Perpendicular axis theorem
For a planar body, , where is an axis perpendicular to the plane and are any two orthogonal axes in the plane.
Theorem 5.3 (Perpendicular Axis Theorem)
For a planar body, the moment of inertia about an axis perpendicular to the plane is the sum of the moments of inertia about any two orthogonal axes in the plane.
Proof
Consider any 2D body with coordinates in its plane. Then
By inspection, we have .
Related
Stated in
- Theorem 5.3 (Perpendicular Axis Theorem)§5.3 Perpendicular Axis Theorem