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lec07b-203-11-CM - Center of Mass Definitions Recall P...

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7-11 Center of Mass Definitions j j initial j j final j j ( m v ) ( m v ) = j j M m tot. mass = = CM j j j x m x / M = Recall P conservation CM j j j v m v / M = j j initial j j final j j ( m v ) ( m v ) M M = CM initial CM final (V ) (V ) = Momentum conservation constant CM velocity CM x i i x i (v ) m (v ) / M = CM y i i y i (v ) m (v ) / M = CM j j j x m x / M = CM j j j y m y / M = 1-dimension 2-dimensions CM i i i (v ) m (v ) / M = v v CM i i i (r ) m (r ) / M = v v In general
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The center of mass of a system is the point where the system can be balanced in a uniform gravitational field. The center of mass accelerates just as though it were a point particle of mass M acted on by F a CM CM CM Center of Mass
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