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The moment of inertia of an area about an axis is equal to the moment of inertia of the area about a parallel axis passing through the centroid plus the product of the area and the square of the perpendicular distance between the axes.
Moment of inertia is the property of a deformable body that determines the moment needed to obtain a desired curvature about an axis. Moment of inertia depends on the shape of the body and may be different around different axes of rotation. Moment-curvature relation: E: Elasticity modulus (characterizes stiffness of the deformable body) : curvature
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Center of Gravity and Moment of Inertia : First and second moment of area and mass, radius of gyration, parallel axis theorem, product of inertia, rotation of axes and principal M. I., Thin plates, M.I. by direct method (integration), composite bodies.
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Calculate the centroid of the composite shape in reference to the bottom of the shape and calculate the moment of inertia about the centroid z-axis.
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Parallel Axis Theorem. • The moment of inertia of a composite area A about a given axis is obtained by adding the moments of inertia of the component areas A 1, A 2, A 3, ... , with respect to the same axis.
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Area moments of inertia are a measure of the distribution of a two-dimensional area around a particular axis. Fundamentally, the portions of a shape which are located farther from the axis are more important than the parts which are closer.
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In following sections we will use the integral definitions of moment of inertia (10.1.3) to find the moments of inertia of five common shapes: rectangle, triangle, circle, semi-circle, and quarter-circle with respect to a specified axis.
