Parallel-axis Theorem

There could be several axes possible along which a rigid body can rotate, and hence correspondingly, there could be various moments of inertia for the same body.

If the moment of inertia, I_CM , about an axis passing through the center of mass is known, then the moment of inertia about any other parallel axis can be obtained using the parallel-axis theorem.

The theorem states that the moment of inertia along any axis parallel to the axis passing through the center of mass is given as the sum of I_CM and the product of the mass of the body and the square of the perpendicular distance between the two axes.

Consider a door of mass M and height 2L. The width of the door is half of the height of the door. The door rotates about its hinges.

The I_CM  of the door is equal to ML² by twelve. The moment of inertia along the rotational axis is thus given as the sum of I_CM  and ML² by four.