Question

Diagram of parllel axis thm.

Answer 1

quantifies the variation of moment of inertia in relation to the distance of rotation axis from the mass center. When the body's rotation axis passes through the mass center, the moment of inertia is said to be minimum, and when the rotation axis moves away from the mass center, the moment of inertia increases.

The application of parallel axis theorem for the rotation axis offset from the center of mass is depicted in the figure below.



According to parallel axis theorem, moment of inertia is the sum of moment of inertia through mass center and product of mass and square of perpendicular distance between mass center and rotation axis.



Here, moment of inertia at mass center is Icm, mass is m and the perpendicular distance between rotation axis and mass center is d.

Apart from mass moment of inertia, the parallel axis theorem can also be utilized to calculate the area moment of inertia (IArea) and radius of gyration (k).

Area moment of inertia, 

Radius of gyration, 

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