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Unformatted text preview: Center of Mass Definitions Recall P conservation M = ∑ m j = tot. mass 1dimension ( ∑ 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 2dimensions (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 711 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 80 1Dexample
problem Before ball thrown 714 Before ball thrown After ball thrown 715 Another approach
momentum conservation
in same problem 716 ...
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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.
 Spring '11
 KODERA
 Center Of Mass, Mass, Momentum

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