An equilateral triangle is made of a string of lenth 60cm and mass 100gm. Find the moment of inertia of the triangle about perpendicular axis through centroid.
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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
solution
Explanation:
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