6.6. CONSERVATION OF MOMENTUM FOR A SYSTEM OF PARTICLES 93
)
*
H
O
D
*
r
n
X
iD1
m
i
*
v
i
C
n
X
iD1
*
r
0
i
m
i
*
v
i
:
By Equation (6.23), the first summation term on the rhs becomes
*
r
n
X
iD1
m
i
*
v
i
D
*
r
m
*
v
;
and the second summation term, by Equation (6.29), is
*
H
G
: erefore, one has the following
important result,
*
H
O
D
*
r
m
*
v
C
*
H
G
: (6.30)
6.6 CONSERVATION OF MOMENTUM FOR A SYSTEM OF
PARTICLES
Now, returning to Equations (6.14) and (6.15), one observes that if there is no external force
acting on the particles of a system, which means that
P
n
iD1
*
F
i
D 0 and
P
n
iD1
*
M
o
i
D 0; then
one has
*
L D 0; (6.31a)
*
H
o
D 0: (6.31b)
Upon integrating w.r.t time t, it becomes
*
L D constant; (6.32a)
*
H
o
D constant: (6.32b)
ese two equations simply state that the momentum of the system of particles and the angular
momentum of the same system of particles about the origin O are conserved.
6.7 WORK ENERGY PRINCIPLE FOR A SYSTEM OF
PARTICLES
e work energy principle for a particle stated in Equation (4.6) can be applied to every particle
in the system of particles. en the form of the work energy principle for a system of particles
is the same as that in Equation (4.6). Of course, now
T
1
D
1
2
n
X
iD1
m
i
v
2
i
1
; T
2
D
1
2
n
X
iD1
m
i
v
2
i
2
;
..................Content has been hidden....................
You can't read the all page of ebook, please click here login for view all page.