18 solution q. E. D

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912
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18–1.
SOLUTION
Q.E.D.
=
1
2
I
IC
v
2
=
1
2
A
mr
2
G
>
IC
+
I
G
B
v
2
However
mr
2
G
>
IC
+
I
G
=
I
IC
=
1
2
m
(
v
r
G
>
IC
)
2
+
1
2
I
G
v
2
T
=
1
2
m
y
2
G
+
1
2
I
G
v
2
where
y
G
=
v
r
G
>
IC
At a given instant the body of mass m has an angular
velocity 
and its mass center has a velocity . Show that
its kinetic energy can be represented as 
, where
is the moment of inertia of the body determined about
the instantaneous axis of zero velocity, located a distance
from the mass center as shown.
r
G
>
IC
I
IC
T
=
1
2
I
IC
v
2