Explanation Given information: The straight line equation is y 1 = m x . The curve equation is y 2 = k x 1 2 . Calculation: Sketch the vertical strip shaded portion as shown in Figure 1. Write the straight line equation as follows: y 1 = m x (1) Write the curve line ( y 2 ) Equation as follows: y 2 = k x 1 2 (2) Refer to Figure 1. For x = a , y 1 = y 2 = b Substitute a for x and b for y 1 in Equation (1). b = m a m = b a y 1 x = b a y 1 = b a ( x ) Substitute a for x and b for y 2 in Equation (2). b = k a 1 2 k = b a 1 2 y 2 x 1 2 = b a 1 2 y 2 = b a 1 2 ( x 1 2 ) Sketch the diagram as shown in figure 2. Find the height ( y ) using the relation: y = y 2 − y 1 (3) Substitute b a ( x ) for y 1 and b a 1 2 ( x 1 2 ) for y 2 in Equation (3). y = b a 1 2 ( x 1 2 ) − b a ( x ) = b ( 1 − x 1 2 a 1 2 ) Determine the area of the strip element d A as shown in below: d A = ( y 2 − y 1 ) d x Determine the moment of inertia ( d I y ) with respect to y axis of a rectangular strip: d I y = x 2 d A (4) Substitute ( y 2 − y 1 ) d x for d A in Equation (4)

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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 9.1, Problem 9.13P

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Find the moment of inertia of the shaded area with respect to y axis by using direct integration.

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Chapter 9.1, Problem 9.12P

Chapter 9.1, Problem 9.14P

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Find the moment of inertia of the shaded area with respect to y axis by using direct integration.

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Find the moment of inertia of the shaded area with respect to y axis by using direct integration.

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