▁with ▁an ▁axis ▁of ▁symmetry ▁and ▁constant ▁density ▁must ▁lie ▁on ▁this ▁axis . ▁ ▁Thus , ▁the ▁center ▁of ▁mass ▁of ▁a ▁circular ▁cyl inder ▁of ▁constant ▁density ▁has ▁its ▁center ▁of ▁mass ▁on ▁the ▁axis ▁of ▁the ▁cyl inder . ▁ ▁In ▁the ▁same ▁way , ▁the ▁center ▁of ▁mass ▁of ▁a ▁spher ically ▁symmetric ▁body ▁of ▁constant ▁density ▁is ▁at ▁the ▁center ▁of ▁the ▁sphere . ▁ ▁In ▁general , ▁for ▁any ▁symmetry ▁of ▁a ▁body , ▁its ▁center ▁of ▁mass ▁will ▁be ▁a ▁fixed ▁point ▁of ▁that ▁symmetry . ▁ ▁In ▁two ▁dimensions ▁An ▁experimental ▁method ▁for ▁loc ating ▁the ▁center ▁of ▁mass ▁is ▁to ▁susp end ▁the ▁object ▁from ▁two ▁locations ▁and ▁to ▁drop ▁pl umb ▁lines ▁from ▁the ▁susp ension ▁points . ▁The ▁intersection ▁of ▁the ▁two ▁lines ▁is ▁the ▁center ▁of ▁mass . ▁ ▁The ▁shape ▁of ▁an ▁object ▁might ▁already ▁be ▁mathemat ically ▁determined , ▁but ▁it ▁may ▁be ▁too ▁complex ▁to ▁use ▁a ▁known ▁formula . ▁In ▁this ▁case , ▁one ▁can ▁sub div ide ▁the ▁complex ▁shape ▁into ▁simpler , ▁more ▁elementary ▁shapes , ▁whose ▁cent ers ▁of ▁mass ▁are ▁easy ▁to ▁find . ▁If ▁the ▁total ▁mass ▁and ▁center ▁of ▁mass ▁can ▁be ▁determined ▁for ▁each ▁area , ▁then ▁the ▁center ▁of ▁mass ▁of ▁the ▁whole ▁is ▁the ▁weight ed ▁average ▁of ▁the ▁cent ers . ▁This ▁method ▁can ▁even ▁work ▁for ▁objects ▁with ▁holes , ▁which ▁can ▁be ▁account ed ▁for ▁as ▁negative ▁masses . ▁ ▁A ▁direct ▁development ▁of ▁the