Units of second moment of area (area moment of inertia): What is the correct dimensional unit for the moment of inertia of an area?

Introduction / Context:

The area moment of inertia (second moment of area) characterizes an area's resistance to bending about an axis. Correct units are crucial when using beam formulas for deflection, slope, and stress (e.g., E * I relations).

Given Data / Assumptions:

• I = ∫ y^2 dA (or ∫ x^2 dA depending on axis).
• Area element dA has units of m^2; distance squared has units of m^2.

Concept / Approach:

Because the definition multiplies an area element by the square of a length, the resulting unit is m^2 * m^2 = m^4. This is distinct from mass moment of inertia (kg·m^2), which involves mass distribution and rotation dynamics.

Step-by-Step Solution:

Verification / Alternative check:

Example: rectangle b by h about its centroidal axis has I = b * h^3 / 12. Units: m * m^3 = m^4, confirming the dimension.

Why Other Options Are Wrong:

• m and m^2 correspond to length and area, not second moment of area.
• m^3 is volume, again incorrect.
• “None of these” fails because m^4 is correct.

Common Pitfalls:

• Confusing area moment of inertia (m^4) with mass moment of inertia (kg·m^2).

Final Answer:

m^4