Three rods each of mass m and length L are joined
to form an equilateral triangle as shown in the
figure. What is the moment of inertia about an axis
passing through the centre of mass of the system
and perpendicular to the plane?
A
L. m
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Explanation:
The centre of mass of equilateral triangle is the centroid of the equilateral triangle.
As shown in figure, OP=
2
L
tan(30
o
)=
2
3
L
Moment of inertia(MOI) of rod about centre of mass, I
cm
=
12
1
mL
2
Using parallel axis theorem of MOI, I=I
cm
+mx
2
, Where I
cm
is MOI about centre of mass and x is distance between centre of mass and axis of rotation.
MOI of the system =3(
12
1
mL
2
+m(
2
3
L
)
2
)=3×
6
1
mL
2
=
2
mL
2
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