Let us consider a thin uniform Rod of length 5 cm and mass 6kg. Calculate moment of inertia and radius of gyration when The rotation axis is at 4 cm away from one end.
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Explanation:
Calculation the M.I of a thin uniform rod of mass 100g and length 60c about an axis perpendicular
where M=100g
l=60cm= length of the rod
Moment of inertia of a thin uniform rod about a transverse axis
Passing through its centre is given by
I−0=I=
12
Ml
2
(for rod)
By parallel axis theorem, we get,
I
0
=I
g
+Mh
2
∴I
0
=
12
Ml
2
+M(
4
l
)
2
∴I
0
=
12
Ml
2
+
16
Ml
2
I
0
=
48
4Ml
2
+3Ml
2
I
0
=
48
7Ml
2
=
48
7×100×60
2
=52500g.cm
2
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