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Question

Find the MOI of the uniform rod about the given axis

A
mL212
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B
mL212cos2θ
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C
mL212sin2θ
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D
mL212sinθ
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Solution

The correct option is C mL212sin2θ

As the rod rotates about the given axis, the element dm goes in a circle of radius r=xsinθ. Thus,
dI=dmr2
=dmx2sin2θ
I=sin2θdmx2
Since dm=mLdx
I=mLsin2θL2L2x2dx
=mLsin2θ×[x33]L2L2
=m3Lsin2θ×[L38(L38)]
I=mL212sin2θ

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