The SI unit for polar moment of inertia is

• A. kg-m2
• B. m2
• C. kg-m4
• D. m4

Answer: (D)

In torsion, the torque-twist relationship uses the polar moment of inertia J of the cross-section in the form T = G J θ / L. To get the correct units for torque (N·m) from the shear modulus G (units N/m^2) and length L (m), J must supply a factor with length raised to the fourth power: (N/m^2) × (m^4) ÷ m = N·m. So the polar moment of inertia in this context has units of length to the fourth power, m^4. This quantity reflects how the cross-section’s area is distributed about the axis—the larger J is, the more resistant the shaft is to twisting. Note that the mass moment of inertia, which applies to rotational dynamics, has units kg·m^2, a different concept. For reference, J depends on geometry, e.g., solid circular shafts have J ∝ r^4.