Explanation Given information: I x y = ∫ x y d m I y z = ∫ y z d m I z x = ∫ z x d m Calculation: Write the derivation of Equations 9.47 as shown below: Refer to Equations 9.47 in section “9.6A Mass product of inertia” in the textbook. I x y = ∫ x y d m I y z = ∫ y z d m I z x = ∫ z x d m Refer to Equations 9.31 in section “9.5B Parallel-Axis Theorem for mass moment of inertia” in the textbook. x = x ′ + x ¯ y = y ′ + y ¯ z = z ′ + z ¯ Consider I x y = x y d m (1) Substitute x ′ + x ¯ for and y ′ + y ¯ for y in Equation (1). I x y = ∫ ( x ′ + x ¯ ) ( y ′ + y ¯ ) d m = ∫ x ′ y ′ d m + y ¯ ∫ x ′ d m + x ¯ ∫ y ′ d m + x ¯ y ¯ ∫ d m By definition of moment of inertia about x y axis

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ISBN: 9781264095032

Author: BEER

Publisher: MCGRAW-HILL HIGHER EDUCATION

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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 9.6, Problem 9.161P

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Complete the derivation of equation 9.47 such that express the parallel axis theorem for mass products of inertia.

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Chapter 9.6, Problem 9.160P

Chapter 9.6, Problem 9.162P

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Complete the derivation of equation 9.47 such that express the parallel axis theorem for mass products of inertia.

Solution Summary: The author explains the parallel axis theorem for mass products of inertia in the book.

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Complete the derivation of equation 9.47 such that express the parallel axis theorem for mass products of inertia.

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