Theorems of Moment of Inertia
- There are two general theorems which proved themselves to be of great importance on moment of inertia
- These enable us to determine moment of inertia of a body about an axis if moment of inertia of body about some other axis is known.
Perpendicular Axis Theorem
The moment of inertia (MI) of a plane area about an axis normal to the plane is equal to the sum of the moments of inertia about any two mutually perpendicular axes lying in the plane and passing through the given axis.
That means the Moment of Inertia Iz = Ix+Iy
Parallel Axis Theorem
The moment of area of an object about any axis parallel to the centroidal axis is the sum of MI about its centroidal axis and the prodcut of area with the square of distance of from the reference axis.
Essentially, IXX= IG+Ad2
A is the cross-sectional area. d is the perpendicuar distance between the centroidal axis and the parallel axis.
