Centre of Mass
Centre of mass definition.
∑
m
i
r
i
= M r
G
(1)
M
- total mass
r
G
- centre of mass position
From diagram,
r
i
= r
G
+
ρ
i
therefore
∑
m
i
r
i
=
∑
m
i
(r
G
+
ρ
i
)
=
∑
m
i
r
G
+
∑
m
i
ρ
i
=
M r
G
+
∑
m
i
ρ
i
Since (1),
therefore
∑
m
i
ρ
i
= 0
(2)
From (1), we can deduce
∑
m
i
=
M
and
∑
m
&
r
i
&
r
G
i
&&
&&
r
Mr
i
G
=
From (2), we can deduce
∑
m
i
&
ρ
i
= 0
and
∑
m
i
&&
ρ
i
= 0
1

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