(a) Explanation Calculation: Refer to Figure 9.12, “Moment of inertia of common geometric shapes” in the textbook. The moment of inertia for ellipse as shown below: Express the moment of inertia ( I A A ′ ) as follows: ( I A A ′ ) = 1 4 π a 3 b Express the moment of inertia ( I B B ′ ) as follows: ( I A A ′ ) = 1 4 π a 3 b Express the mass ( m ) as shown below: m = ρ V = ρ t A m A = ρ t Here, m is mass of the ring, ρ is density area, t is thickness ring, and A is the area of the thin ring. Find the moment of inertia of mass as shown in below: I mass = ρ t I area Find the mass moment of inertia of the plate with respect to centroid axes A A ′ . I mass = ρ t I area (1) Substitute 1 4 π a 3 b for I area in Equation (1) (b) To determine Find the centroid axis C C ′ such that perpendicular to the plate.

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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 9.5, Problem 9.113P

(a)

To determine

Find the mass moment of inertia of the plate with respect to centroid axes AA′ and BB′.

(b)

To determine

Find the centroid axis CC′ such that perpendicular to the plate.

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Chapter 9.5, Problem 9.112P

Chapter 9.5, Problem 9.114P

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Find the mass moment of inertia of the plate with respect to centroid axes A A ′ and B B ′ .

Solution Summary: The author analyzes the moment of inertia of the plate with respect to centroid axes AAprime and BB