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Unformatted text preview: MOMENT OF MOMENT OF INERTIA INERTIA Moment of Inertia by Integration Moment of Inertia by Integration LEARNING OBJECTIVES LEARNING OBJECTIVES Be able to define the moment of Be able to define the moment of inertia for an area inertia for an area Be able to determine the moment of Be able to determine the moment of inertia for an area by integration inertia for an area by integration Be able to determine the radii of Be able to determine the radii of gyration gyration PREREQUISITE KNOWLEDGE PREREQUISITE KNOWLEDGE Units of measurements Units of measurements Concepts of center of gravity, center Concepts of center of gravity, center of mass and centroid of mass and centroid Integration over lines, areas and Integration over lines, areas and volumes volumes MOMENTS OF INERTIA Moment of inertia is defined by a measure of a body's resistance to angular acceleration, equal to the sum of the products of each element of an area multiplied by the square of its distance from a coplanar axis. Moment of inertia is used to relate the normal stress to the applied external moment. MOMENTS OF INERTIA ∫ = A 2 x dA I y ∫ = A 2 y dA I x y x A 2 I I dA J + = = ∫ r Moment of inertia about xaxis : Moment of inertia about yaxis : Polar moment of inertia : PARALLEL AXIS THEOREM PARALLEL AXIS THEOREM The moment of inertia of an area about an axis is The moment of inertia of an area about an axis is equal to the moment of inertia of the area about a equal to the moment of inertia of the area about a parallel axis passing through the area’s centroid plus...
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This note was uploaded on 07/26/2009 for the course CE 221 taught by Professor Buch during the Spring '08 term at Michigan State University.
 Spring '08
 Buch

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