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Mechanical Engineering QUESTION #2546
Question 1
The product of inertia \(I_{xy}=\int xy\,dA\) is ZERO when:
  • The area has no curved boundaries
  • The area is symmetric about EITHER the x- OR y-axis✔️
  • The second moments \(I_x\) and \(I_y\) are equal
  • The area is a polygon
Correct Answer Explanation
The product of inertia is zero whenever the area has an axis of symmetry that coincides with either the x- or y-axis. The symmetric pairs of elemental areas contribute equal and opposite \(xy\,dA\) terms that cancel.