ނp        @ނisapproximately43%ofsegmentlength        @ނ        @ނWPCXX81%XX81%(3'XXXX____9"%2&R/# R/# %R/#.%`L13Y #C /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO SegmentMass.+%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 RegularODefinitionWPC XX81%XX81%(3'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%+3'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/#%`L'13Y (/#@O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO TableofProportions        @Y.+%19׿3aQ `)R//OROWPCXX81%XX81%23'XXXX____9"/2"R/# R/# /R/#.%`L13Y -C /#O, \AZ"Arial RegularO     `L   @Y  Q QO, \AZ"Arial RegularO TotalBodyCentreofGravity.+%19׿3aQ `.R// R WPCXX81%XX81%23'XXXX____9"1=/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$   1/.+%#13# 05F/O, \AZ"Arial RegularO     #   @#  Q QO, \AZ"Arial RegularONeedtocomputecentresofeachsegmentWPCXX81%XX81%23'XXXX____9      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuwxyz{|}~",Q -NBQ -NC @@, \AZ"Arial Regular +C 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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