Explanation Calculation: Find the differential element of mass ( d m ) as shown below: m = ρ V = ρ t A m A = ρ t Here, m is mass of the sheet metal, ρ is density sheet metal, t is thickness sheet metal, and A is the area of the sheet metal. Find the mass moment of inertia mass as shown below: I mass = ρ t I area (1) Substitute m A for ρ t in Equation (1). I mass = m A I area Here, I area is area of moment of inertia. The area ( A ) of the thin plate is 1 2 b h Find the moment of inertia of area ( I A A , area ) as shown in below: ( I A A , area ) = 2 ( 1 12 b h 3 ) (2) Here, b is width of the thin plate and h is the height of the thin plate. Substitute h for b and ( b 2 ) for h in Equation (2). ( I A A , area ) = 2 ( 1 12 h ( b 2 ) 3 ) = ( 1 6 h ( b 3 8 ) ) = 1 48 h b 3 Find the moment of inertia mass with respect to axes A A ′ as shown in below: I A A ′ , mass = m a I A A ′ , area (3) Substitute 1 2 b h for a and 1 48 h b 3 for I A A ′ , area in equation (3). I A A ′ , mass = m 1 2 b h ( 1 48 h b 3 ) = 2 m b h ( 1 48 h b 3 ) = 2 m ( 1 48 b 2 ) = 1 24 m b 2 Find the moment of inertia mass with respect to axis B B ′ as shown in below: I B B ′ , mass = m a I B B ′ , area (4) Substitute 1 2 b h for a and 1 36 b h 3 for I B B ′ , area in equation (4)

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ISBN: 9781259977121

Author: BEER

Publisher: MCG

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Moment of Inertia

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 9.118P

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Find the mass moment of inertia with respect to axes DD′ and EE′.

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Chapter 9.5, Problem 9.117P

Chapter 9.5, Problem 9.119P

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Find the mass moment of inertia with respect to axes D D ′ and E E ′ .

Solution Summary: The author calculates the mass moment of inertia with respect to axes DDprime and EE

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Find the mass moment of inertia with respect to axes DD′ and EE′.

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