(a) Explanation Given information: Refer Problem 9.167. Show the moment of inertia as follows: I x = 1 2 W g a 2 I y = W g a 2 I z = 5 6 W g a 2 I x y = 1 4 W g a 2 I y z = 1 8 W g a 2 I z x = 3 8 W g a 2 Calculation: Show the Equation 9.56 as follows: { K 3 − ( I x + I y + I z ) K 2 + ( I x I y + I y I z + I z I x − I x y 2 − I y z 2 − I z x 2 ) K − ( I x I y I z − I x I y z 2 − I y I z x 2 − I z I x y 2 − 2 I x y I y z I z x ) } = 0 Substitute 1 2 W g a 2 for I x , W g a 2 for I y , 5 6 W g a 2 for I z , 1 4 W g a 2 for I x y , 1 8 W g a 2 for I y z , and 3 8 W g a 2 for I z x (b) To determine Find the angles made by the principal axis of inertia at O with the coordinate axis. Sketch the body and show the orientation of the principal axis of inertia relative to x , y , and z axis.

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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 9.182P

(a)

To determine

Find the principal mass moment of inertia at the origin O.

(b)

To determine

Find the angles made by the principal axis of inertia at O with the coordinate axis.

Sketch the body and show the orientation of the principal axis of inertia relative to x, y, and z axis.

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Chapter 9.6, Problem 9.181P

Chapter 9.6, Problem 9.183P

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Find the principal mass moment of inertia at the origin O .

Solution Summary: The author explains how to find the principal mass moment of inertia at the origin O.

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Find the principal mass moment of inertia at the origin O.

Find the angles made by the principal axis of inertia at O with the coordinate axis.

Sketch the body and show the orientation of the principal axis of inertia relative to x, y, and z axis.

Want to see the full answer?

Chapter 9 Solutions

Find the principal mass moment of inertia at the origin O .

Solution Summary: The author explains how to find the principal mass moment of inertia at the origin O.

Concept explainers

Videos

Find the principal mass moment of inertia at the origin O.

Find the angles made by the principal axis of inertia at O with the coordinate axis. Sketch the body and show the orientation of the principal axis of inertia relative to x, y, and z axis.

Want to see the full answer?

Chapter 9 Solutions

Find the angles made by the principal axis of inertia at O with the coordinate axis.

Sketch the body and show the orientation of the principal axis of inertia relative to x, y, and z axis.