This holds true for all regular polygons. On comparing equation II with the formula of the kinetic energy of the whole rotating body in linear motion, it is evident that mass in linear motion is analogous to the moment of inertia in rotational motion.

The small change r in rgives us two concentric circles and the small change in gives us an angular wedge. Parametric equations of a circle, intersection of a circle with a straight. Let suppose we have a small change in rand. moment of inertia of uniform bodies with simple geometrical shapes. The dimensional formula of the moment of inertia is given by, M 1 L 2 T 0. r Distance from the axis of the rotation. The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through the origin. Polar coordinates and applications Let’s suppose that either the integrand or the region of integration comes out simpler in polar coordinates (x rcos and y rsin ). In general form, moment of inertia is expressed as I m × r2.