First slide

Moment of intertia

Question

Moment of inertia of a thin square plate about an axis passing through its diagonal is I. Its moment of inertia about an axis passing through its centre in the plane of the plate and making an angle θ with the diagonal is

Moderate

A

I
B

I cosθ
C

I sinθ
D

I tanθ

Solution

I_BD = I = I_AC
By perpendicular axis Theorem
I_BD + I_AC = I_Z⇒ 2I = I_Z ......(1)
Since I₁ and I₂ are mutually perpendicular and I₁ = I₂
by perpendicular axis Theorem I₁ + I₂ = I_z = 2I
$\large \therefore$ 2I₁ = 2I ⇒ I₁ = I

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