The definition of the centroid of volume is written in terms of ratios of integrals over the volume of the body. In addition to the type of drive, the vehicle’s moment of inertia J Z, V around the vertical axis is the determining factor for its cornering performance. Integrating curvatures over beam length, the deflection, at some point along x-axis, should also be reversely proportional to I. If the density is uniform throughout the body, then the center of mass and center of gravity correspond to the centroid of volume. The position of its centre of gravity and the variables of the moment of inertia are usually determined with the basic design of a vehicle (drive, wheelbase, dimensions and weight). Therefore, it can be seen from the former equation, that when a certain bending moment M is applied to a beam cross-section, the developed curvature is reversely proportional to the moment of inertia I. Where Ixy is the product of inertia, relative to centroidal axes x,y, and Ixy' is the product of inertia, relative to axes that are parallel to centroidal x,y ones, having offsets from them d_. Solid Rectangular Plate: If the mass of the plate is M, length l, and width b, then the moment of inertia passing through the center of gravity and about an axis perpendicular to the plane of the plate. Where I' is the moment of inertia in respect to an arbitrary axis, I the moment of inertia in respect to a centroidal axis, parallel to the first one, d the distance between the two parallel axes and A the area of the shape (=bh in case of a rectangle).įor the product of inertia Ixy, the parallel axes theorem takes a similar form: Moment of Inertia of Some Regular Bodies. The so-called Parallel Axes Theorem is given by the following equation:
The moment of inertia of any shape, in respect to an arbitrary, non centroidal axis, can be found if its moment of inertia in respect to a centroidal axis, parallel to the first one, is known.