Polar Moment of Inertia of a Shaft
Polar Moment of Inertia of a Shaft
The polar moment of inertia governs a circular shaft’s torsional stiffness and strength, so it is the first property computed in shaft design.
For a solid circle J = π·d⁴/32. where d is the shaft diameter.
Inputs
d := 50 mm=50 mm
Apply the solid-circle polar moment formula.
J := pi·d^4/32=6.14e-07 m^4
Results
Because it grows with the fourth power of diameter, a small increase in shaft diameter sharply raises torsional capacity. It feeds directly into the torsion stress and twist formulas.
Assumptions & limitations
- Solid circular section.
- About the axis of the shaft.
- Used with linear-elastic torsion theory.