Explanation Calculation: Sketch the shaded area with vertical strip as shown in Figure 1. Express the variable terms in y as shown in below: y = − h b x (1) Select a vertical strip as differential element of area. Applying the parallel axis theorem. d I x y = d I x ′ y ′ + x ¯ E L y ¯ E L d A Here, x ¯ E L and y ¯ E L are the coordinates of the centroid of the element of area d A . When the x axis, the y axis or both axis of symmetry. d I ¯ x ′ y ′ = 0 Express the variables in terms of x and y . x ¯ E L = x Find the coordinate of centroid element y ¯ E L as shown below: y ¯ E L = 1 2 y (2) Substitute − h b x for y in Equation (2). y ¯ E L = 1 2 ( − h b x ) = − 1 2 h b x Consider the element strip as follows: d A = y d x = ( − h b x )

Vector Mechanics for Engineers: Statics and Dynamics

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ISBN: 9781259977251

Author: BEER

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Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provi…

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Chapter 9.3, Problem 9.70P

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Find the product of inertia of the area with respect to x and y axes by using direct integration method.

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Chapter 9.3, Problem 9.69P

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Find the product of inertia of the area with respect to x and y axes by using direct integration method.

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Find the product of inertia of the area with respect to x and y axes by using direct integration method.

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