▁Var ignon , ▁and ▁Alex is ▁Cla ira ut . ▁ ▁Newton ' s ▁second ▁law ▁is ▁reform ulated ▁with ▁respect ▁to ▁the ▁center ▁of ▁mass ▁in ▁E uler ' s ▁first ▁law . ▁ ▁Definition ▁The ▁center ▁of ▁mass ▁is ▁the ▁unique ▁point ▁at ▁the ▁center ▁of ▁a ▁distribution ▁of ▁mass ▁in ▁space ▁that ▁has ▁the ▁property ▁that ▁the ▁weight ed ▁position ▁vectors ▁relative ▁to ▁this ▁point ▁sum ▁to ▁zero . ▁In ▁anal ogy ▁to ▁statistics , ▁the ▁center ▁of ▁mass ▁is ▁the ▁mean ▁location ▁of ▁a ▁distribution ▁of ▁mass ▁in ▁space . ▁ ▁A ▁system ▁of ▁particles ▁In ▁the ▁case ▁of ▁a ▁system ▁of ▁particles ▁, ▁each ▁with ▁mass ▁ ▁that ▁are ▁located ▁in ▁space ▁with ▁coordinates ▁, ▁the ▁coordinates ▁R ▁of ▁the ▁center ▁of ▁mass ▁satisfy ▁the ▁condition ▁ ▁Sol ving ▁this ▁equation ▁for ▁R ▁yields ▁the ▁formula ▁ ▁where ▁ ▁is ▁the ▁sum ▁of ▁the ▁masses ▁of ▁all ▁of ▁the ▁particles . ▁ ▁A ▁continuous ▁volume ▁If ▁the ▁mass ▁distribution ▁is ▁continuous ▁with ▁the ▁density ▁ ρ ( r ) ▁within ▁a ▁solid ▁Q , ▁then ▁the ▁integral ▁of ▁the ▁weight ed ▁position ▁coordinates ▁of ▁the ▁points ▁in ▁this ▁volume ▁relative ▁to ▁the ▁center ▁of ▁mass ▁R ▁over ▁the ▁volume ▁V ▁is ▁zero , ▁that ▁is ▁ ▁Sol ve ▁this ▁equation ▁for ▁the ▁coordinates ▁R ▁to ▁obtain ▁ ▁where ▁M ▁is ▁the ▁total ▁mass ▁in ▁the ▁volume . ▁ ▁If ▁a ▁continuous ▁mass ▁distribution ▁has ▁uniform ▁density , ▁which ▁means ▁ ρ ▁is ▁constant , ▁then ▁the ▁center ▁of