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Standard XII
Physics
Moment of Inertia of a Rod
Find the mome...
Question
Find the moment of inertia of a rod of length l and mass m rotating about an axis by making an angle of theta with the vertical direction.
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Solution
S
i
n
c
e
t
h
e
r
o
d
m
a
k
e
s
a
n
a
n
g
l
e
θ
w
i
t
h
t
h
e
d
i
r
e
c
t
i
o
n
o
f
v
e
r
t
i
c
a
l
s
o
n
o
r
m
a
l
d
i
s
tan
c
e
o
f
i
t
s
s
m
a
l
l
p
e
r
t
a
t
a
d
i
s
tan
c
e
x
f
r
o
m
t
h
e
v
e
r
t
i
c
a
l
a
x
i
s
p
a
s
sin
g
t
h
r
o
u
g
h
i
t
s
c
e
n
t
r
e
i
s
,
M
.
I
.
=
m
l
d
x
.
x
sin
θ
2
o
r
M
.
I
.
=
m
l
∫
-
l
2
l
2
x
2
d
x
sin
2
θ
=
m
l
sin
2
θ
∫
-
l
2
l
2
x
2
d
x
o
r
=
m
l
s
i
n
2
θ
x
3
3
-
l
2
l
2
=
m
3
l
s
i
n
2
θ
l
3
8
+
l
3
8
=
m
l
2
12
s
i
n
2
θ
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