▁by ▁considering ▁the ▁result ant ▁of ▁the ▁gravity ▁forces ▁on ▁a ▁continuous ▁body . ▁ ▁Consider ▁a ▁body ▁Q ▁of ▁volume ▁V ▁with ▁density ▁ ρ ( r ) ▁at ▁each ▁point ▁ ▁r ▁in ▁the ▁volume . ▁ ▁In ▁a ▁parallel ▁gravity ▁field ▁the ▁force ▁f ▁at ▁each ▁point ▁r ▁is ▁given ▁by , ▁ ▁where ▁d m ▁is ▁the ▁mass ▁at ▁the ▁point ▁r , ▁g ▁is ▁the ▁acceleration ▁of ▁gravity , ▁and ▁k ▁is ▁a ▁unit ▁vector ▁defining ▁the ▁vertical ▁direction . ▁Cho ose ▁a ▁reference ▁point ▁R ▁in ▁the ▁volume ▁and ▁compute ▁the ▁result ant ▁force ▁and ▁tor que ▁at ▁this ▁point , ▁ ▁and ▁ ▁If ▁the ▁reference ▁point ▁R ▁is ▁chosen ▁so ▁that ▁it ▁is ▁the ▁center ▁of ▁mass , ▁then ▁ ▁which ▁means ▁the ▁result ant ▁tor que ▁T = 0 . ▁ ▁Because ▁the ▁result ant ▁tor que ▁is ▁zero ▁the ▁body ▁will ▁move ▁as ▁though ▁it ▁is ▁a ▁particle ▁with ▁its ▁mass ▁concentr ated ▁at ▁the ▁center ▁of ▁mass . ▁ ▁By ▁selecting ▁the ▁center ▁of ▁gravity ▁as ▁the ▁reference ▁point ▁for ▁a ▁rig id ▁body , ▁the ▁gravity ▁forces ▁will ▁not ▁cause ▁the ▁body ▁to ▁rotate , ▁which ▁means ▁the ▁weight ▁of ▁the ▁body ▁can ▁be ▁considered ▁to ▁be ▁concentr ated ▁at ▁the ▁center ▁of ▁mass . ▁ ▁Linear ▁and ▁angular ▁momentum ▁The ▁linear ▁and ▁angular ▁momentum ▁of ▁a ▁collection ▁of ▁particles ▁can ▁be ▁simplified ▁by ▁meas uring ▁the ▁position ▁and ▁velocity ▁of ▁the ▁particles ▁relative ▁to ▁the ▁center ▁of ▁mass . ▁