Abstract: The moment of inertia of a plane mass particles system about its centroid-through-axis can be expressed as follows： computing the square of distance of two arbitrary particles,then multiplying it with the two masses,respectively,all of such obtained product sum dividing the mass of the system.It is not needed to determine the centroid of the system but the lengths of lines connecting the two arbitrary particles is needed.Several applications in both rod and plate systems are presented.The examples also include the mixed structure of rod and plate,fractal plate and so on.The proposed expression has both important theoretical and practical value.

Key words: rigid body, system of particles, centroid, moment of inertia