The parallel axis theorem also hold for the polar moment of inertia. Where is the distance between the two parallel axes. 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.
CENTROID AND MOMENT OF INERTIA PLUS
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. Figure 1: A tethered tennis ball rotating about a central point. Cross sectional area Centroid Second moment of area or moment of inertia Radius of gyration Section modulus (elastic) Section modulus (plastic) Cross Sectional Area Section Properties Cross sectional area implies the total area of a cross section which is a two dimensional section. It is also sometimes called the second moment of mass the 'second' here refers to the fact that it depends on the length of the moment arm squared. The term equals zero because and (measured from the axis) because passes through the centroid. Rotational inertia is also commonly known as moment of inertia. 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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