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

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Unformatted text preview: Center of Mass Definitions Recall P conservation M = ∑ m j = tot. mass 1-dimension ( ∑ m j v j )initial = ( ∑ m j v j )final j j v CM = ∑ m j v j / M j ( ∑ m j v j )initial j xCM = ∑ m jx j / M j M j i xCM = ∑ m jx j / M j y CM = ∑ m j y j / M j j M Momentum conservation ⇔ constant CM velocity (v CM )x = ∑ m i (v i )x / M i = (VCM )initial = (VCM )final 2-dimensions (v CM )y = ∑ m i (v i )y / M ( ∑ m j v j )final In general v v (v CM ) = ∑ m i (v i ) / M i v v (r CM ) = ∑ m i (r i ) / M i 7-11 Center of Mass The center of mass of a system is the point where the system can be balanced in a uniform gravitational field. CM The center of mass accelerates just as though it were a point particle of mass M acted on by F CM aCM Center of Mass: breaks motion down into simpler organized view rotation about CM at constant angular speed ω. constant vCM along dotted line. Internal forces (EXPLOSION) rearrange mass parabolic CM motion g rotation about CM constant angular speed ω. parabolic CM motion g 8-0 1D-example problem Before ball thrown 7-14 Before ball thrown After ball thrown 7-15 Another approach momentum conservation in same problem 7-16 ...
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This note was uploaded on 04/03/2012 for the course PHY 1020 taught by Professor Kodera during the Spring '11 term at University of Florida.

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

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