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25-momentum

# 25-momentum - Phys 211 Chapter 9 Systems Center of Mass...

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Phys 211 3/25/09 Chapter 9 - Systems Center of Mass Momentum Conservation of Momentum

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Review Center of Mass - (CM, COM) - Point that moves as though (1) all of the system’s mass were concentrated there (2) all external forces were applied there x cm = m 1 x 1 + m 2 x 2 + ... + m n x n m 1 + m 2 + ... + m n = m i x i i m i i = m i x i i M In general Works in x,y,z independently! CM motion of a system! F net = M a CM
Center of Mass The disk shown below in (1) clearly has its center of mass at the center. Suppose the disk is cut in half and the pieces arranged as shown in (2). Where is the center of mass of (2) as compared to (1) ? (1) X CM (2) 1) higher 2) lower 3) at the same place 4) there is no definable CM in this case

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CM Motion Determine the velocity of the center of mass. v CM = d dt r cm = d dt m 1 r 1 + m 2 r 2 + ... + m n r n m 1 + m 2 + ... + m n v CM = m 1 v 1 + m 2 v 2 + ... + m n v n m 1 + m 2 + ... + m n Individual particles add vectorially to give overall CM motion.
CM Motion Two equal-mass particles (A and B) are located at some distance from each other.

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