![]() ![]() ![]() If is a point in the plane of an area and distant from the centroid of the area as shown in Fig. The parallel axis theorem also hold for the polar moment of inertia. This is because the axis of rotation is closer to the center of mass of the system in (b). We see that the moment of inertia is greater in (a) than (b). Where is the distance between the two parallel axes. Using the parallel-axis theorem eases the computation of the moment of inertia of compound objects. If is an axis crossing, and a parallel axis to as shown in Fig. Įquation 10.7 can be written for any two parallel axes with one crossing the centroid of the area. Which reads the moment of inertia about an axis is equal to the moment of inertia about a parallel axis that crosses the centroid of, plus the product of area and the square distance between and. The term equals zero because and (measured from the axis) because passes through the centroid. If is a differential element of the area, its (perpendicular) distance to the axis can be written as where is the distance between the two parallel axes shown in Fig. ![]() 10.9 Terms involved in deriving the parallel axis theorem. ![]() Relationships between Load, Shear, and Momentsįig.Shear and moment equations and their diagrams.Conditions for two dimensional rigid-body equilibrium.Equilibrium of Particles and Rigid Bodies.Simplification of force and couple systems.Vector operations using Cartesian vector notation.Vector operations using the parallelogram rule and trigonometry. ![]()
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