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Define and calculate the moment of inertia using the parallel axis theorem with respect to an axis other than the centroidal axis. • Calculate the moment of inertia G is used for several kinds of rigid body rotation problems, including: (a) F=ma analysis moment equation ( ?M. G. = I. G ? ). (b) Rotational kinetic energy ( T = ? I. Moments of Inertia of. Common Geometric Shapes. Rectangle. Triangle. Circle Thin rectangular plate. Rectangular prism. Thin disk. Circular cylinder. CircularDerivation (cont'd). • Consider an axis BB' parallel to AA' through the centroid C of the area, known as the centroidal axis. The equation of the moment inertia. Consider the square tube shown below. From the appendix, we know the moment of inertia of a rectangle about each of its centroidal axis is: Moment The moment of inertia of an area with respect to any given axis is equal to the moment of inertia with respect to the centroidal axis plus the product of the area and the square of the distance between the 2 axes. The parallel axis theorem is used to determine the moment of inertia of composite sections. The moment of inertia of a composite area A about a given axis is obtained by adding the moments of and in calculation of MI about rotated axes. It may be Note: All formulas shown assume objects of uniform mass density. . Point mass at a radius R. . . . . Thin rod about axis through. (c) Moment of inertia about the x axis (Icx = ? ) Formulas: (a) Area of the triangle (A = ?) (b) Centroid of the triangle ( y = ? ) PDF-PROBLEMS & EXAMPLES.