MOTION OF A CENTER OF MASS
Consider a system of particles where the position of the CM is given by:
Taking the derivative wrt time gives:
11
ii
cm
i
cm
i
i i
th
i
cm
i i
i
sys
mr
dr
d
dt
dt
M
dr
v
m
m v
M
dt
M
v
velocity of i
particle
Mv
m v
p
P
sys
cm
P
Mv
Total Linear Momentum of a System
1. The total linear momentum of the system is equal to the total mass of the system
times the velocity of the center of mass of the system.
2. The total linear momentum of the system is equal to that of a single particle of
mass M located at the center of mass and moving with a velocity equal to that of
the center of mass.
cm
r
M
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 Spring '11
 Luna
 Center Of Mass, Force, Mass, dt

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