A symmetric lamina of mass M consists of a square shape with a semicircular section over each of the edge of the square as shown in figure. The side of the square is 2a. The moment of inertia of the lamina about an axis through its centre of mass and perpendicular to the plane is 1.6 Ma2. The moment of inertia of the lamina about the tangent AB in the plane of the lamina is ……… .
Hi Jay,
First apply perpendicular axis theorem.
Consider two axes, each through O in the plane of the lamina, where one axis L is parallel to AB and the other axis L" is perpendicular to AB.
So now by perpendicular axis theorem, we have IL + IL" = Io = 1.6Ma2.
But IL=IL" (due to symmetry). So IL = 0.8Ma2.
Now use parallel axis theorem. IAB = IL + M(a+a)2
So IAB = 4.8Ma2.
Hope that helps.
All the best.
Regards,
Ashwin (IIT Madras).
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