Explanation Given information: Consider the arbitrary body. Consider the three rectangular axes are denoted by x , y , z . The moment of inertia of the body with respect to the x , y , and z axis are denoted by I x , I y , and I z . Calculation: Show the relation for the moment of inertia I y and I z as follows: I y = ∫ ( z 2 + x 2 ) d m (1) I z = ∫ ( x 2 + y 2 ) d m (2) Add Equation (1) and (2). I y + I z = ∫ ( z 2 + x 2 ) d m + ∫ ( x 2 + y 2 ) d m = ∫ ( y 2 + z 2 ) d m + 2 ∫ <

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill 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 9.176P

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Prove the condition of inequality with the expression Iy+Iz≥Ix.

Prove the condition of inequality with the expression Iy≥12Ix.

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Chapter 9.6, Problem 9.175P

Chapter 9.6, Problem 9.177P

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Chapter 9 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - 9.1 through 9.4 Determine by direct integration...Ch. 9.1 - Prob. 9.3P Ch. 9.1 - Prob. 9.4P Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - 9.5 through 9.8 Determine by direct integration...Ch. 9.1 - Prob. 9.7P Ch. 9.1 - Prob. 9.8P Ch. 9.1 - 9.9 through 9.11 Determine by direct integration...Ch. 9.1 - Prob. 9.10P

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Prove the condition of inequality with the expression I y + I z ≥ I x . Prove the condition of inequality with the expression I y ≥ 1 2 I x .

Solution Summary: The author demonstrates the condition of inequality with the expression I_yge. The moment of inertia of the body with respect to the x, y, and

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Prove the condition of inequality with the expression Iy+Iz≥Ix.

Prove the condition of inequality with the expression Iy≥12Ix.

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Chapter 9 Solutions

Prove the condition of inequality with the expression I y + I z ≥ I x . Prove the condition of inequality with the expression I y ≥ 1 2 I x .

Solution Summary: The author demonstrates the condition of inequality with the expression I_yge. The moment of inertia of the body with respect to the x, y, and

Concept explainers

Videos

Prove the condition of inequality with the expression Iy+Iz≥Ix. Prove the condition of inequality with the expression Iy≥12Ix.

Want to see the full answer?

Chapter 9 Solutions

Prove the condition of inequality with the expression Iy+Iz≥Ix.

Prove the condition of inequality with the expression Iy≥12Ix.