Moment of inertia of a rigid rod about an axis through its Centre isMl^2/13. Find the moment of inertia of the rod about the axis through one end ?
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Answer:
The total length of the rod is L. Since, the rod is bent at the middle, so each part of it will have same length
2
L
and mass
2
M
.
Moment of inertia of each part about an axis passing through its one end
=
3
1
(
2
M
)(
2
L
)
2
Hence, net moment of inertia about an axis Passing through its Middle point O is
l=
3
1
[
2
M
][
2
L
]
2
+
3
1
[
2
m
][
2
L
]
2
=
3
1
[
8
ML
2
+
8
ML
2
]=
12
ML
2
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